Blueprint for a Scalable Photonic Fault-Tolerant Quantum Computer

J. Eli Bourassa; Rafael N. Alexander; Michael Vasmer; Ashlesha Patil; Ilan Tzitrin; Takaya Matsuura; Daiqin Su; Ben Q. Baragiola; Saikat Guha; Guillaume Dauphinais; Krishna K. Sabapathy; Nicolas C. Menicucci; Ish Dhand

doi:10.22331/q-2021-02-04-392

Blueprint for a Scalable Photonic Fault-Tolerant Quantum Computer

J. Eli Bourassa^1,2, Rafael N. Alexander^1,3,4, Michael Vasmer^5,6, Ashlesha Patil^1,7, Ilan Tzitrin^1,2, Takaya Matsuura^1,8, Daiqin Su¹, Ben Q. Baragiola^1,4, Saikat Guha^1,7, Guillaume Dauphinais¹, Krishna K. Sabapathy¹, Nicolas C. Menicucci^1,4, and Ish Dhand¹

¹Xanadu, Toronto, ON, M5G 2C8, Canada
²Department of Physics, University of Toronto, Toronto, Canada
³Center for Quantum Information and Control, University of New Mexico, Albuquerque, NM 87131, USA
⁴Centre for Quantum Computation and Communication Technology, School of Science, RMIT University, Melbourne, VIC 3000, Australia
⁵Perimeter Institute for Theoretical Physics, Waterloo, ON N2L 2Y5, Canada
⁶Institute for Quantum Computing, University of Waterloo, Waterloo, ON N2L 3G1, Canada
⁷College of Optical Sciences, University of Arizona, Tucson, Arizona 85719, USA
⁸Department of Applied Physics, Graduate School of Engineering, The University of Tokyo, 7–3–1 Hongo, Bunkyo-ku, Tokyo 113–8656, Japan

Published:	2021-02-04, volume 5, page 392
Eprint:	arXiv:2010.02905v2
Doi:	https://doi.org/10.22331/q-2021-02-04-392
Citation:	Quantum 5, 392 (2021).

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.

Abstract

Photonics is the platform of choice to build a modular, easy-to-network quantum computer operating at room temperature. However, no concrete architecture has been presented so far that exploits both the advantages of qubits encoded into states of light and the modern tools for their generation. Here we propose such a design for a scalable fault-tolerant photonic quantum computer informed by the latest developments in theory and technology. Central to our architecture is the generation and manipulation of three-dimensional resource states comprising both bosonic qubits and squeezed vacuum states. The proposal exploits state-of-the-art procedures for the non-deterministic generation of bosonic qubits combined with the strengths of continuous-variable quantum computation, namely the implementation of Clifford gates using easy-to-generate squeezed states. Moreover, the architecture is based on two-dimensional integrated photonic chips used to produce a qubit cluster state in one temporal and two spatial dimensions. By reducing the experimental challenges as compared to existing architectures and by enabling room-temperature quantum computation, our design opens the door to scalable fabrication and operation, which may allow photonics to leap-frog other platforms on the path to a quantum computer with millions of qubits.

Popular summary

The prototypical quantum computer ought to be universal, fault-tolerant, and scalable: ready to run any quantum algorithm, detect and correct the accruing errors, and accommodate scores of qubits. But there is a lot more to the design of a practical quantum computer, where one also looks for qualities like modularity, networkability, speed, and room-temperature operation. The photonic platform – a computer based on quantum states of light – gives perhaps the best hope to satisfy these criteria. In our paper we present the first detailed, comprehensive, top-down blueprint for such a computer. Our main theoretical innovation is to utilize a hybrid quantum state of light consisting of powerful but experimentally challenging checkerboard states, and more limited but easier-to-produce squeezed states. We lay out a complete mechanism for generating, processing, and measuring this state in the course of a fault-tolerant computation. The device we propose needs only planar, specialized, moderately-sized integrated photonic chips, a technology familiar to the telecommunications industry. The cryostats it needs – for the moment – are small and commercially available. And the quantum processor in our design establishes a brisk clock speed. These features, made possible by the flexibility of the photonic platform and by theoretical advancements in encoding and decoding that we detail, bring us closer to an operational quantum computer and its remarkable consequences.

► BibTeX data

@article{Bourassa2021blueprintscalable,
  doi = {10.22331/q-2021-02-04-392},
  url = {https://doi.org/10.22331/q-2021-02-04-392},
  title = {Blueprint for a {S}calable {P}hotonic {F}ault-{T}olerant {Q}uantum {C}omputer},
  author = {Bourassa, J. Eli and Alexander, Rafael N. and Vasmer, Michael and Patil, Ashlesha and Tzitrin, Ilan and Matsuura, Takaya and Su, Daiqin and Baragiola, Ben Q. and Guha, Saikat and Dauphinais, Guillaume and Sabapathy, Krishna K. and Menicucci, Nicolas C. and Dhand, Ish},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {5},
  pages = {392},
  month = feb,
  year = {2021}
}

► References

[1] Nicolas C. Menicucci. Fault-tolerant measurement-based quantum computing with continuous-variable cluster states. Phys. Rev. Lett., 112: 120504, Mar 2014. 10.1103/PhysRevLett.112.120504.
https://doi.org/10.1103/PhysRevLett.112.120504

[2] Ulrik L Andersen, Jonas S Neergaard-Nielsen, Peter van Loock, and Akira Furusawa. Hybrid discrete- and continuous-variable quantum information. Nat. Phys., 11 (9): 713–719, 2015. 10.1038/nphys3410.
https://doi.org/10.1038/nphys3410

[3] Emanuel Knill, Raymond Laflamme, and Gerald J Milburn. A scheme for efficient quantum computation with linear optics. Nature, 409 (6816): 46–52, 2001. 10.1038/35051009.
https://doi.org/10.1038/35051009

[4] Casey R. Myers and Timothy C. Ralph. Coherent state topological cluster state production. New J. Phys., 13 (11): 115015, 2011. 10.1088/1367-2630/13/11/115015.
https://doi.org/10.1088/1367-2630/13/11/115015

[5] Kosuke Fukui, Akihisa Tomita, Atsushi Okamoto, and Keisuke Fujii. High-Threshold Fault-Tolerant Quantum Computation with Analog Quantum Error Correction. Phys. Rev. X, 8 (2): 21054, 2018a. 10.1103/PhysRevX.8.021054.
https://doi.org/10.1103/PhysRevX.8.021054

[6] James M. Auger, Hussain Anwar, Mercedes Gimeno-Segovia, Thomas M. Stace, and Dan E. Browne. Fault-tolerant quantum computation with nondeterministic entangling gates. Phys. Rev. A, 97 (3): 5–9, 2018. 10.1103/PhysRevA.97.030301.
https://doi.org/10.1103/PhysRevA.97.030301

[7] Kyungjoo Noh and Christopher Chamberland. Fault-tolerant bosonic quantum error correction with the surface–Gottesman-Kitaev-Preskill code. Phys. Rev. A, 101: 012316, Jan 2020. 10.1103/PhysRevA.101.012316.
https://doi.org/10.1103/PhysRevA.101.012316

[8] Nicolas C. Menicucci, Peter van Loock, Mile Gu, Christian Weedbrook, Timothy C. Ralph, and Michael A. Nielsen. Universal quantum computation with continuous-variable cluster states. Phys. Rev. Lett., 97: 110501, Sep 2006. 10.1103/PhysRevLett.97.110501.
https://doi.org/10.1103/PhysRevLett.97.110501

[9] Shota Yokoyama, Ryuji Ukai, Seiji C Armstrong, Chanond Sornphiphatphong, Toshiyuki Kaji, Shigenari Suzuki, Jun-ichi Yoshikawa, Hidehiro Yonezawa, Nicolas C. Menicucci, and Akira Furusawa. Ultra-large-scale continuous-variable cluster states multiplexed in the time domain. Nat. Photonics, 7 (12): 982–986, 2013. 10.1038/nphoton.2013.287.
https://doi.org/10.1038/nphoton.2013.287

[10] Moran Chen, Nicolas C. Menicucci, and Olivier Pfister. Experimental realization of multipartite entanglement of 60 modes of a quantum optical frequency comb. Phys. Rev. Lett., 112 (12): 120505, 2014. 10.1103/PhysRevLett.112.120505.
https://doi.org/10.1103/PhysRevLett.112.120505

[11] Jun-ichi Yoshikawa, Shota Yokoyama, Toshiyuki Kaji, Chanond Sornphiphatphong, Yu Shiozawa, Kenzo Makino, and Akira Furusawa. Invited article: Generation of one-million-mode continuous-variable cluster state by unlimited time-domain multiplexing. APL Photonics, 1 (6): 060801, 2016. 10.1063/1.4962732.
https://doi.org/10.1063/1.4962732

[12] Rafael N. Alexander, Pei Wang, Niranjan Sridhar, Moran Chen, Olivier Pfister, and Nicolas C. Menicucci. One-way quantum computing with arbitrarily large time-frequency continuous-variable cluster states from a single optical parametric oscillator. Phys. Rev. A, 94: 032327, Sep 2016. 10.1103/PhysRevA.94.032327.
https://doi.org/10.1103/PhysRevA.94.032327

[13] Mikkel V. Larsen, Xueshi Guo, Casper R. Breum, Jonas S. Neergaard-Nielsen, and Ulrik L. Andersen. Deterministic generation of a two-dimensional cluster state. Science, 366 (6463): 369–372, Oct 2019. 10.1126/science.aay4354.
https://doi.org/10.1126/science.aay4354

[14] Mikkel V. Larsen, Jonas S. Neergaard-Nielsen, and Ulrik L. Andersen. Architecture and noise analysis of continuous-variable quantum gates using two-dimensional cluster states. Phys. Rev. A, 102: 042608, Oct 2020. 10.1103/PhysRevA.102.042608.
https://doi.org/10.1103/PhysRevA.102.042608

[15] Rafael N. Alexander, Shota Yokoyama, Akira Furusawa, and Nicolas C. Menicucci. Universal quantum computation with temporal-mode bilayer square lattices. Phys. Rev. A, 97: 032302, Mar 2018. 10.1103/PhysRevA.97.032302.
https://doi.org/10.1103/PhysRevA.97.032302

[16] Warit Asavanant, Yu Shiozawa, Shota Yokoyama, Baramee Charoensombutamon, Hiroki Emura, Rafael N. Alexander, Shuntaro Takeda, Jun-ichi Yoshikawa, Nicolas C. Menicucci, Hidehiro Yonezawa, and et al. Generation of time-domain-multiplexed two-dimensional cluster state. Science, 366 (6463): 373–376, Oct 2019. 10.1126/science.aay2645.
https://doi.org/10.1126/science.aay2645

[17] Pei Wang, Moran Chen, Nicolas C. Menicucci, and Olivier Pfister. Weaving quantum optical frequency combs into continuous-variable hypercubic cluster states. Phys. Rev. A, 90 (3): 032325, 2014. 10.1103/PhysRevA.90.032325.
https://doi.org/10.1103/PhysRevA.90.032325

[18] Bo-Han Wu, Rafael N Alexander, Shuai Liu, and Zheshen Zhang. Quantum computing with multidimensional continuous-variable cluster states in a scalable photonic platform. Phys. Rev. Res., 2 (2): 023138, 2020. 10.1103/PhysRevResearch.2.023138.
https://doi.org/10.1103/PhysRevResearch.2.023138

[19] Kosuke Fukui, Warit Asavanant, and Akira Furusawa. Temporal-mode continuous-variable three-dimensional cluster state for topologically protected measurement-based quantum computation. Phys. Rev. A, 102: 032614, Sep 2020. 10.1103/PhysRevA.102.032614.
https://doi.org/10.1103/PhysRevA.102.032614

[20] Daniel Gottesman, Alexei Kitaev, and John Preskill. Encoding a qubit in an oscillator. Phys. Rev. A, 64: 012310, Jun 2001. 10.1103/PhysRevA.64.012310.
https://doi.org/10.1103/PhysRevA.64.012310

[21] Austin P. Lund, Timothy C. Ralph, and Henry L. Haselgrove. Fault-tolerant linear optical quantum computing with small-amplitude coherent states. Phys. Rev. Lett., 100: 030503, Jan 2008. 10.1103/PhysRevLett.100.030503.
https://doi.org/10.1103/PhysRevLett.100.030503

[22] Kosuke Fukui, Akihisa Tomita, Atsushi Okamoto, and Keisuke Fujii. High-threshold fault-tolerant quantum computation with analog quantum error correction. Phys. Rev. X, 8: 021054, May 2018b. 10.1103/PhysRevX.8.021054.
https://doi.org/10.1103/PhysRevX.8.021054

[23] Kosuke Fukui. High-threshold fault-tolerant quantum computation with the GKP qubit and realistically noisy devices. arXiv preprint arXiv:1906.09767, 2019.
arXiv:1906.09767

[24] Terry Rudolph. Why I am optimistic about the silicon-photonic route to quantum computing. APL Photonics, 2 (3): 030901, 2017. 10.1063/1.4976737.
https://doi.org/10.1063/1.4976737

[25] M. Dakna, J. Clausen, L. Knöll, and D.-G. Welsch. Generation of arbitrary quantum states of traveling fields. Phys. Rev. A, 59: 1658–1661, Feb 1999. 10.1103/PhysRevA.59.1658.
https://doi.org/10.1103/PhysRevA.59.1658

[26] Jaromír Fiurášek, Raúl García-Patrón, and Nicolas J. Cerf. Conditional generation of arbitrary single-mode quantum states of light by repeated photon subtractions. Phys. Rev. A, 72: 033822, Sep 2005. 10.1103/PhysRevA.72.033822.
https://doi.org/10.1103/PhysRevA.72.033822

[27] Krishna Kumar Sabapathy, Haoyu Qi, Josh Izaac, and Christian Weedbrook. Production of photonic universal quantum gates enhanced by machine learning. Phys. Rev. A, 100: 012326, Jul 2019. 10.1103/PhysRevA.100.012326.
https://doi.org/10.1103/PhysRevA.100.012326

[28] Daiqin Su, Casey R. Myers, and Krishna Kumar Sabapathy. Conversion of Gaussian states to non-Gaussian states using photon-number-resolving detectors. Phys. Rev. A, 100: 052301, Nov 2019. 10.1103/PhysRevA.100.052301.
https://doi.org/10.1103/PhysRevA.100.052301

[29] N. Quesada, L. G. Helt, J. Izaac, J. M. Arrazola, R. Shahrokhshahi, C. R. Myers, and K. K. Sabapathy. Simulating realistic non-Gaussian state preparation. Phys. Rev. A, 100: 022341, Aug 2019. 10.1103/PhysRevA.100.022341.
https://doi.org/10.1103/PhysRevA.100.022341

[30] Ilan Tzitrin, J. Eli Bourassa, Nicolas C. Menicucci, and Krishna Kumar Sabapathy. Progress towards practical qubit computation using approximate Gottesman-Kitaev-Preskill codes. Phys. Rev. A, 101: 032315, Mar 2020. 10.1103/PhysRevA.101.032315.
https://doi.org/10.1103/PhysRevA.101.032315

[31] Hilma M Vasconcelos, Liliana Sanz, and Scott Glancy. All-optical generation of states for ``Encoding a qubit in an oscillator''. Opt. Lett., 35 (19): 3261–3263, 2010. 10.1364/OL.35.003261.
https://doi.org/10.1364/OL.35.003261

[32] Daniel J. Weigand and Barbara M. Terhal. Generating grid states from Schrödinger-cat states without postselection. Phys. Rev. A, 97: 022341, Feb 2018. 10.1103/PhysRevA.97.022341.
https://doi.org/10.1103/PhysRevA.97.022341

[33] Miller Eaton, Rajveer Nehra, and Olivier Pfister. Non-Gaussian and Gottesman–Kitaev–Preskill state preparation by photon catalysis. New J. Phys., 21 (11): 113034, nov 2019. 10.1088/1367-2630/ab5330.
https://doi.org/10.1088/1367-2630/ab5330

[34] Keith R. Motes, Ben Q. Baragiola, Alexei Gilchrist, and Nicolas C. Menicucci. Encoding qubits into oscillators with atomic ensembles and squeezed light. Phys. Rev. A, 95: 053819, May 2017. 10.1103/PhysRevA.95.053819.
https://doi.org/10.1103/PhysRevA.95.053819

[35] Stefano Pirandola, Stefano Mancini, David Vitali, and Paolo Tombesi. Generating continuous variable quantum codewords in the near-field atomic lithography. J. Phys. B, 39 (4): 997, 2006. 10.1088/0953-4075/39/4/023.
https://doi.org/10.1088/0953-4075/39/4/023

[36] Adriana E. Lita, Aaron J. Miller, and Sae Woo Nam. Counting near-infrared single-photons with 95% efficiency. Opt. Express, 16 (5): 3032, 2008. 10.1364/oe.16.003032.
https://doi.org/10.1364/oe.16.003032

[37] J. Sperling, D. S. Phillips, J. F. F Bulmer, G. S. Thekkadath, A. Eckstein, T. A. W. Wolterink, J. Lugani, S. W. Nam, A. Lita, T. Gerrits, W. Vogel, G. S. Agarwal, C. Silberhorn, and I. A. Walmsley. Detector-agnostic phase-space distributions. Phys. Rev. Lett., 124: 013605, Jan 2020. 10.1103/PhysRevLett.124.013605.
https://doi.org/10.1103/PhysRevLett.124.013605

[38] G. S. Thekkadath, D. S. Phillips, J. F. F. Bulmer, W. R. Clements, A. Eckstein, B. A. Bell, J. Lugani, T. A. W. Wolterink, A. Lita, S. W. Nam, T. Gerrits, C. G. Wade, and I. A. Walmsley. Tuning between photon-number and quadrature measurements with weak-field homodyne detection. Phys. Rev. A, 101: 031801, Mar 2020. 10.1103/PhysRevA.101.031801.
https://doi.org/10.1103/PhysRevA.101.031801

[39] V. D. Vaidya, B. Morrison, L. G. Helt, R. Shahrokshahi, D. H. Mahler, M. J. Collins, K. Tan, J. Lavoie, A. Repingon, M. Menotti, N. Quesada, R. C. Pooser, A. E. Lita, T. Gerrits, S. W. Nam, and Z. Vernon. Broadband quadrature-squeezed vacuum and nonclassical photon number correlations from a nanophotonic device. Sci. Adv., 6 (39): eaba9186, September 2020. 10.1126/sciadv.aba9186.
https://doi.org/10.1126/sciadv.aba9186

[40] Robert Raussendorf, Sergey Bravyi, and Jim Harrington. Long-range quantum entanglement in noisy cluster states. Phys. Rev. A, 71: 062313, Jun 2005. 10.1103/PhysRevA.71.062313.
https://doi.org/10.1103/PhysRevA.71.062313

[41] Robert Raussendorf, Jim Harrington, and Kovid Goyal. A fault-tolerant one-way quantum computer. Ann. Phys. (N. Y.), 321 (9): 2242–2270, 2006. 10.1016/j.aop.2006.01.012.
https://doi.org/10.1016/j.aop.2006.01.012

[42] Robert Raussendorf, Jim Harrington, and Kovid Goyal. Topological fault-tolerance in cluster state quantum computation. New J. Phys., 9 (6): 199, 2007. 10.1088/1367-2630/9/6/199.
https://doi.org/10.1088/1367-2630/9/6/199

[43] Giacomo Pantaleoni, Ben Q. Baragiola, and Nicolas C. Menicucci. Modular bosonic subsystem codes. Phys. Rev. Lett., 125 (4): 040501, 2020. 10.1103/PhysRevLett.125.040501.
https://doi.org/10.1103/PhysRevLett.125.040501

[44] Stephen D Bartlett, Barry C Sanders, Samuel L Braunstein, and Kae Nemoto. Efficient classical simulation of continuous variable quantum information processes. Phys. Rev. Lett., 88 (9): 097904, 2002. 10.1103/PhysRevLett.88.097904.
https://doi.org/10.1103/PhysRevLett.88.097904

[45] Thomas M Stace, Sean D Barrett, and Andrew C Doherty. Thresholds for topological codes in the presence of loss. Phys. Rev. Lett., 102 (20): 200501, 2009. 10.1103/PhysRevLett.102.200501.
https://doi.org/10.1103/PhysRevLett.102.200501

[46] Sean D Barrett and Thomas M Stace. Fault tolerant quantum computation with very high threshold for loss errors. Phys. Rev. Lett., 105 (20): 200502, 2010. 10.1103/PhysRevLett.105.200502.
https://doi.org/10.1103/PhysRevLett.105.200502

[47] Adam C. Whiteside and Austin G. Fowler. Upper bound for loss in practical topological-cluster-state quantum computing. Phys. Rev. A, 90: 052316, Nov 2014. 10.1103/PhysRevA.90.052316.
https://doi.org/10.1103/PhysRevA.90.052316

[48] Henning Vahlbruch, Moritz Mehmet, Karsten Danzmann, and Roman Schnabel. Detection of 15 dB squeezed states of light and their application for the absolute calibration of photoelectric quantum efficiency. Phys. Rev. Lett., 117: 110801, Sep 2016. 10.1103/PhysRevLett.117.110801.
https://doi.org/10.1103/PhysRevLett.117.110801

[49] M.J. Collins, C. Xiong, I.H. Rey, T.D. Vo, J. He, S. Shahnia, C. Reardon, T.F. Krauss, M.J. Steel, A.S. Clark, and B.J. Eggleton. Integrated spatial multiplexing of heralded single-photon sources. Nat. Commun., 4 (1), Oct 2013. 10.1038/ncomms3582.
https://doi.org/10.1038/ncomms3582

[50] Seth Lloyd and Samuel L Braunstein. Quantum computation over continuous variables. Phys. Rev. Lett., 82 (8): 1784, 1999. 10.1103/PhysRevLett.82.1784.
https://doi.org/10.1103/PhysRevLett.82.1784

[51] Daniel Gottesman. Stabilizer codes and quantum error correction. arXiv preprint quant-ph/9705052, 1997.
arXiv:quant-ph/9705052

[52] Emanuel Knill. Non-binary unitary error bases and quantum codes. arXiv preprint quant-ph/9608048, 1996.
arXiv:quant-ph/9608048

[53] Avanti Ketkar, Andreas Klappenecker, Santosh Kumar, and Pradeep Kiran Sarvepalli. Nonbinary stabilizer codes over finite fields. IEEE Trans. Inf. Theory, 52 (11): 4892–4914, 2006. 10.1109/TIT.2006.883612.
https://doi.org/10.1109/TIT.2006.883612

[54] Isaac L Chuang and Yoshihisa Yamamoto. Simple quantum computer. Phys. Rev. A, 52 (5): 3489, 1995. 10.1103/PhysRevA.52.3489.
https://doi.org/10.1103/PhysRevA.52.3489

[55] P. T. Cochrane, G. J. Milburn, and W. J. Munro. Macroscopically distinct quantum-superposition states as a bosonic code for amplitude damping. Phys. Rev. A, 59: 2631–2634, Apr 1999. 10.1103/PhysRevA.59.2631.
https://doi.org/10.1103/PhysRevA.59.2631

[56] Timothy C. Ralph, Alexei Gilchrist, Gerard J Milburn, William J Munro, and Scott Glancy. Quantum computation with optical coherent states. Phys. Rev. A, 68 (4): 042319, 2003. 10.1103/PhysRevA.68.042319.
https://doi.org/10.1103/PhysRevA.68.042319

[57] Zaki Leghtas, Gerhard Kirchmair, Brian Vlastakis, Robert J. Schoelkopf, Michel H. Devoret, and Mazyar Mirrahimi. Hardware-efficient autonomous quantum memory protection. Phys. Rev. Lett., 111: 120501, Sep 2013. 10.1103/PhysRevLett.111.120501.
https://doi.org/10.1103/PhysRevLett.111.120501

[58] Mazyar Mirrahimi, Zaki Leghtas, Victor V Albert, Steven Touzard, Robert J Schoelkopf, Liang Jiang, and Michel H Devoret. Dynamically protected cat-qubits: a new paradigm for universal quantum computation. New J. Phys., 16 (4): 045014, April 2014. 10.1088/1367-2630/16/4/045014.
https://doi.org/10.1088/1367-2630/16/4/045014

[59] Marios H. Michael, Matti Silveri, R. T. Brierley, Victor V. Albert, Juha Salmilehto, Liang Jiang, and S. M. Girvin. New class of quantum error-correcting codes for a bosonic mode. Phys. Rev. X, 6: 031006, Jul 2016. 10.1103/PhysRevX.6.031006.
https://doi.org/10.1103/PhysRevX.6.031006

[60] Arne L. Grimsmo, Joshua Combes, and Ben Q. Baragiola. Quantum computing with rotation-symmetric bosonic codes. Phys. Rev. X, 10: 011058, Mar 2020. 10.1103/PhysRevX.10.011058.
https://doi.org/10.1103/PhysRevX.10.011058

[61] A. I. Lvovsky and M. G. Raymer. Continuous-variable optical quantum-state tomography. Rev. Mod. Phys., 81: 299–332, Mar 2009. 10.1103/RevModPhys.81.299.
https://doi.org/10.1103/RevModPhys.81.299

[62] Kazunori Miyata, Hisashi Ogawa, Petr Marek, Radim Filip, Hidehiro Yonezawa, Jun-ichi Yoshikawa, and Akira Furusawa. Implementation of a quantum cubic gate by an adaptive non-Gaussian measurement. Phys. Rev. A, 93 (2): 022301, 2016. 10.1103/PhysRevA.93.022301.
https://doi.org/10.1103/PhysRevA.93.022301

[63] Jacob Hastrup, Mikkel V Larsen, Jonas S Neergaard-Nielsen, Nicolas C Meniccuci, and Ulrik L Andersen. Cubic phase gates are not suitable for non-Clifford operations on GKP states. arXiv preprint arXiv:2009.05309, 2020.
arXiv:2009.05309

[64] Victor V. Albert, Kyungjoo Noh, Kasper Duivenvoorden, Dylan J. Young, R. T. Brierley, Philip Reinhold, Christophe Vuillot, Linshu Li, Chao Shen, S. M. Girvin, Barbara M. Terhal, and Liang Jiang. Performance and structure of single-mode bosonic codes. Phys. Rev. A, 97: 032346, Mar 2018. 10.1103/PhysRevA.97.032346.
https://doi.org/10.1103/PhysRevA.97.032346

[65] Kyungjoo Noh, Victor V Albert, and Liang Jiang. Quantum capacity bounds of Gaussian thermal loss channels and achievable rates with Gottesman-Kitaev-Preskill codes. IEEE Trans. Inf. Theory, 65 (4): 2563–2582, 2018. 10.1109/TIT.2018.2873764.
https://doi.org/10.1109/TIT.2018.2873764

[66] Takaya Matsuura, Hayata Yamasaki, and Masato Koashi. Equivalence of approximate Gottesman-Kitaev-Preskill codes. Phys. Rev. A, 102: 032408, Sep 2020. 10.1103/PhysRevA.102.032408.
https://doi.org/10.1103/PhysRevA.102.032408

[67] S. Glancy and E. Knill. Error analysis for encoding a qubit in an oscillator. Phys. Rev. A, 73: 012325, Jan 2006. 10.1103/PhysRevA.73.012325.
https://doi.org/10.1103/PhysRevA.73.012325

[68] Hans J Briegel and Robert Raussendorf. Persistent entanglement in arrays of interacting particles. Phys. Rev. Lett., 86 (5): 910, 2001. 10.1103/PhysRevLett.86.910.
https://doi.org/10.1103/PhysRevLett.86.910

[69] Robert Raussendorf and Hans J Briegel. A one-way quantum computer. Phys. Rev. Lett., 86 (22): 5188, 2001. 10.1103/PhysRevLett.86.5188.
https://doi.org/10.1103/PhysRevLett.86.5188

[70] Mile Gu, Christian Weedbrook, Nicolas C. Menicucci, Timothy C. Ralph, and Peter van Loock. Quantum computing with continuous-variable clusters. Phys. Rev. A, 79: 062318, Jun 2009. 10.1103/PhysRevA.79.062318.
https://doi.org/10.1103/PhysRevA.79.062318

[71] Peter W. Shor. Scheme for reducing decoherence in quantum computer memory. Phys. Rev. A, 52 (4): 2493–2496, 1995. 10.1103/PhysRevA.52.R2493.
https://doi.org/10.1103/PhysRevA.52.R2493

[72] A. M. Steane. Error correcting codes in quantum theory. Phys. Rev. Lett., 77 (5): 793–797, 1996a. 10.1103/PhysRevLett.77.793.
https://doi.org/10.1103/PhysRevLett.77.793

[73] Dorit Aharonov and Michael Ben-Or. Fault-tolerant quantum computation with constant error rate. SIAM J. Comput., 38 (4): 1207–1282, 2008. 10.1137/S0097539799359385.
https://doi.org/10.1137/S0097539799359385

[74] Emanuel Knill, Raymond Laflamme, and Wojciech H. Zurek. Resilient quantum computation. Science, 279 (5349): 342–345, 1998. 10.1126/science.279.5349.342.
https://doi.org/10.1126/science.279.5349.342

[75] Earl T. Campbell, Barbara M. Terhal, and Christophe Vuillot. Roads towards fault-tolerant universal quantum computation. Nature, 549 (7671): 172–179, Sep 2017. 10.1038/nature23460.
https://doi.org/10.1038/nature23460

[76] A.Yu. Kitaev. Fault-tolerant quantum computation by anyons. Ann. Phys. (N. Y.), 303 (1): 2 – 30, 2003. 10.1016/S0003-4916(02)00018-0.
https://doi.org/10.1016/S0003-4916(02)00018-0

[77] Sergey B Bravyi and A Yu Kitaev. Quantum codes on a lattice with boundary. arXiv preprint quant-ph/9811052, 1998.
arXiv:quant-ph/9811052

[78] Robert Raussendorf and Jim Harrington. Fault-tolerant quantum computation with high threshold in two dimensions. Phys. Rev. Lett., 98 (19), May 2007. 10.1103/PhysRevLett.98.190504.
https://doi.org/10.1103/PhysRevLett.98.190504

[79] Austin G. Fowler, Ashley M. Stephens, and Peter Groszkowski. High-threshold universal quantum computation on the surface code. Phys. Rev. A, 80: 052312, Nov 2009. 10.1103/PhysRevA.80.052312.
https://doi.org/10.1103/PhysRevA.80.052312

[80] Austin G. Fowler, Matteo Mariantoni, John M. Martinis, and Andrew N. Cleland. Surface codes: Towards practical large-scale quantum computation. Phys. Rev. A, 86 (3), Sep 2012. 10.1103/PhysRevA.86.032324.
https://doi.org/10.1103/PhysRevA.86.032324

[81] A. R. Calderbank and Peter W. Shor. Good quantum error-correcting codes exist. Phys. Rev. A, 54 (2): 1098–1105, aug 1996. 10.1103/PhysRevA.54.1098.
https://doi.org/10.1103/PhysRevA.54.1098

[82] Andrew Steane. Multiple-particle interference and quantum error correction. Proc. R. Soc. A, 452 (1954): 2551–2577, 1996b. 10.1098/rspa.1996.0136.
https://doi.org/10.1098/rspa.1996.0136

[83] A. Bolt, G. Duclos-Cianci, D. Poulin, and T. M. Stace. Foliated Quantum Error-Correcting Codes. Phys. Rev. Lett., 117 (7), 2016. 10.1103/PhysRevLett.117.070501.
https://doi.org/10.1103/PhysRevLett.117.070501

[84] Austin G Fowler and Kovid Goyal. Topological cluster state quantum computing. Quantum Inf. Comput., 9 (9-10): 0721–0738, 2009. 10.26421/QIC9.9-10.
https://doi.org/10.26421/QIC9.9-10

[85] Naomi Nickerson and Héctor Bombín. Measurement based fault tolerance beyond foliation. arXiv preprint arXiv:1810.09621, 2018.
arXiv:1810.09621

[86] Hector Bombin. 2D quantum computation with 3D topological codes. arXiv preprint arXiv:1810.09571, 2018a.
arXiv:1810.09571

[87] Hector Bombin. Transversal gates and error propagation in 3D topological codes. arXiv preprint arXiv:1810.09575, 2018b.
arXiv:1810.09575

[88] Benjamin J. Brown and Sam Roberts. Universal fault-tolerant measurement-based quantum computation. Phys. Rev. Research, 2: 033305, Aug 2020. 10.1103/PhysRevResearch.2.033305.
https://doi.org/10.1103/PhysRevResearch.2.033305

[89] Christophe Vuillot, Hamed Asasi, Yang Wang, Leonid P. Pryadko, and Barbara M. Terhal. Quantum error correction with the toric Gottesman-Kitaev-Preskill code. Phys. Rev. A, 99: 032344, Mar 2019. 10.1103/PhysRevA.99.032344.
https://doi.org/10.1103/PhysRevA.99.032344

[90] Lisa Hänggli, Margret Heinze, and Robert König. Enhanced noise resilience of the surface–gottesman-kitaev-preskill code via designed bias. Phys. Rev. A, 102: 052408, Nov 2020. 10.1103/PhysRevA.102.052408.
https://doi.org/10.1103/PhysRevA.102.052408

[91] B M Terhal, J Conrad, and C Vuillot. Towards scalable bosonic quantum error correction. Quantum Science and Technology, 5 (4): 043001, Jul 2020. 10.1088/2058-9565/ab98a5.
https://doi.org/10.1088/2058-9565/ab98a5

[92] Hayata Yamasaki, Kosuke Fukui, Yuki Takeuchi, Seiichiro Tani, and Masato Koashi. Polylog-overhead highly fault-tolerant measurement-based quantum computation: all-Gaussian implementation with Gottesman-Kitaev-Preskill code. arXiv preprint arXiv:2006.05416, 2020.
arXiv:2006.05416

[93] Damien Bonneau, Gabriel J Mendoza, Jeremy L O'Brien, and Mark G Thompson. Effect of loss on multiplexed single-photon sources. New J. Phys., 17 (4): 043057, April 2015. 10.1088/1367-2630/17/4/043057.
https://doi.org/10.1088/1367-2630/17/4/043057

[94] Francesco Lenzini, Ben Haylock, Juan C. Loredo, Raphael A. Abrahão, Nor A. Zakaria, Sachin Kasture, Isabelle Sagnes, Aristide Lemaitre, Hoang-Phuong Phan, Dzung Viet Dao, Pascale Senellart, Marcelo P. Almeida, Andrew G. White, and Mirko Lobino. Active demultiplexing of single photons from a solid-state source. Laser & Photonics Reviews, 11 (3): 1600297, April 2017. 10.1002/lpor.201600297.
https://doi.org/10.1002/lpor.201600297

[95] Nicolas C. Menicucci. Temporal-mode continuous-variable cluster states using linear optics. Phys. Rev. A, 83: 062314, Jun 2011. 10.1103/PhysRevA.83.062314.
https://doi.org/10.1103/PhysRevA.83.062314

[96] Ish Dhand, Melanie. Engelkemeier, Linda. Sansoni, Sonja Barkhofen, Christine Silberhorn, and Martin B. Plenio. Proposal for quantum simulation via all-optically-generated tensor network states. Phys. Rev. Lett., 120: 130501, 2018. 10.1103/PhysRevLett.120.130501.
https://doi.org/10.1103/PhysRevLett.120.130501

[97] Michael Lubasch, Antonio A. Valido, Jelmer J. Renema, W. Steven Kolthammer, Dieter Jaksch, M. S. Kim, Ian Walmsley, and Raúl García-Patrón. Tensor network states in time-bin quantum optics. Phys. Rev. A, 97: 062304, Jun 2018. 10.1103/PhysRevA.97.062304.
https://doi.org/10.1103/PhysRevA.97.062304

[98] Michael JW Hall. Gaussian noise and quantum-optical communication. Phys. Rev. A, 50 (4): 3295, 1994. 10.1103/PhysRevA.50.3295.
https://doi.org/10.1103/PhysRevA.50.3295

[99] Ben Q. Baragiola, Giacomo Pantaleoni, Rafael N. Alexander, Angela Karanjai, and Nicolas C. Menicucci. All-Gaussian universality and fault tolerance with the Gottesman-Kitaev-Preskill code. Phys. Rev. Lett., 123: 200502, Nov 2019. 10.1103/PhysRevLett.123.200502.
https://doi.org/10.1103/PhysRevLett.123.200502

[100] Christopher Bishop. Pattern recognition and machine learning. Springer, New York, 2006. ISBN 0-387-31073-8.

[101] Christoph Buchheim, Ruth Hübner, and Anita Schöbel. Ellipsoid bounds for convex quadratic integer programming. SIAM J. Optim., 25 (2): 741–769, January 2015. 10.1137/130929187.
https://doi.org/10.1137/130929187

[102] Jaehyun Park and Stephen Boyd. A semidefinite programming method for integer convex quadratic minimization. Optim. Lett., 12 (3): 499–518, March 2017. 10.1007/s11590-017-1132-y.
https://doi.org/10.1007/s11590-017-1132-y

[103] Jack Edmonds. Optimum branchings. J. Res. Natl. Bur. Stand. Sect. B Math. Math. Phys., 71B (4): 233, oct 1967. 10.6028/jres.071B.032.
https://doi.org/10.6028/jres.071B.032

[104] Eric Dennis, Alexei Kitaev, Andrew Landahl, and John Preskill. Topological quantum memory. J. Math. Phys., 43 (9): 4452–4505, Sep 2002. 10.1063/1.1499754.
https://doi.org/10.1063/1.1499754

[105] David S. Wang, Austin G. Fowler, and Lloyd C. L. Hollenberg. Surface code quantum computing with error rates over 1%. Phys. Rev. A, 83: 020302, Feb 2011. 10.1103/PhysRevA.83.020302.
https://doi.org/10.1103/PhysRevA.83.020302

[106] Nicolas Delfosse and Naomi H Nickerson. Almost-linear time decoding algorithm for topological codes. arXiv preprint arXiv:1709.06218, 2017.
arXiv:1709.06218

[107] Sergey Bravyi, Martin Suchara, and Alexander Vargo. Efficient algorithms for maximum likelihood decoding in the surface code. Phys. Rev. A, 90 (3): 032326, sep 2014. 10.1103/PhysRevA.90.032326.
https://doi.org/10.1103/PhysRevA.90.032326

[108] Guillaume Duclos-Cianci and David Poulin. Fast decoders for topological quantum codes. Phys. Rev. Lett., 104 (5): 1–5, 2010. 10.1103/PhysRevLett.104.050504.
https://doi.org/10.1103/PhysRevLett.104.050504

[109] Guillaume Duclos-Cianci and David Poulin. Fault-tolerant renormalization group decoder for Abelian topological codes. Quantum Inf. Comput., 14 (9-10): 721–740, 2014. 10.5555/2638670.2638671.
https://doi.org/10.5555/2638670.2638671

[110] Sergey Bravyi and Jeongwan Haah. Quantum self-correction in the 3D cubic code model. Phys. Rev. Lett., 111 (20), dec 2013. 10.1103/PhysRevLett.111.200501.
https://doi.org/10.1103/PhysRevLett.111.200501

[111] Hussain Anwar, Benjamin J. Brown, Earl T. Campbell, and Dan E. Browne. Fast decoders for qudit topological codes. New J. Phys., 16: 1–20, 2014. 10.1088/1367-2630/16/6/063038.
https://doi.org/10.1088/1367-2630/16/6/063038

[112] James R. Wootton and Daniel Loss. High Threshold Error Correction for the Surface Code. Phys. Rev. Lett., 109 (16), 2012. 10.1103/PhysRevLett.109.160503.
https://doi.org/10.1103/PhysRevLett.109.160503

[113] Adrian Hutter, James R. Wootton, and Daniel Loss. Efficient Markov chain Monte Carlo algorithm for the surface code. Phys. Rev. A, 89 (2): 1–10, 2014. 10.1103/PhysRevA.89.022326.
https://doi.org/10.1103/PhysRevA.89.022326

[114] Pavel Panteleev and Gleb Kalachev. Degenerate quantum LDPC codes with good finite length performance. arXiv preprint arXiv:1904.02703, 2019.
arXiv:1904.02703

[115] Joschka Roffe, David R. White, Simon Burton, and Earl Campbell. Decoding across the quantum low-density parity-check code landscape. Phys. Rev. Research, 2: 043423, Dec 2020. 10.1103/PhysRevResearch.2.043423.
https://doi.org/10.1103/PhysRevResearch.2.043423

[116] Austin G. Fowler. Minimum weight perfect matching of fault-tolerant topological quantum error correction in average O(1) parallel time. Quantum Inf. Comput., 15 (1-2): 145–158, 2014. 10.5555/2685188.2685197.
https://doi.org/10.5555/2685188.2685197

[117] Giacomo Torlai and Roger G. Melko. Neural Decoder for Topological Codes. Phys. Rev. Lett., 119 (3): 1–6, 2017. 10.1103/PhysRevLett.119.030501.
https://doi.org/10.1103/PhysRevLett.119.030501

[118] Savvas Varsamopoulos, Ben Criger, and Koen Bertels. Decoding small surface codes with feedforward neural networks. Quantum Sci. Technol., 3 (1): 1–13, 2018. 10.1088/2058-9565/aa955a.
https://doi.org/10.1088/2058-9565/aa955a

[119] David K. Tuckett, Stephen D. Bartlett, and Steven T. Flammia. Ultrahigh Error Threshold for Surface Codes with Biased Noise. Phys. Rev. Lett., 120 (5): 1–6, 2018. 10.1103/PhysRevLett.120.050505.
https://doi.org/10.1103/PhysRevLett.120.050505

[120] Michael Herold, Earl T. Campbell, Jens Eisert, and Michael J. Kastoryano. Cellular-automaton decoders for topological quantum memories. npj Quantum Inf., 1 (1): 15010, dec 2015. 10.1038/npjqi.2015.10.
https://doi.org/10.1038/npjqi.2015.10

[121] Michael Herold, Michael J. Kastoryano, Earl T. Campbell, and Jens Eisert. Cellular automaton decoders of topological quantum memories in the fault tolerant setting. New J. Phys., 19 (6), 2017. 10.1088/1367-2630/aa7099.
https://doi.org/10.1088/1367-2630/aa7099

[122] J Harrington. Analysis of quantum error-correcting codes: symplectic lattice codes and toric codes. PhD thesis, Caltech, 2004.

[123] Guillaume Dauphinais and David Poulin. Fault-tolerant quantum error correction for non-abelian anyons. Commun. Math. Phys., 355 (2): 519–560, Jul 2017. 10.1007/s00220-017-2923-9.
https://doi.org/10.1007/s00220-017-2923-9

[124] E. Knill. Quantum computing with realistically noisy devices. Nature, 434 (7029): 39–44, Mar 2005. 10.1038/nature03350.
https://doi.org/10.1038/nature03350

[125] Clare Horsman, Austin G Fowler, Simon Devitt, and Rodney Van Meter. Surface code quantum computing by lattice surgery. New J. Phys., 14 (12): 123011, dec 2012. 10.1088/1367-2630/14/12/123011.
https://doi.org/10.1088/1367-2630/14/12/123011

[126] Benjamin J. Brown, Katharina Laubscher, Markus S. Kesselring, and James R. Wootton. Poking holes and cutting corners to achieve Clifford gates with the surface code. Phys. Rev. X, 7: 021029, May 2017. 10.1103/PhysRevX.7.021029.
https://doi.org/10.1103/PhysRevX.7.021029

[127] Daniel Litinski and Felix von Oppen. Lattice surgery with a twist: Simplifying Clifford gates of surface codes. Quantum, 2: 62, May 2018. 10.22331/q-2018-05-04-62.
https://doi.org/10.22331/q-2018-05-04-62

[128] Daniel Litinski. A Game of Surface Codes: Large-Scale Quantum Computing with Lattice Surgery. Quantum, 3: 128, March 2019. 10.22331/q-2019-03-05-128.
https://doi.org/10.22331/q-2019-03-05-128

[129] Daniel Herr, Alexandru Paler, Simon J Devitt, and Franco Nori. Lattice surgery on the Raussendorf lattice. Quantum Sci. Technol., 3 (3): 035011, jun 2018. 10.1088/2058-9565/aac450.
https://doi.org/10.1088/2058-9565/aac450

[130] Daniel Herr, Franco Nori, and Simon J. Devitt. Optimization of lattice surgery is NP-hard. npj Quantum Inf., 3 (1), Sep 2017. 10.1038/s41534-017-0035-1.
https://doi.org/10.1038/s41534-017-0035-1

[131] H. Bombin. Topological order with a twist: Ising anyons from an Abelian model. Phys. Rev. Lett., 105 (3), Jul 2010. 10.1103/PhysRevLett.105.030403.
https://doi.org/10.1103/PhysRevLett.105.030403

[132] Ying Li. A magic state's fidelity can be superior to the operations that created it. New J. Phys., 17 (2): 023037, feb 2015. 10.1088/1367-2630/17/2/023037.
https://doi.org/10.1088/1367-2630/17/2/023037

[133] Sergey Bravyi and Alexei Kitaev. Universal quantum computation with ideal Clifford gates and noisy ancillas. Phys. Rev. A, 71: 022316, Feb 2005. 10.1103/PhysRevA.71.022316.
https://doi.org/10.1103/PhysRevA.71.022316

[134] Sergey Bravyi and Jeongwan Haah. Magic-state distillation with low overhead. Phys. Rev. A, 86 (5), Nov 2012. 10.1103/PhysRevA.86.052329.
https://doi.org/10.1103/PhysRevA.86.052329

[135] Jeongwan Haah and Matthew B. Hastings. Codes and Protocols for Distilling $T$, controlled-$S$, and Toffoli Gates. Quantum, 2: 71, June 2018. 10.22331/q-2018-06-07-71.
https://doi.org/10.22331/q-2018-06-07-71

[136] Jeongwan Haah, Matthew B. Hastings, D. Poulin, and D. Wecker. Magic state distillation with low space overhead and optimal asymptotic input count. Quantum, 1: 31, October 2017. 10.22331/q-2017-10-03-31.
https://doi.org/10.22331/q-2017-10-03-31

[137] Cody Jones. Multilevel distillation of magic states for quantum computing. Phys. Rev. A, 87: 042305, Apr 2013. 10.1103/PhysRevA.87.042305.
https://doi.org/10.1103/PhysRevA.87.042305

[138] Matthew B. Hastings and Jeongwan Haah. Distillation with sublogarithmic overhead. Phys. Rev. Lett., 120 (5), Jan 2018. 10.1103/PhysRevLett.120.050504.
https://doi.org/10.1103/PhysRevLett.120.050504

[139] Alastair Kay. Tutorial on the quantikz package. arXiv preprint arXiv:1809.03842, 2018. 10.17637/rh.7000520.
https://doi.org/10.17637/rh.7000520
arXiv:1809.03842

[140] Daniel Litinski and Felix von Oppen. Quantum computing with Majorana fermion codes. Phys. Rev. B, 97: 205404, May 2018. 10.1103/PhysRevB.97.205404.
https://doi.org/10.1103/PhysRevB.97.205404

[141] Vadym Kliuchnikov, Dmitri Maslov, and Michele Mosca. Fast and efficient exact synthesis of single-qubit unitaries generated by Clifford and $T$ gates. Quantum Info. Comput., 13 (7–8): 607–630, July 2013a. 10.5555/2535649.2535653.
https://doi.org/10.5555/2535649.2535653

[142] Vadym Kliuchnikov, Dmitri Maslov, and Michele Mosca. Asymptotically optimal approximation of single qubit unitaries by Clifford and $T$ circuits using a constant number of ancillary qubits. Phys. Rev. Lett., 110: 190502, May 2013b. 10.1103/PhysRevLett.110.190502.
https://doi.org/10.1103/PhysRevLett.110.190502

[143] David Gosset, Vadym Kliuchnikov, Michele Mosca, and Vincent Russo. An algorithm for the t-count. arXiv preprint arXiv:1308.4134, 2013.
arXiv:1308.4134

[144] Luke E Heyfron and Earl T Campbell. An efficient quantum compiler that reduces $T$ count. Quantum Sci. Technol., 4 (1): 015004, sep 2018. 10.1088/2058-9565/aad604.
https://doi.org/10.1088/2058-9565/aad604

[145] M. Amy, D. Maslov, M. Mosca, and M. Roetteler. A meet-in-the-middle algorithm for fast synthesis of depth-optimal quantum circuits. IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst., 32 (6): 818–830, 2013. 10.1109/TCAD.2013.2244643.
https://doi.org/10.1109/TCAD.2013.2244643

[146] Peter Selinger. Quantum circuits of $T$-depth one. Phys. Rev. A, 87: 042302, Apr 2013. 10.1103/PhysRevA.87.042302.
https://doi.org/10.1103/PhysRevA.87.042302

[147] M. Amy, D. Maslov, and M. Mosca. Polynomial-time $T$-depth optimization of Clifford+$T$ circuits via matroid partitioning. IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst., 33 (10): 1476–1489, 2014. 10.1109/TCAD.2014.2341953.
https://doi.org/10.1109/TCAD.2014.2341953

[148] John Preskill. Reliable Quantum Computers. Proc. R. Soc. Lond. A, 454: 385–410, 1997. 10.1098/rspa.1998.0167.
https://doi.org/10.1098/rspa.1998.0167

[149] A Yu Kitaev. Quantum computations: algorithms and error correction. Russ. Math. Surv., 52 (6): 1191–1249, dec 1997. 10.1070/RM1997v052n06ABEH002155.
https://doi.org/10.1070/RM1997v052n06ABEH002155

[150] Panos Aliferis, Daniel Gottesman, and John Preskill. Quantum accuracy threshold for concatenated distance-3 codes. Quantum Inf. Comput., 6 (2): 097–165, 2006. 10.26421/QIC6.2.
https://doi.org/10.26421/QIC6.2

[151] David P. Divincenzo and Panos Aliferis. Effective fault-tolerant quantum computation with slow measurements. Phys. Rev. Lett., 98 (2): 020501, 2007. 10.1103/PhysRevLett.98.020501.
https://doi.org/10.1103/PhysRevLett.98.020501

[152] Panos Aliferis and John Preskill. Fault-tolerant quantum computation against biased noise. Phys. Rev. A, 78 (5): 052331, 2008. 10.1103/PhysRevA.78.052331.
https://doi.org/10.1103/PhysRevA.78.052331

[153] Panos Aliferis, Daniel Gottesman, and John Preskill. Accuracy threshold for postselected quantum computation. Quantum Inf. Comput., 8 (3-4): 181–244, mar 2008. 10.26421/QIC8.3-4.
https://doi.org/10.26421/QIC8.3-4

[154] Alexey A. Kovalev and Leonid P. Pryadko. Fault tolerance of quantum low-density parity check codes with sublinear distance scaling. Phys. Rev. A, 87 (2): 020304, feb 2013. 10.1103/PhysRevA.87.020304.
https://doi.org/10.1103/PhysRevA.87.020304

[155] Daniel Gottesman. Fault-tolerant quantum computation with constant overhead. Quantum Inf. Comput., 14 (15-16): 1338–1372, oct 2014. 10.26421/QIC14.15-16.
https://doi.org/10.26421/QIC14.15-16

[156] Omar Fawzi, Antoine Grospellier, and Anthony Leverrier. Constant overhead quantum fault-tolerance with quantum expander codes. In Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS, volume 2018-Octob, pages 743–754. IEEE, oct 2018. 10.1109/FOCS.2018.00076.
https://doi.org/10.1109/FOCS.2018.00076

[157] Barbara M. Terhal. Quantum error correction for quantum memories. Rev. Mod. Phys., 87: 307–346, Apr 2015. 10.1103/RevModPhys.87.307.
https://doi.org/10.1103/RevModPhys.87.307

[158] Scott Aaronson and Daniel Gottesman. Improved simulation of stabilizer circuits. Phys. Rev. A, 70: 052328, Nov 2004. 10.1103/PhysRevA.70.052328.
https://doi.org/10.1103/PhysRevA.70.052328

[159] D. S. Wang, A. G. Fowler, A. M. Stephens, and L. C.L. Hollenberg. Threshold error rates for the toric and planar codes. Quantum Inf. Comput., 10 (5-6): 456–469, may 2010. 10.5555/2011362.2011368.
https://doi.org/10.5555/2011362.2011368

[160] E. W. Dijkstra. A note on two problems in connexion with graphs. Numer. Math., 1 (1): 269–271, December 1959. 10.1007/bf01386390.
https://doi.org/10.1007/bf01386390

[161] Christian D. Lorenz and Robert M. Ziff. Precise determination of the bond percolation thresholds and finite-size scaling corrections for the sc, fcc, and bcc lattices. Phys. Rev. E, 57: 230–236, Jan 1998. 10.1103/PhysRevE.57.230.
https://doi.org/10.1103/PhysRevE.57.230

[162] Blayney W. Walshe, Ben Q. Baragiola, Rafael N. Alexander, and Nicolas C. Menicucci. Continuous-variable gate teleportation and bosonic-code error correction. Phys. Rev. A, 102: 062411, Dec 2020. 10.1103/PhysRevA.102.062411.
https://doi.org/10.1103/PhysRevA.102.062411

[163] Daiqin Su, Krishna Kumar Sabapathy, Casey R. Myers, Haoyu Qi, Christian Weedbrook, and Kamil Brádler. Implementing quantum algorithms on temporal photonic cluster states. Phys. Rev. A, 98: 032316, Sep 2018. 10.1103/PhysRevA.98.032316.
https://doi.org/10.1103/PhysRevA.98.032316

[164] Yunong Shi, Christopher Chamberland, and Andrew Cross. Fault-tolerant preparation of approximate GKP states. New J. Phys., 21 (9): 093007, 2019. 10.1088/1367-2630/ab3a62.
https://doi.org/10.1088/1367-2630/ab3a62

[165] Yong Zhang, M Menotti, K Tan, VD Vaidya, DH Mahler, L Zatti, M Liscidini, B Morrison, and Z Vernon. Single-mode quadrature squeezing using dual-pump four-wave mixing in an integrated nanophotonic device. arXiv preprint arXiv:2001.09474, 2020.
arXiv:2001.09474

[166] Matthew Collins and Zachary Vernon. On the road to room temperature quantum computation. https://bit.ly/2NR5xvm, 2020.
https://bit.ly/2NR5xvm

[167] Adrian Cho. IBM promises 1000-qubit quantum computer—a milestone—by 2023. Science, September 2020. 10.1126/science.abe8122.
https://doi.org/10.1126/science.abe8122

[168] Radim Filip, Petr Marek, and Ulrik L. Andersen. Measurement-induced continuous-variable quantum interactions. Phys. Rev. A, 71: 042308, Apr 2005. 10.1103/PhysRevA.71.042308.
https://doi.org/10.1103/PhysRevA.71.042308

[169] Ryuji Ukai, Shota Yokoyama, Jun-ichi Yoshikawa, Peter van Loock, and Akira Furusawa. Demonstration of a controlled-phase gate for continuous-variable one-way quantum computation. Phys. Rev. Lett., 107: 250501, Dec 2011. 10.1103/PhysRevLett.107.250501.
https://doi.org/10.1103/PhysRevLett.107.250501

[170] Jun-ichi Yoshikawa, Yoshichika Miwa, Alexander Huck, Ulrik L. Andersen, Peter van Loock, and Akira Furusawa. Demonstration of a quantum nondemolition sum gate. Phys. Rev. Lett., 101: 250501, Dec 2008. 10.1103/PhysRevLett.101.250501.
https://doi.org/10.1103/PhysRevLett.101.250501

[171] Filippo Caruso, Vittorio Giovannetti, and Alexander S Holevo. One-mode bosonic Gaussian channels: a full weak-degradability classification. New J. Phys., 8 (12): 310, 2006. 10.1088/1367-2630/8/12/310.
https://doi.org/10.1088/1367-2630/8/12/310

[172] J. Solomon Ivan, Krishna Kumar Sabapathy, and R. Simon. Operator-sum representation for bosonic Gaussian channels. Phys. Rev. A, 84: 042311, Oct 2011. 10.1103/PhysRevA.84.042311.
https://doi.org/10.1103/PhysRevA.84.042311

[173] Krishna Kumar Sabapathy, J Solomon Ivan, and R Simon. Robustness of non-Gaussian entanglement against noisy amplifier and attenuator environments. Phys. Rev. Lett., 107 (13): 130501, 2011. 10.1103/PhysRevLett.107.130501.
https://doi.org/10.1103/PhysRevLett.107.130501

[174] Raul Garcia-Patron, Carlos Navarrete-Benlloch, Seth Lloyd, Jeffrey H Shapiro, and Nicolas J. Cerf. Majorization theory approach to the Gaussian channel minimum entropy conjecture. Phys. Rev. Lett., 108 (11): 110505, 2012. 10.1103/PhysRevLett.108.110505.
https://doi.org/10.1103/PhysRevLett.108.110505

[175] Tommaso F. Demarie, Trond Linjordet, Nicolas C. Menicucci, and Gavin K. Brennen. Detecting topological entanglement entropy in a lattice of quantum harmonic oscillators. New J. Phys., 16 (8): 085011, 2014. 10.1088/1367-2630/16/8/085011.
https://doi.org/10.1088/1367-2630/16/8/085011

[176] Matteo G.A. Paris. Displacement operator by beam splitter. Phys. Lett. A, 217 (2-3): 78–80, July 1996. 10.1016/0375-9601(96)00339-8.
https://doi.org/10.1016/0375-9601(96)00339-8

[177] Nathan Killoran, Josh Izaac, Nicolás Quesada, Ville Bergholm, Matthew Amy, and Christian Weedbrook. Strawberry fields: A software platform for photonic quantum computing. Quantum, 3: 129, March 2019. 10.22331/q-2019-03-11-129.
https://doi.org/10.22331/q-2019-03-11-129

Cited by

[1] Zoltán Kolarovszki, Dániel T. R. Nagy, and Zoltán Zimborás, 2024 IEEE International Conference on Quantum Computing and Engineering (QCE) 750 (2024) ISBN:979-8-3315-4137-8.

[2] Ashlesha Patil and Saikat Guha, "A Graphical Rule Book for Clifford Manipulations of Stabilizer States", IEEE Transactions on Quantum Engineering 7, 1 (2026).

[3] Italo Pereira Bezerra, Hilma M. Vasconcelos, and Scott Glancy, "Quadrature squeezing and temperature estimation from the Fock distribution", Quantum Information Processing 21 11, 365 (2022).

[4] Nicolas Dalbec-Constant, Guillaume Thekkadath, Duncan England, Benjamin Sussman, Thomas Gerrits, and Nicolás Quesada, "Accurate Unsupervised Photon Counting from Transition Edge Sensor Signals", (2026).

[5] Rishabh, Chandan Kumar, Geetu Narang, and Arvind, "Evolution of two-mode quantum states under a dissipative environment: Comparison of the robustness of squeezing and entanglement resources", Physical Review A 105 4, 042405 (2022).

[6] E. R. Zinatullin, S. B. Korolev, A. D. Manukhova, and T. Yu. Golubeva, "Error of an arbitrary single-mode Gaussian transformation on a weighted cluster state using a cubic phase gate", Physical Review A 106 3, 032414 (2022).

[7] Jacques Ding, Hudson A. Loughlin, and Vivishek Sudhir, "Analysis, synthesis, and measurement of linear time-invariant quantum systems", Newton 100696 (2026).

[8] Sophie Verclas, Christian Darsow-Fromm, Benedict Tohermes, and Roman Schnabel, "Fiber distribution of phase-stabilized GHz-bandwidth squeezed vacuum states of light between two buildings", Optica Quantum 4 1, 1 (2026).

[9] Jyoti Gavhane, Gayatri Shirke, and Ayush Nakod, 2026 International Conference on Trends in Quantum Computing and Emerging Business Technologies (TQCEBT) 1 (2026) ISBN:979-8-3315-6126-0.

[10] Jérémie Boudreault, Ross Shillito, Jean-Baptiste Bertrand, and Baptiste Royer, "Using a Self-Kerr Nonlinearity for Magic State Preparation in Grid Codes", Physical Review Letters 136 12, 120601 (2026).

[11] Emma Lomonte, Maik Stappers, Linus Krämer, Wolfram H.P. Pernice, and Francesco Lenzini, "Scalable and efficient grating couplers on low-index photonic platforms enabled by cryogenic deep silicon etching", (2023).

[12] Eric Sabo, Lane G. Gunderman, Benjamin Ide, Michael Vasmer, and Guillaume Dauphinais, "Weight-Reduced Stabilizer Codes with Lower Overhead", PRX Quantum 5 4, 040302 (2024).

[13] Luca Bianchi, Carlo Marconi, Laura Ares, Davide Bacco, and Jan Sperling, "Unified boson sampling", Physical Review Research 7 4, L042068 (2025).

[14] Patrick Tritschler, Torsten Ohms, André Zimmermann, and Peter Degenfeld-Schonburg, "Steady-state dynamics of quantum frequency combs in microring resonators", Physical Review A 113 5, 053706 (2026).

[15] Nai-Tao Liu, Qing-Yuan Zhao, Yang-Hui Huang, Long Wang, Zhen Liu, Jie Deng, Fan Yang, Sai-Ying Ru, Zhen-Guo Li, Yao-Yao Pan, Yu Nie, Shun-Hua Wang, Kang-He Lv, Xue-Cou Tu, Xiao-Qing Jia, La-Bao Zhang, Jian Chen, Lin Kang, and Pei-Heng Wu, "A tunable coincidence counter based on superconducting nanowire cryotrons", Applied Physics Letters 128 26, 262601 (2026).

[16] Shohei Kiryu, Kosuke Fukui, Atsushi Okamoto, and Akihisa Tomita, "Linear optical quantum computing with a hybrid squeezed-cat code", Physical Review A 112 4, 042615 (2025).

[17] Nobu‐Hisa Kaneko, "Metrology for Quantum Hardware Standardization—Charting a Pathway: A Strategic Review", IEEJ Transactions on Electrical and Electronic Engineering 21 9, 1282 (2026).

[18] Rhea Alexander, Si Gvirtz-Chen, Nikolaos Koukoulekidis, and David Jennings, "General Entropic Constraints on Calderbank-Shor-Steane Codes within Magic Distillation Protocols", PRX Quantum 4 2, 020359 (2023).

[19] Kasper H. Nielsen, Ying Wang, Edward C. R. Deacon, Patrik I. Sund, Zhe Liu, Sven Scholz, Andreas D. Wieck, Arne Ludwig, Leonardo Midolo, Anders S. Sørensen, Stefano Paesani, and Peter Lodahl, "Programmable nonlinear quantum photonic circuits", Nature Communications 16 1, 11397 (2025).

[20] J. A. Mendoza-Fierro, L. M. Arévalo Aguilar, and M. M. Méndez Otero, "Probability and fidelity of teleportation in a two-mode continuous-variable cluster state via a finite-resolution measurement device", Quantum Information Processing 25 1, 13 (2026).

[21] Shiran Even-Haim, Gefen Baranes, Ron Ruimy, Alexey Gorlach, Raphael Dahan, Asaf A. Diringer, Shay Hacohen-Gourgy, and Ido Kaminer, CLEO 2023 FM3A.6 (2023) ISBN:978-1-957171-25-8.

[22] "Quantum non-Gaussianity certification in continuous-variable optics", Sorbonne université (2023).

[23] Hyunho Cha and Jungwoo Lee, "Binary integer programming for optimizing ebit cost in distributed quantum circuits with fixed module allocation", Quantum Information Processing 25 3, 97 (2026).

[24] Shayan Srinivasa Garani, Priya J. Nadkarni, and Ankur Raina, "Theory Behind Quantum Error Correcting Codes: An Overview", Journal of the Indian Institute of Science 103 2, 449 (2023).

[25] Duong The Do, Ni Trieu, and Duong Tung Nguyen, 2023 IEEE Cloud Summit 52 (2023) ISBN:979-8-3503-2217-0.

[26] "Accelerating optimisation algorithms via optical propagation in complex media", Sorbonne université (2024).

[27] Mohamad Taghi Dejpasand and Morteza Sasani Ghamsari, "Research Trends in Quantum Computers by Focusing on Qubits as Their Building Blocks", Quantum Reports 5 3, 597 (2023).

[28] Cédric Bruynsteen, Michael Vanhoecke, Johan Bauwelinck, and Xin Yin, "Integrated balanced homodyne photonic–electronic detector for beyond 20 GHz shot-noise-limited measurements", Optica 8 9, 1146 (2021).

[29] Christian Drago and Agata M. Brańczyk, "Hong–Ou–Mandel interference: a spectral–temporal analysis", Canadian Journal of Physics 102 8, 411 (2024).

[30] Ryotatsu Yanagimoto, Rajveer Nehra, Ryan Hamerly, Edwin Ng, Alireza Marandi, and Hideo Mabuchi, "Quantum Nondemolition Measurements with Optical Parametric Amplifiers for Ultrafast Universal Quantum Information Processing", PRX Quantum 4 1, 010333 (2023).

[31] Ulysse Chabaud and Mattia Walschaers, "Resources for Bosonic Quantum Computational Advantage", Physical Review Letters 130 9, 090602 (2023).

[32] Wei Luo, Lin Cao, Yuzhi Shi, Lingxiao Wan, Hui Zhang, Shuyi Li, Guanyu Chen, Yuan Li, Sijin Li, Yunxiang Wang, Shihai Sun, Muhammad Faeyz Karim, Hong Cai, Leong Chuan Kwek, and Ai Qun Liu, "Recent progress in quantum photonic chips for quantum communication and internet", Light: Science & Applications 12 1, 175 (2023).

[33] Ilan Tzitrin, Takaya Matsuura, Rafael N. Alexander, Guillaume Dauphinais, J. Eli Bourassa, Krishna K. Sabapathy, Nicolas C. Menicucci, and Ish Dhand, "Fault-Tolerant Quantum Computation with Static Linear Optics", PRX Quantum 2 4, 040353 (2021).

[34] Arne L. Grimsmo and Shruti Puri, "Quantum Error Correction with the Gottesman-Kitaev-Preskill Code", PRX Quantum 2 2, 020101 (2021).

[35] E. R. Zinatullin, S. B. Korolev, and T. Yu. Golubeva, "Teleportation with a cubic phase gate", Physical Review A 104 3, 032420 (2021).

[36] Luca Bianchi, Carlo Marconi, and Davide Bacco, 2026 International Conference on Quantum Communications, Networking, and Computing (QCNC) 43 (2026) ISBN:979-8-3315-6110-9.

[37] Samantha I. Davis, Andrew Mueller, Raju Valivarthi, Nikolai Lauk, Lautaro Narvaez, Boris Korzh, Andrew D. Beyer, Olmo Cerri, Marco Colangelo, Karl K. Berggren, Matthew D. Shaw, Si Xie, Neil Sinclair, and Maria Spiropulu, "Improved Heralded Single-Photon Source with a Photon-Number-Resolving Superconducting Nanowire Detector", Physical Review Applied 18 6, 064007 (2022).

[38] Zhaoyi Li, Isaac Kim, and Patrick Hayden, "Concatenation Schemes for Topological Fault-tolerant Quantum Error Correction", Quantum 7, 1089 (2023).

[39] Mikhail S. Podoshvedov and Sergey A. Podoshvedov, "Transfer of entanglement from a nonlocal photon to non-Gaussian quantum states", Journal of the Optical Society of America B 43 3, 433 (2026).

[40] Maxwell T. West, Martin Sevior, and Muhammad Usman, "Boosted Ensembles of Qubit and Continuous Variable Quantum Support Vector Machines for B Meson Flavor Tagging", Advanced Quantum Technologies 6 10, 2300130 (2023).

[41] Jonathan Conrad, Jens Eisert, and Francesco Arzani, "Gottesman-Kitaev-Preskill codes: A lattice perspective", Quantum 6, 648 (2022).

[42] Lucas J. Mensen, Ben Q. Baragiola, and Nicolas C. Menicucci, "Phase-space methods for representing, manipulating, and correcting Gottesman-Kitaev-Preskill qubits", Physical Review A 104 2, 022408 (2021).

[43] Shiran Even-Haim, Gefen Baranes, Ron Ruimy, Alexey Gorlach, Raphael Dahan, Asaf A. Diringer, Shay Hacohen-Gourgy, and Ido Kaminer, Optica Quantum 2.0 Conference and Exhibition QTu4A.4 (2023) ISBN:978-1-957171-27-2.

[44] Kyungjoo Noh, Christopher Chamberland, and Fernando G.S.L. Brandão, "Low-Overhead Fault-Tolerant Quantum Error Correction with the Surface-GKP Code", PRX Quantum 3 1, 010315 (2022).

[45] Yuxuan Zhang, Daoheng Niu, Alireza Shabani, and Hassan Shapourian, "Quantum Volume for Photonic Quantum Processors", Physical Review Letters 130 11, 110602 (2023).

[46] Robbe De Prins, Yuan Yao, Anuj Apte, and Filippo M. Miatto, "A Quadratic Speedup in the Optimization of Noisy Quantum Optical Circuits", Quantum 7, 1097 (2023).

[47] Maryam Khanahmadi and Klaus Mølmer, "Environment-Assisted Generation of Non-Gaussian Wave-Packet Quantum States", Physical Review Letters 137 2, 020802 (2026).

[48] Atharv Joshi, Kyungjoo Noh, and Yvonne Y Gao, "Quantum information processing with bosonic qubits in circuit QED", Quantum Science and Technology 6 3, 033001 (2021).

[49] Eric S. Cooper, Philipp Kunkel, Avikar Periwal, and Monika Schleier-Smith, "Graph states of atomic ensembles engineered by photon-mediated entanglement", Nature Physics 20 5, 770 (2024).

[50] Ulrik L. Andersen, "Photonic chip brings optical quantum computers a step closer", Nature 591 7848, 40 (2021).

[51] Milica Banić, Valerio Crescimanna, J. Eli Bourassa, Carlos González-Arciniegas, Rafael N. Alexander, and Khabat Heshami, "Exact simulation of realistic Gottesman-Kitaev-Preskill cluster states", Physical Review A 112 5, 052425 (2025).

[52] Blayney W. Walshe, Rafael N. Alexander, Nicolas C. Menicucci, and Ben Q. Baragiola, "Streamlined quantum computing with macronode cluster states", Physical Review A 104 6, 062427 (2021).

[53] Zhenyu Cai, Adam Siegel, and Simon Benjamin, "Looped Pipelines Enabling Effective 3D Qubit Lattices in a Strictly 2D Device", PRX Quantum 4 2, 020345 (2023).

[54] Ben M. Burridge, Imad I. Faruque, John G. Rarity, and Jorge Barreto, "Integrate and scale: a source of spectrally separable photon pairs", Optica 10 11, 1471 (2023).

[55] Guillaume Thekkadath, Martin Houde, Duncan England, Philip Bustard, Frédéric Bouchard, Nicolás Quesada, and Ben Sussman, "Gain-Induced Group Delay in Spontaneous Parametric Down-Conversion", Physical Review Letters 133 20, 203601 (2024).

[56] Narasinga Rao Miniskar, Mohammad Alaul Haque Monil, Elaine Wong, Vicente Leyton Ortega, Jeffrey S Vetter, Seth R Johnson, and Travis Humble, Proceedings of the Supercomputing Asia and International Conference on High Performance Computing in Asia Pacific Region Workshops 323 (2026) ISBN:9798400723285.

[57] Warit Asavanant and Akira Furusawa, "Multipartite continuous-variable optical quantum entanglement: Generation and application", Physical Review A 109 4, 040101 (2024).

[58] Timo Hillmann, Fernando Quijandría, Arne L. Grimsmo, and Giulia Ferrini, "Performance of Teleportation-Based Error-Correction Circuits for Bosonic Codes with Noisy Measurements", PRX Quantum 3 2, 020334 (2022).

[59] Roohollah Ghobadi, "Nonclassical kernels in continuous-variable systems", Physical Review A 104 5, 052403 (2021).

[60] Filip Rozpędek, Kyungjoo Noh, Qian Xu, Saikat Guha, and Liang Jiang, "Quantum repeaters based on concatenated bosonic and discrete-variable quantum codes", npj Quantum Information 7 1, 102 (2021).

[61] Christopher L. Panuski, Ian Christen, Momchil Minkov, Cole J. Brabec, Sivan Trajtenberg-Mills, Alexander D. Griffiths, Jonathan J. D. McKendry, Gerald L. Leake, Daniel J. Coleman, Cung Tran, Jeffrey St Louis, John Mucci, Cameron Horvath, Jocelyn N. Westwood-Bachman, Stefan F. Preble, Martin D. Dawson, Michael J. Strain, Michael L. Fanto, and Dirk R. Englund, "A full degree-of-freedom spatiotemporal light modulator", Nature Photonics 16 12, 834 (2022).

[62] Takahiro Kashiwazaki, Taichi Yamashima, Naoto Takanashi, Asuka Inoue, Takeshi Umeki, and Akira Furusawa, "Fabrication of low-loss quasi-single-mode PPLN waveguide and its application to a modularized broadband high-level squeezer", Applied Physics Letters 119 25, 251104 (2021).

[63] Qianke Wang, Dawei Lyu, Jun Liu, and Jian Wang, "Polarization and Orbital Angular Momentum Encoded Quantum Toffoli Gate Enabled by Diffractive Neural Networks", Physical Review Letters 133 14, 140601 (2024).

[64] Jasper Kranias, Christian Drago, Colin Vendromin, and J. E. Sipe, "Photodetection of squeezed light: A Whittaker-Shannon analysis", Physical Review A 113 6, 063719 (2026).

[65] Kinjol Barua, Samuel Peana, Arya Deepak Keni, Vahagn Mkhitaryan, Vladimir M. Shalaev, Yong P. Chen, Alexandra Boltasseva, and Hadiseh Alaeian, "Bottom-up fabrication of 2D Rydberg exciton arrays in cuprous oxide", Communications Materials 6 1, 21 (2025).

[66] Mark Dong, Matthew Zimmermann, David Heim, Hyeongrak Choi, Genevieve Clark, Andrew J. Leenheer, Kevin J. Palm, Alex Witte, Daniel Dominguez, Gerald Gilbert, Matt Eichenfield, and Dirk Englund, "Programmable photonic integrated meshes for modular generation of optical entanglement links", npj Quantum Information 9 1, 42 (2023).

[67] Jonathan Conrad, Joseph T. Iosue, Ansgar G. Burchards, and Victor V. Albert, "Continuous-Variable Designs and Design-Based Shadow Tomography from Random Lattices", Physical Review Letters 135 6, 060802 (2025).

[68] Sheron Blair, Francesco Arzani, Giulia Ferrini, and Alessandro Ferraro, "Toward fault-tolerant quantum memory with universal continuous-variable gates", Physical Review Research 8 4, L042006 (2026).

[69] Alexandre M. Souza, Eldues O. Martins, Itzhak Roditi, Nahum Sá, Roberto S. Sarthour, and Ivan S. Oliveira, "An Application of Quantum Annealing Computing to Seismic Inversion", Frontiers in Physics 9, 748285 (2022).

[70] Ron Ruimy, Offek Tziperman, Alexey Gorlach, Klaus Mølmer, and Ido Kaminer, "Many-body entanglement via ‘which-path’ information", npj Quantum Information 10 1, 121 (2024).

[71] Jan Provazník, Petr Marek, Julien Laurat, and Radim Filip, "Adapting coherent-state superpositions in noisy channels", Optics Express 33 7, 16520 (2025).

[72] Priya J. Nadkarni, Serge Adonsou, Guillaume Dauphinais, David W. Kribs, and Michael Vasmer, "Unified and Generalized Approach to Entanglement-Assisted Quantum Error Correction", IEEE Transactions on Quantum Engineering 7, 2101132 (2026).

[73] Guillaume Dauphinais, David W. Kribs, and Michael Vasmer, "Stabilizer Formalism for Operator Algebra Quantum Error Correction", Quantum 8, 1261 (2024).

[74] Roberto Salazar and Fereshte Shahbeigi, "Dephasing noise simulation for coherence-generating devices", Physica Scripta 100 8, 085110 (2025).

[75] Joel F. Tasker, Jonathan Frazer, Giacomo Ferranti, and Jonathan C. F. Matthews, "A Bi-CMOS electronic photonic integrated circuit quantum light detector", Science Advances 10 20, eadk6890 (2024).

[76] "The interplay between quantum contextuality and Wigner negativity", Sorbonne université (2021).

[77] Xu Xu, Yu Liu, Yingling Mao, and Yuanyuan Yang, 2026 IEEE 46th International Conference on Distributed Computing Systems (ICDCS) 1004 (2026) ISBN:979-8-3195-2979-4.

[78] 邓娟 Deng Juan, 郭龑强 Guo Yangqiang, 林鸿 Lin Hong, 林杰弘 Lin Jiehong, and 郭晓敏 Guo Xiaomin, " 面向连续变量量子随机数产生的宽带高平坦度平衡零拍探测器", Laser & Optoelectronics Progress 61 9, 0904001 (2024).

[79] Shunya Konno, Warit Asavanant, Kosuke Fukui, Atsushi Sakaguchi, Fumiya Hanamura, Petr Marek, Radim Filip, Jun-ichi Yoshikawa, and Akira Furusawa, "Non-Clifford gate on optical qubits by nonlinear feedforward", Physical Review Research 3 4, 043026 (2021).

[80] Jacob Hastrup and Ulrik L. Andersen, "Protocol for Generating Optical Gottesman-Kitaev-Preskill States with Cavity QED", Physical Review Letters 128 17, 170503 (2022).

[81] Lucas Caron, Hector Simon, Hugo Basset, Romaric Journet, and Rosa Tualle-Brouri, "Generation of Large Coherent-State Superpositions in Free-Space Optical Pulses", Physical Review X 16 3, 031047 (2026).

[82] Jihye Jung and In-Chan Choi, "A New Multicommodity Network Flow Model and Branch and Cut for Optimal Quantum Boolean Circuit Synthesis", INFORMS Journal on Computing 37 1, 42 (2025).

[83] Christophe H. Valahu, Tomas Navickas, Michael J. Biercuk, and Ting Rei Tan, "Benchmarking Bosonic Modes for Quantum Information with Randomized Displacements", PRX Quantum 5 4, 040337 (2024).

[84] Jan Provazník, Olga Solodovnikova, Radim Filip, and Petr Marek, "Optical states with higher stellar rank", Optics Express 33 24, 50761 (2025).

[85] Stefano Paesani and Benjamin J. Brown, "High-Threshold Quantum Computing by Fusing One-Dimensional Cluster States", Physical Review Letters 131 12, 120603 (2023).

[86] Tao Jiang, Jianbin Cai, Junxiang Huang, Naibin Zhou, Yukun Zhang, Jiahao Bei, Guoqing Cai, Sirui Cao, Fusheng Chen, Jiang Chen, Kefu Chen, Xiawei Chen, Xiqing Chen, Zhe Chen, Zhiyuan Chen, Zihua Chen, Wenhao Chu, Hui Deng, Zhibin Deng, Pei Ding, Xun Ding, Zhuzhengqi Ding, Shuai Dong, Bo Fan, Daojin Fan, Yuanhao Fu, Dongxin Gao, Lei Ge, Jiacheng Gui, Cheng Guo, Shaojun Guo, Xiaoyang Guo, Lianchen Han, Tan He, Linyin Hong, Yisen Hu, He-Liang Huang, Yong-Heng Huo, Zuokai Jiang, Honghong Jin, Yunxiang Leng, Dayu Li, Dongdong Li, Fangyu Li, Jiaqi Li, Jinjin Li, Junyan Li, Junyun Li, Na Li, Shaowei Li, Wei Li, Yuhuai Li, Yuan Li, Futian Liang, Xuelian Liang, Nanxing Liao, Jin Lin, Weiping Lin, Dailin Liu, Hongxiu Liu, Maliang Liu, Xinyu Liu, Xuemeng Liu, Yancheng Liu, Haoxin Lou, Yuwei Ma, Lingxin Meng, Hao Mou, Kailiang Nan, Binghan Nie, Meijuan Nie, Jie Ning, Le Niu, Wenyi Peng, Haoran Qian, Hao Rong, Tao Rong, Huiyan Shen, Qiong Shen, Hong Su, Feifan Su, Chenyin Sun, Liangchao Sun, Tianzuo Sun, Yingxiu Sun, Yimeng Tan, Jun Tan, Longyue Tang, Wenbing Tu, Jiafei Wang, Biao Wang, Chang Wang, Chen Wang, Chu Wang, Jian Wang, Liangyuan Wang, Rui Wang, Shengtao Wang, Xiaomin Wang, Xinzhe Wang, Xunxun Wang, Yeru Wang, Zuolin Wei, Jiazhou Wei, Dachao Wu, Gang Wu, Jin Wu, Yulin Wu, Shiyong Xie, Lianjie Xin, Yu Xu, Chun Xue, Kai Yan, Weifeng Yang, Xinpeng Yang, Yang Yang, Yangsen Ye, Zhenping Ye, Chong Ying, Jiale Yu, Qinjing Yu, Wenhu Yu, Xiangdong Zeng, Chen Zha, Shaoyu Zhan, Feifei Zhang, Haibin Zhang, Kaili Zhang, Wen Zhang, Yiming Zhang, Yongzhuo Zhang, Lixiang Zhang, Guming Zhao, Peng Zhao, Xintao Zhao, Youwei Zhao, Zhong Zhao, Luyuan Zheng, Fei Zhou, Liang Zhou, Na Zhou, Shifeng Zhou, Shuang Zhou, Zhengxiao Zhou, Chengjun Zhu, Qingling Zhu, Guihong Zou, Haonan Zou, Qiang Zhang, Chao-Yang Lu, Cheng-Zhi Peng, Xiao Yuan, Ming Gong, Xiaobo Zhu, and Jian-Wei Pan, "One- and two-dimensional cluster states for topological phase simulation and measurement-based quantum computation", Nature Physics 22 3, 430 (2026).

[87] Zheng-Hao Liu, Hui-Xian Meng, Zhen-Peng Xu, Jie Zhou, Jing-Ling Chen, Jin-Shi Xu, Chuan-Feng Li, Guang-Can Guo, and Adán Cabello, "Experimental Test of High-Dimensional Quantum Contextuality Based on Contextuality Concentration", Physical Review Letters 130 24, 240202 (2023).

[88] Kosuke Fukui and Shuntaro Takeda, "Building a large-scale quantum computer with continuous-variable optical technologies", Journal of Physics B: Atomic, Molecular and Optical Physics 55 1, 012001 (2022).

[89] Anthony J. Brady, Jing Wu, and Quntao Zhuang, "Safeguarding Oscillators and Qudits with Distributed Two-Mode Squeezing", Quantum 8, 1478 (2024).

[90] Arik Avagyan, Emanuel Knill, and Scott Glancy, "Multimode Gaussian state analysis with one bounded photon counter", Physical Review A 111 3, 033713 (2025).

[91] Jorge García-Beni, Iris Paparelle, Valentina Parigi, Gian Luca Giorgi, Miguel C. Soriano, and Roberta Zambrini, "Quantum machine learning via continuous-variable cluster states and teleportation", EPJ Quantum Technology 12 1, 63 (2025).

[92] Ming Lai Chan, Aliki Anna Capatos, Peter Lodahl, Anders Søndberg Sørensen, and Stefano Paesani, "Practical blueprint for low-depth photonic quantum computing with quantum dots", npj Quantum Information 12 1, 155 (2026).

[93] Yu Dian Lim and Chuan Seng Tan, "Three-dimensional modeling of near-field beam profiles from grating couplers using a deep neural network", Applied Optics 63 26, 6969 (2024).

[94] Eric Huang, Arthur Pesah, Christopher T. Chubb, Michael Vasmer, and Arpit Dua, "Tailoring Three-Dimensional Topological Codes for Biased Noise", PRX Quantum 4 3, 030338 (2023).

[95] Shikha Bangar, Leanto Sunny, Kübra Yeter-Aydeniz, and George Siopsis, "Experimentally realizable continuous-variable quantum neural networks", Physical Review A 108 4, 042414 (2023).

[96] Songyang Wu, Wenqi Sun, Yingying Wang, Jiawei Liu, and Qingle Wang, "A Secure Quantum Private Set Computation Protocol with Identity Authentication Utilizing GHZ States", International Journal of Theoretical Physics 63 5, 135 (2024).

[97] Francesco Arzani, "Harmonizing continuous noise to build a modular photonic quantum computer", Quantum Views 5, 51 (2021).

[98] Jonas Vinther and Michael J. Kastoryano, "Variational tensor network simulation of Gaussian boson sampling and beyond", Physical Review A 112 2, 022605 (2025).

[99] Chon-Fai Kam and Xuedong Hu, "Fast and high-fidelity dispersive readout of a spin qubit with squeezed microwave and resonator nonlinearity", npj Quantum Information 10 1, 133 (2024).

[100] J. Eli Bourassa, Nicolás Quesada, Ilan Tzitrin, Antal Száva, Theodor Isacsson, Josh Izaac, Krishna Kumar Sabapathy, Guillaume Dauphinais, and Ish Dhand, "Fast Simulation of Bosonic Qubits via Gaussian Functions in Phase Space", PRX Quantum 2 4, 040315 (2021).

[101] Tian-Yu Yang, Yi-Xin Shen, Zhou-Kai Cao, and Xiang-Bin Wang, "Post-selection in noisy Gaussian boson sampling: part is better than whole", Quantum Science and Technology 8 4, 045020 (2023).

[102] Anthony J. Brady, Alec Eickbusch, Shraddha Singh, Jing Wu, and Quntao Zhuang, "Advances in bosonic quantum error correction with Gottesman–Kitaev–Preskill Codes: Theory, engineering and applications", Progress in Quantum Electronics 93, 100496 (2024).

[103] Antonio Cobarrubia, Sancia M. Tauro, Joshua R. Hendrickson, and Sanjay K. Behura, "Characterization of Hexagonal Boron Nitride Quantum Emitter as an SLH Tensor Network", The Journal of Physical Chemistry C 129 32, 14430 (2025).

[104] Shohei Beppu, Kosuke Mitarai, Toshio Mori, Noboru Yoshikane, and Kazuhiro Saito, 2023 Opto-Electronics and Communications Conference (OECC) 1 (2023) ISBN:978-1-6654-6213-6.

[105] Eun Oh, Xuanying Lai, Jianming Wen, and Shengwang Du, "Distributed Quantum Computing with Photons and Atomic Memories", Advanced Quantum Technologies 6 6, 2300007 (2023).

[106] Soshun Naito, Yasunari Suzuki, and Yuuki Tokunaga, "Network-Based Quantum Computing: An Efficient Design Framework for Many-Small-Node Distributed Fault-Tolerant Quantum Computing", IEEE Transactions on Quantum Engineering 7, 3104632 (2026).

[107] Sivaprasad Omanakuttan and Jonathan A. Gross, "Multispin Clifford codes for angular momentum errors in spin systems", Physical Review A 108 2, 022424 (2023).

[108] Mahnaz Jafarzadeh, Jonathan Conrad, Rafael N. Alexander, and Ben Q. Baragiola, "Logical channels in approximate Gottesman-Kitaev-Preskill error correction", Physical Review A 112 6, 062413 (2025).

[109] Miller Eaton, Carlos González-Arciniegas, Rafael N. Alexander, Nicolas C. Menicucci, and Olivier Pfister, "Measurement-based generation and preservation of cat and grid states within a continuous-variable cluster state", Quantum 6, 769 (2022).

[110] Jonathan Wei Zhong Lau, Kian Hwee Lim, Harshank Shrotriya, and Leong Chuan Kwek, "NISQ computing: where are we and where do we go?", AAPPS Bulletin 32 1, 27 (2022).

[111] Francesco A. Mele, Salvatore F.E. Oliviero, Varun Upreti, and Ulysse Chabaud, "Symplectic Rank of Non-Gaussian Quantum States", PRX Quantum 7 2, 020366 (2026).

[112] Alon Eldan, Ofek Gillon, Asher Lagemi, Elai F. Furman, and Avi Pe’er, "Multiplexed processing of quantum information across an ultrawide optical bandwidth", Science Advances 12 11, eadw5085 (2026).

[113] Petr Marek, "Ground State Nature and Nonlinear Squeezing of Gottesman-Kitaev-Preskill States", Physical Review Letters 132 21, 210601 (2024).

[114] Matthew S. Winnel, Joshua J. Guanzon, Deepesh Singh, and Timothy C. Ralph, "Deterministic Preparation of Optical Squeezed Cat and Gottesman-Kitaev-Preskill States", Physical Review Letters 132 23, 230602 (2024).

[115] Amanuel Anteneh, Léandre Brunel, Carlos González-Arciniegas, and Olivier Pfister, "Deep reinforcement learning for near-deterministic preparation of cubic-phase gates and direct preparation of quartic-phase gates in photonic quantum computing", Physical Review Research 8 1, L012048 (2026).

[116] Jonah Townsend, Enzo Conceição Picinini, and Rogério de Sousa, "Scattering-induced loss in ferroelectric photonic devices", Applied Physics Letters 128 26, 261113 (2026).

[117] Matteo Rosati, "A learning theory for quantum photonic processors and beyond", Quantum 8, 1433 (2024).

[118] Jixuan Ruan, Xiang Fang, Hezi Zhang, Ang Li, Travis Humble, and Yufei Ding, Proceedings of the 30th ACM International Conference on Architectural Support for Programming Languages and Operating Systems, Volume 3 163 (2025) ISBN:9798400710803.

[119] Andrea D’Urbano, Mario Angelelli, and Christian Catalano, Lecture Notes in Computer Science 14484, 60 (2024) ISBN:978-3-031-49268-6.

[120] Jeremy C Adcock, Davide Bacco, and Yunhong Ding, "Enhancement of a silicon waveguide single photon source by temporal multiplexing", Quantum Science and Technology 7 2, 025025 (2022).

[121] Valerio Crescimanna, Jacob Taylor, Aaron Z. Goldberg, and Khabat Heshami, "Quantum Control of Rydberg Atoms for Mesoscopic Quantum State and Circuit Preparation", Physical Review Applied 20 3, 034019 (2023).

[122] Phillip W. K. Jensen, Lasse Bjørn Kristensen, Cyrille Lavigne, and Alán Aspuru-Guzik, "Toward Quantum Computing with Molecular Electronics", Journal of Chemical Theory and Computation 18 6, 3318 (2022).

[123] Gabrielle Tournaire, Marvin Schwiering, Robert Raussendorf, and Sven Bachmann, "A 3D lattice defect and efficient computations in topological MBQC", Quantum 10, 1997 (2026).

[124] Chon-Fai Kam and Xuedong Hu, "Submicrosecond high-fidelity dispersive readout of a spin qubit with squeezed photons", Physical Review A 109 4, L040402 (2024).

[125] Zhifei Li and Daiqin Su, "Correcting biased noise using Gottesman-Kitaev-Preskill repetition code with noisy ancilla", Physical Review A 109 5, 052420 (2024).

[126] Dayton C. Closser and Zbigniew J. Kabala, "Pushing the Limits of Large Language Models in Quantum Operations", Quantum Reports 8 1, 7 (2026).

[127] Zhifan Zhou, Luís E. E. de Araujo, Matt DiMario, Jing Su, Meng-Chang Wu, B. E. Anderson, Jie Zhao, Kevin M. Jones, and Paul D. Lett, "Generation of reconfigurable hypercubic graph states in one to four dimensions in a simple optical system", Science Advances 12 17, eaea8426 (2026).

[128] Victor Roman-Rodriguez, David Fainsin, Guilherme L. Zanin, Nicolas Treps, Eleni Diamanti, and Valentina Parigi, "Multimode squeezed state for reconfigurable quantum networks at telecommunication wavelengths", Physical Review Research 6 4, 043113 (2024).

[129] Albert B Dinkins V, Austin Bristow, and Kwang-Cheng Chen, 2023 26th International Symposium on Wireless Personal Multimedia Communications (WPMC) 242 (2023) ISBN:979-8-3503-0890-7.

[130] Zhihua Han and Hoi-Kwan Lau, "Downloading Many-Qubit Entanglement from Continuous-Variable Cluster States", Physical Review Letters 136 4, 040202 (2026).

[131] Gefen Baranes, Shiran Even-Haim, Ron Ruimy, Alexey Gorlach, Raphael Dahan, Asaf A. Diringer, Shay Hacohen-Gourgy, and Ido Kaminer, "Free-electron interactions with photonic GKP states: Universal control and quantum error correction", Physical Review Research 5 4, 043271 (2023).

[132] Abhinav Deshpande, Arthur Mehta, Trevor Vincent, Nicolás Quesada, Marcel Hinsche, Marios Ioannou, Lars Madsen, Jonathan Lavoie, Haoyu Qi, Jens Eisert, Dominik Hangleiter, Bill Fefferman, and Ish Dhand, "Quantum computational advantage via high-dimensional Gaussian boson sampling", Science Advances 8 1, eabi7894 (2022).

[133] Lautaro Labarca, Sara Turcotte, Alexandre Blais, and Baptiste Royer, "Quantum Sensing of Displacements with Stabilized Gottesman-Kitaev-Preskill States", PRX Quantum 7 2, 020301 (2026).

[134] Changhun Oh and Youngrong Lim, "Classical Algorithms for Measurement-Adaptive Gaussian Circuits", PRX Quantum 7 1, 010329 (2026).

[135] Kou Hamada, Yasunari Suzuki, and Yuuki Tokunaga, "Efficient and high-performance routing of lattice-surgery paths on three-dimensional lattice", Quantum 10, 2061 (2026).

[136] T. J. Volkoff and Yiğit Subaşı, "Ancilla-free continuous-variable SWAP test", Quantum 6, 800 (2022).

[137] Hamza Hasnaoui, Leonardo Limongi, Taira Giordani, Beatrice Polacchi, Alberto Quaranta, Martino Bernard, Fabio Sciarrino, and Mirko Lobino, "Optical quantum computing", Applied Physics Reviews 13 3, 031306 (2026).

[138] Shuhong Hao, Meihong Wang, Dong Wang, and Xiaolong Su, "Topological error correction with a Gaussian cluster state", Physical Review A 103 5, 052407 (2021).

[139] Chaohan Cui, William Horrocks, Shuhong Hao, Saikat Guha, Nasser Peyghambarian, Quntao Zhuang, and Zheshen Zhang, "Quantum receiver enhanced by adaptive learning", Light: Science & Applications 11 1, 344 (2022).

[140] Vojtěch Kuchař and Petr Marek, "Nonlinear squeezing of superpositions of quadrature eigenstates", Physical Review A 112 5, 053706 (2025).

[141] Blayney W. Walshe, Rafael N. Alexander, Takaya Matsuura, Ben Q. Baragiola, and Nicolas C. Menicucci, "Equivalent noise properties of scalable continuous-variable cluster states", Physical Review A 108 4, 042602 (2023).

[142] Jintae Kim, Jung Hoon Han, and Isaac H. Kim, "Fault-tolerant Quantum Error Correction Using a Linear Array of Emitters", Quantum 9, 1676 (2025).

[143] Hayata Yamasaki and Masato Koashi, "Time-Efficient Constant-Space-Overhead Fault-Tolerant Quantum Computation", Nature Physics 20 2, 247 (2024).

[144] Vidur Raj, Adan Azem, Max Patterson, Devendra Kumar Namburi, Jeff F Young, and Robert H Hadfield, "Waveguide integrated superconducting nanowire single-photon detectors for integrated photonics", Journal of Physics D: Applied Physics 58 24, 243001 (2025).

[145] Peilin Du, Jing Zhang, Tiancai Zhang, Rongguo Yang, and Jiangrui Gao, "A complete continuous-variable quantum computation architecture based on the 2D spatiotemporal cluster state", Scientific Reports 15 1, 18199 (2025).

[146] Dennis Delali Kwesi Wayo, Rodrigo Alves Dias, Leonardo Goliatt, and Sven Groppe, "DifGa: differentiable error mitigation for multi-mode Gaussian and non-Gaussian noise in quantum photonic circuits", Journal of Physics: Photonics 8 3, 035004 (2026).

[147] Lars S. Madsen, Fabian Laudenbach, Mohsen Falamarzi. Askarani, Fabien Rortais, Trevor Vincent, Jacob F. F. Bulmer, Filippo M. Miatto, Leonhard Neuhaus, Lukas G. Helt, Matthew J. Collins, Adriana E. Lita, Thomas Gerrits, Sae Woo Nam, Varun D. Vaidya, Matteo Menotti, Ish Dhand, Zachary Vernon, Nicolás Quesada, and Jonathan Lavoie, "Quantum computational advantage with a programmable photonic processor", Nature 606 7912, 75 (2022).

[148] Kevin C. Cox, Przemyslaw Bienias, David H. Meyer, Donald P. Fahey, Paul D. Kunz, and Alexey V. Gorshkov, "Spin-wave quantum computing with atoms in a single-mode cavity", Physical Review Research 4 3, 033149 (2022).

[149] Mirko Arienzo, Dmitry Grinko, Martin Kliesch, and Markus Heinrich, "Bosonic Randomized Benchmarking with Passive Transformations", PRX Quantum 6 2, 020305 (2025).

[150] Taira Giordani, Francesco Hoch, Gonzalo Carvacho, Nicolò Spagnolo, and Fabio Sciarrino, "Integrated photonics in quantum technologies", La Rivista del Nuovo Cimento 46 2, 71 (2023).

[151] John R. Scott and Krishna C. Balram, "Timing Constraints Due to Real-Time Graph-Traversal Algorithms on Incomplete Cluster States in Photonic Measurement-Based Quantum Computing", Physical Review Applied 20 2, 024019 (2023).

[152] Timothy C. Ralph, Matthew S. Winnel, S. Nibedita Swain, and Ryan J. Marshman, "Noise Transfer Approach to GKP Quantum Circuits", Entropy 26 10, 874 (2024).

[153] Xiruo Yan, Sebastian Gitt, Becky Lin, Donald Witt, Mahssa Abdolahi, Abdelrahman Afifi, Adan Azem, Adam Darcie, Jingda Wu, Kashif Awan, Matthew Mitchell, Andreas Pfenning, Lukas Chrostowski, and Jeff F. Young, "Silicon photonic quantum computing with spin qubits", APL Photonics 6 7, 070901 (2021).

[154] Kamil Wereszczyński, Agnieszka Michalczuk, Marcin Paszkuta, and Jacek Gumiela, "High-Precision Voltage Measurement for Optical Quantum Computation", Energies 15 12, 4205 (2022).

[155] Carlos E. Lopetegui, Mathieu Isoard, Nicolas Treps, and Mattia Walschaers, "Detection of mode-intrinsic quantum entanglement", Optica Quantum 3 4, 312 (2025).

[156] Haowen Wang, Yunjia Xue, Yingjie Qu, Xiaoyi Mu, and Hongyang Ma, "Multidimensional Bose quantum error correction based on neural network decoder", npj Quantum Information 8 1, 134 (2022).

[157] M. V. Larsen, J. E. Bourassa, S. Kocsis, J. F. Tasker, R. S. Chadwick, C. González-Arciniegas, J. Hastrup, C. E. Lopetegui-González, F. M. Miatto, A. Motamedi, R. Noro, G. Roeland, R. Baby, H. Chen, P. Contu, I. Di Luch, C. Drago, M. Giesbrecht, T. Grainge, I. Krasnokutska, M. Menotti, B. Morrison, C. Puviraj, K. Rezaei Shad, B. Hussain, J. McMahon, J. E. Ortmann, M. J. Collins, C. Ma, D. S. Phillips, M. Seymour, Q. Y. Tang, B. Yang, Z. Vernon, R. N. Alexander, and D. H. Mahler, "Integrated photonic source of Gottesman–Kitaev–Preskill qubits", Nature 642 8068, 587 (2025).

[158] Muhammad AbuGhanem, "Information processing at the speed of light", Frontiers of Optoelectronics 17 1, 33 (2024).

[159] Marina Kudra, Mikael Kervinen, Ingrid Strandberg, Shahnawaz Ahmed, Marco Scigliuzzo, Amr Osman, Daniel Pérez Lozano, Mats O. Tholén, Riccardo Borgani, David B. Haviland, Giulia Ferrini, Jonas Bylander, Anton Frisk Kockum, Fernando Quijandría, Per Delsing, and Simone Gasparinetti, "Robust Preparation of Wigner-Negative States with Optimized SNAP-Displacement Sequences", PRX Quantum 3 3, 030301 (2022).

[160] Tarek Nouioua and Nour El-Houda Yahiaoui, 2023 5th International Conference on Pattern Analysis and Intelligent Systems (PAIS) 1 (2023) ISBN:979-8-3503-8145-0.

[161] Yuan Liu, Shraddha Singh, Kevin C. Smith, Eleanor Crane, John M. Martyn, Alec Eickbusch, Alexander Schuckert, Richard D. Li, Jasmine Sinanan-Singh, Micheline B. Soley, Takahiro Tsunoda, Isaac L. Chuang, Nathan Wiebe, and Steven M. Girvin, "Hybrid Oscillator-Qubit Quantum Processors: Instruction Set Architectures, Abstract Machine Models, and Applications", PRX Quantum 7 1, 010201 (2026).

[162] Shiro Tamiya, Masato Koashi, and Hayata Yamasaki, "Fault-tolerant quantum computation with polylogarithmic time and constant space overheads", Nature Physics 22 1, 27 (2026).

[163] Alexandre C Ricardo, Gubio G de Lima, Amanda G Valério, Tiago de S Farias, and Celso J Villas-Boas, "Continuous-variable quantum computing on a trapped ion: neural network applications", Physica Scripta 100 12, 125109 (2025).

[164] "Generation and characterization of Gaussian and non-Gaussian states of light", Sorbonne université (2025).

[165] Timo Hillmann, Lucas Berent, Armanda O. Quintavalle, Jens Eisert, Robert Wille, and Joschka Roffe, "Localized statistics decoding for quantum low-density parity-check codes", Nature Communications 16 1, 8214 (2025).

[166] Kianna Wan, Soonwon Choi, Isaac H. Kim, Noah Shutty, and Patrick Hayden, "Fault-Tolerant Qubit from a Constant Number of Components", PRX Quantum 2 4, 040345 (2021).

[167] Sivaprasad Omanakuttan and T. J. Volkoff, "Spin-squeezed Gottesman-Kitaev-Preskill codes for quantum error correction in atomic ensembles", Physical Review A 108 2, 022428 (2023).

[168] Tigran Sedrakyan and Alexia Salavrakos, "Photonic quantum generative adversarial networks for classical data", Optica Quantum 2 6, 458 (2024).

[169] Tom B. Harris, Takaya Matsuura, Ben Q. Baragiola, and Nicolas C. Menicucci, "Logical channel for heralded and pure loss with the Gottesman-Kitaev-Preskill code", Physical Review A 112 4, 042417 (2025).

[170] Wendy Otieno, Alexandre Zagoskin, Alexander G. Balanov, Juan Totero Gongora, and Sergey E. Savel’ev, "A quantum reservoir computing approach to quantum stock price forecasting in technology-markets", EPJ Quantum Technology 13 1, 97 (2026).

[171] "Manipulation of solid-state single-photon emitters by deterministic coupling into polymer-based photonic structures", université Paris-Saclay (2023).

[172] Hamza Hasnaoui, Matteo Leonardi, Jean-Pierre Zendri, Marco Bazzan, and Mirko Lobino, "Integrated waveguide sources of squeezed vacuum for gravitational wave detection and quantum metrology", Frontiers in Sensors 6, 1603365 (2025).

[173] Šimon Bräuer, Tomáš Opatrný, and Petr Marek, "Generalized squeezing as a witness of various quantum properties", Physical Review Research 7 3, 033176 (2025).

[174] Yan-Jun Xie, Yi-Yi Mao, Fei-Fei Wu, Xian-Da Zuo, Hui Sun, Zhen-Sheng Yuan, Yi Jiang, Yu-Ao Chen, Han-Ning Dai, and Jian-Wei Pan, "Exploring a fracton model through Floquet engineering of four-body ring-exchange interactions", Physical Review A 113 1, 012605 (2026).

[175] Apurav Tehri and Jaskaran Singh, "Efficient circuit compression by multiqudit entangling gates in linear optical quantum computation", Physical Review A 113 6, 062622 (2026).

[176] Yi-Ru Chen, Hsien-Yi Hsieh, Jingyu Ning, Hsun-Chung Wu, Hua Li Chen, Zi-Hao Shi, Popo Yang, Ole Steuernagel, Chien-Ming Wu, and Ray-Kuang Lee, "Generation of heralded optical cat states by photon addition", Physical Review A 110 2, 023703 (2024).

[177] "Charge control in semiconductor quantum-dot arrays and prospects for large-scale integration", Université Grenoble Alpes (2021).

[178] Peter Namdar, Patrick Folge, Carlos E. Lopetegui, Silia Babel, Benjamin Brecht, Christine Silberhorn, and Valentina Parigi, "Spectro-temporally tailored non-Gaussian quantum operations in thin-film waveguides", Optica Quantum 4 6, 518 (2026).

[179] Nikolaos Koukoulekidis and David Jennings, "Constraints on magic state protocols from the statistical mechanics of Wigner negativity", npj Quantum Information 8 1, 42 (2022).

[180] Aaron Z. Goldberg and Khabat Heshami, "How squeezed states both maximize and minimize the same notion of quantumness", Physical Review A 104 3, 032425 (2021).

[181] Shahnawaz Ahmed, Carlos Sánchez Muñoz, Franco Nori, and Anton Frisk Kockum, "Classification and reconstruction of optical quantum states with deep neural networks", Physical Review Research 3 3, 033278 (2021).

[182] Hua-Liang Liu, Hao Su, Yu-Hao Deng, Si-Qiu Gong, Yi-Chao Gu, Hao-Yang Tang, Meng-Hao Jia, Qian Wei, Yu-Kun Song, Dong-Zhou Wang, Ming-Yang Zheng, Fa-Xi Chen, Li-Bo Li, Si-Yu Ren, Xue-Zhi Zhu, Mei-Hong Wang, Yao-Jian Chen, Yan-Fei Liu, Long-Sheng Song, Peng-Yu Yang, Jun-Shi Chen, Hong An, Lei Zhang, Lin Gan, Guang-wen Yang, Jia-Min Xu, Yu-Ming He, Hui Wang, Han-Sen Zhong, Ming-Cheng Chen, Xiao Jiang, Li Li, Nai-Le Liu, Xiao-Long Su, Qiang Zhang, Chao-Yang Lu, and Jian-Wei Pan, "Gaussian boson sampling with 1,024 squeezed states in 8,176 modes", Nature 653 8115, 687 (2026).

[183] Jacob DeLange, Kinjol Barua, Anindya Sundar Paul, Hamid Ohadi, Val Zwiller, Stephan Steinhauer, and Hadiseh Alaeian, "Highly-excited Rydberg excitons in synthetic thin-film cuprous oxide", Scientific Reports 13 1, 16881 (2023).

[184] Samuel E. Fontaine, Colin Vendromin, Trevor J. Steiner, Amirali Atrli, Lillian Thiel, Joshua Castro, Galan Moody, John Bowers, Marco Liscidini, and J. E. Sipe, "Photon-pair generation via down-conversion in III-V semiconductor microrings: Modal dispersion and quasi-phase-matching", Physical Review A 111 2, 023705 (2025).

[185] Blayney W. Walshe, Ben Q. Baragiola, Hugo Ferretti, José Gefaell, Michael Vasmer, Ryohei Weil, Takaya Matsuura, Thomas Jaeken, Giacomo Pantaleoni, Zhihua Han, Timo Hillmann, Nicolas C. Menicucci, Ilan Tzitrin, and Rafael N. Alexander, "Linear-Optical Quantum Computation with Arbitrary Error-Correcting Codes", Physical Review Letters 134 10, 100602 (2025).

[186] Mattia Walschaers, "Non-Gaussian Quantum States and Where to Find Them", PRX Quantum 2 3, 030204 (2021).

[187] Mikko Kiviranta and Leif Grönberg, "Components for Multiplexed DC-SQUID Readouts of Transition Edge Sensor Arrays", IEEE Transactions on Applied Superconductivity 33 5, 1 (2023).

[188] Nicolas Dalbec-Constant, Guillaume Thekkadath, Duncan England, Benjamin Sussman, Thomas Gerrits, and Nicolás Quesada, "Accurate unsupervised photon counting from transition-edge-sensor signals", Physical Review Applied 24 3, 034018 (2025).

[189] Jaehak Lee, Nuri Kang, Seok-Hyung Lee, Hyunseok Jeong, Liang Jiang, and Seung-Woo Lee, "Fault-Tolerant Quantum Computation by Hybrid Qubits with Bosonic Cat Code and Single Photons", PRX Quantum 5 3, 030322 (2024).

[190] Jun-Yi Wu and Shin-Tza Wu, "Linear-optical approach to encoding qubits into harmonic-oscillator modes via quantum walks", Physical Review Research 7 1, 013154 (2025).

[191] Changhun Oh, "Classical simulability of constant-depth linear-optical circuits with noise", npj Quantum Information 11 1, 126 (2025).

[192] Timo Hillmann, Guillaume Dauphinais, Ilan Tzitrin, and Michael Vasmer, "Single-shot and measurement-based quantum error correction via fault complexes", Physical Review A 112 4, L040401 (2025).

[193] Paul Renault, Patrick Yard, Raphael C. Pooser, Miller Eaton, and Hussain Asim Zaidi, "End-to-end switchless architecture for fault-tolerant photonic quantum computing", Quantum 9, 1796 (2025).

[194] Lucas Daguerre and Isaac H. Kim, "Code switching revisited: Low-overhead magic state preparation using color codes", Physical Review Research 7 2, 023080 (2025).

[195] David T. Stephen, Arpit Dua, Ali Lavasani, and Rahul Nandkishore, "Nonlocal Finite-Depth Circuits for Constructing Symmetry-Protected Topological States and Quantum Cellular Automata", PRX Quantum 5 1, 010304 (2024).

[196] Kosuke Fukui, "High-threshold fault-tolerant quantum computation with the Gottesman-Kitaev-Preskill qubit under noise in an optical setup", Physical Review A 107 5, 052414 (2023).

[197] Haoyuan Luo and Sahand Mahmoodian, "Efficient generation of optical cat states using squeezed few-photon superposition states", Physical Review Applied 25 2, 024046 (2026).

[198] Ravi Monani, Brian Rogers, Amin Rezaei, and Ava Hedayatipour, 2022 IEEE Green Energy and Smart System Systems (IGESSC) 1 (2022) ISBN:978-1-6654-9866-1.

[199] Aditya Ranjan, Tirthak Patel, Harshitta Gandhi, Daniel Silver, William Cutler, and Devesh Tiwari, Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis 1 (2023) ISBN:9798400701092.

[200] Xiaosi Xu, Simon Benjamin, Jianxin Chen, Jinzhao Sun, Xiao Yuan, and Pan Zhang, "A Herculean task: classical simulation of quantum computers", Science Bulletin 70 23, 4104 (2025).

[201] Kaavya Sahay, Jahan Claes, and Shruti Puri, "Tailoring Fusion-Based Error Correction for High Thresholds to Biased Fusion Failures", Physical Review Letters 131 12, 120604 (2023).

[202] C. Drago and J. E. Sipe, "Deconstructing squeezed light: Schmidt decomposition versus the Whittaker-Shannon interpolation", Physical Review A 110 2, 023710 (2024).

[203] Nikita Stroev and Natalia G. Berloff, "Analog Photonics Computing for Information Processing, Inference, and Optimization", Advanced Quantum Technologies 6 9, 2300055 (2023).

[204] Jaehak Lee, Srikrishna Omkar, Yong Siah Teo, Seok-Hyung Lee, Hyukjoon Kwon, M.S. Kim, and Hyunseok Jeong, "Photonic hybrid quantum computing", Newton 2 3, 100359 (2026).

[205] Giacomo Pantaleoni, Ben Q. Baragiola, and Nicolas C. Menicucci, "Hidden qubit cluster states", Physical Review A 104 1, 012431 (2021).

[206] Bruno F. E. Matarèse and Arnie Purushotham, "Quantum Oncology", Quantum Reports 7 1, 9 (2025).

[207] Bharat Thotakura and Tzu-Chieh Wei, "Quantum state transfer: interplay between gate and readout errors", Quantum Information Processing 22 7, 275 (2023).

[208] Basheir Khan, Inam Ul Haq, Sohaib Rana, and Haroon Ul Rasheed, 2022 19th International Bhurban Conference on Applied Sciences and Technology (IBCAST) 653 (2022) ISBN:978-1-6654-6051-4.

[209] Hezi Zhang, Jixuan Ruan, Dean Tullsen, Yufei Ding, Ang Li, and Travis Humble, Proceedings of the 58th IEEE/ACM International Symposium on Microarchitecture 733 (2025) ISBN:9798400715730.

[210] Dominic A. Sulway, Yuya Yonezu, Lawrence M. Rosenfeld, Pisu Jiang, Takao Aoki, and Joshua W. Silverstone, "High-performance, adiabatically nanotapered fiber-chip couplers in silicon at 2 microns wavelength", Optics Express 31 16, 25350 (2023).

[211] Mark Webber, Vincent Elfving, Sebastian Weidt, and Winfried K. Hensinger, "The impact of hardware specifications on reaching quantum advantage in the fault tolerant regime", AVS Quantum Science 4 1, 013801 (2022).

[212] Christophe H. Valahu, Matthew P. Stafford, Zixin Huang, Vassili G. Matsos, Maverick J. Millican, Teerawat Chalermpusitarak, Nicolas C. Menicucci, Joshua Combes, Ben Q. Baragiola, and Ting Rei Tan, "Quantum-enhanced multiparameter sensing in a single mode", Science Advances 11 39, eadw9757 (2025).

[213] Hakan Doga, Bryan Raubenolt, Fabio Cumbo, Jayadev Joshi, Frank P. DiFilippo, Jun Qin, Daniel Blankenberg, and Omar Shehab, "A Perspective on Protein Structure Prediction Using Quantum Computers", Journal of Chemical Theory and Computation 20 9, 3359 (2024).

[214] Gia Long Ngo, Jean-Pierre Hermier, and Ngoc Diep Lai, "Single-photon splitting by polymeric submicropillars structures", AVS Quantum Science 5 1, 011403 (2023).

[215] Anders J. E. Bjerrum, Ulrik L. Andersen, and Peter Rabl, "Mapping of a many-qubit state onto an oscillator using controlled displacements", Physical Review A 111 6, 062613 (2025).

[216] Natalia Costas, Nadia Belabas, and David Barral, "Spatio-spectral quantum networks in nonlinear photonic lattices", Physical Review Research 7 4, 043320 (2025).

[217] Juan Li, Peng Liu, Xing‐Hua Li, Xue‐Ying Yang, Xiao Xiang, Tao Liu, Shao‐Feng Wang, Rui‐Fang Dong, and Shou‐Gang Zhang, "Parallel Construction of Cluster States From Quantum Frequency Combs via Multipixel Homodyne Detection", Advanced Quantum Technologies 9 3, e00929 (2026).

[218] H. Aghaee Rad, T. Ainsworth, R. N. Alexander, B. Altieri, M. F. Askarani, R. Baby, L. Banchi, B. Q. Baragiola, J. E. Bourassa, R. S. Chadwick, I. Charania, H. Chen, M. J. Collins, P. Contu, N. D’Arcy, G. Dauphinais, R. De Prins, D. Deschenes, I. Di Luch, S. Duque, P. Edke, S. E. Fayer, S. Ferracin, H. Ferretti, J. Gefaell, S. Glancy, C. González-Arciniegas, T. Grainge, Z. Han, J. Hastrup, L. G. Helt, T. Hillmann, J. Hundal, S. Izumi, T. Jaeken, M. Jonas, S. Kocsis, I. Krasnokutska, M. V. Larsen, P. Laskowski, F. Laudenbach, J. Lavoie, M. Li, E. Lomonte, C. E. Lopetegui, B. Luey, A. P. Lund, C. Ma, L. S. Madsen, D. H. Mahler, L. Mantilla Calderón, M. Menotti, F. M. Miatto, B. Morrison, P. J. Nadkarni, T. Nakamura, L. Neuhaus, Z. Niu, R. Noro, K. Papirov, A. Pesah, D. S. Phillips, W. N. Plick, T. Rogalsky, F. Rortais, J. Sabines-Chesterking, S. Safavi-Bayat, E. Sazhaev, M. Seymour, K. Rezaei Shad, M. Silverman, S. A. Srinivasan, M. Stephan, Q. Y. Tang, J. F. Tasker, Y. S. Teo, R. B. Then, J. E. Tremblay, I. Tzitrin, V. D. Vaidya, M. Vasmer, Z. Vernon, L. F. S. S. M. Villalobos, B. W. Walshe, R. Weil, X. Xin, X. Yan, Y. Yao, M. Zamani Abnili, and Y. Zhang, "Scaling and networking a modular photonic quantum computer", Nature 638 8052, 912 (2025).

[219] Yuxun Wang, Junyu Quan, and Qin Li, 2022 14th International Conference on Wireless Communications and Signal Processing (WCSP) 804 (2022) ISBN:978-1-6654-5085-0.

[220] Love A. Pettersson, Anders S. Sørensen, and Stefano Paesani, "Deterministic Generation of Concatenated Graph Codes from Quantum Emitters", PRX Quantum 6 1, 010305 (2025).

[221] Mansoor A. Khan, Muhammad N. Aman, and Biplab Sikdar, "Beyond Bits: A Review of Quantum Embedding Techniques for Efficient Information Processing", IEEE Access 12, 46118 (2024).

[222] D. F. Walls and Gerard J. Milburn, Graduate Texts in Physics 269 (2025) ISBN:978-3-031-84176-7.

[223] E. R. Zinatullin, S. B. Korolev, and T. Yu. Golubeva, "Teleportation protocols with non-Gaussian operations: Conditional photon subtraction versus cubic phase gate", Physical Review A 107 2, 022422 (2023).

[224] Saif Kinyori, Edna C. Too, David G. Mwathi, and Juster N. Mungiria, Signals and Communication Technology 293 (2025) ISBN:978-3-031-91801-8.

[225] Mikkel V. Larsen, Christopher Chamberland, Kyungjoo Noh, Jonas S. Neergaard-Nielsen, and Ulrik L. Andersen, "Fault-Tolerant Continuous-Variable Measurement-based Quantum Computation Architecture", PRX Quantum 2 3, 030325 (2021).

[226] Brendan Pankovich, Angus Kan, Kwok Ho Wan, Maike Ostmann, Alex Neville, Srikrishna Omkar, Adel Sohbi, and Kamil Brádler, "High-Photon-Loss Threshold Quantum Computing Using GHZ-State Measurements", Physical Review Letters 133 5, 050604 (2024).

[227] Zoltán Kolarovszki, Tomasz Rybotycki, Péter Rakyta, Ágoston Kaposi, Boldizsár Poór, Szabolcs Jóczik, Dániel T. R. Nagy, Henrik Varga, Kareem H. El-Safty, Gregory Morse, Michał Oszmaniec, Tamás Kozsik, and Zoltán Zimborás, "Piquasso: A Photonic Quantum Computer Simulation Software Platform", Quantum 9, 1708 (2025).

[228] Ido Kaplan, Haim Suchowski, and Yaron Oz, "Correlation thresholds for effective composite pulse quantum error mitigation", Physical Review A 110 5, 052614 (2024).

[229] M. AbuGhanem, "Information Processing at The Speed of Light", (2024).

[230] Iris Paparelle, Johan Henaff, Jorge García-Beni, Émilie Gillet, Daniel Montesinos, Gian Luca Giorgi, Miguel C. Soriano, Roberta Zambrini, and Valentina Parigi, "Experimental memory control in continuous-variable optical quantum reservoir computing", Nature Photonics 20 4, 413 (2026).

[231] Axel M. Eriksson, Théo Sépulcre, Mikael Kervinen, Timo Hillmann, Marina Kudra, Simon Dupouy, Yong Lu, Maryam Khanahmadi, Jiaying Yang, Claudia Castillo-Moreno, Per Delsing, and Simone Gasparinetti, "Universal control of a bosonic mode via drive-activated native cubic interactions", Nature Communications 15 1, 2512 (2024).

[232] Yu Zheng, Alessandro Ferraro, Anton Frisk Kockum, and Giulia Ferrini, "Gaussian conversion protocol for heralded generation of generalized Gottesman-Kitaev-Preskill states", Physical Review A 108 1, 012603 (2023).

[233] Tiphaine Kouadou, F. Sansavini, M. Ansquer, J. Henaff, N. Treps, and V. Parigi, "Spectrally shaped and pulse-by-pulse multiplexed multimode squeezed states of light", APL Photonics 8 8, 086113 (2023).

[234] Leonardo Rincón, David Fainsin, Peter Namdar, Victor Roman-Rodriguez, Guilherme Zanin, Nicolas Treps, Eleni Diamanti, and Valentina Parigi, Quantum 2.0 Conference and Exhibition QM2B.5 (2024) ISBN:978-1-55752-518-5.

[235] Dennis Delali Kwesi Wayo, Rodrigo Alves Dias, Masoud Darvish Ganji, Camila Martins Saporetti, and Leonardo Goliatt, "Traversing Gaussian and non-Gaussian regimes in photonic quantum simulators: a review", EPJ Quantum Technology 13 1, 85 (2026).

[236] Spyros Tserkis, Kade Head-Marsden, and Prineha Narang, "Information back-flow in quantum non-Markovian dynamics and its connection to teleportation", Physics Letters A 553, 130649 (2025).

[237] Robert Bogdan Staszewski, Ali Esmailiyan, Hongying Wang, Eugene Koskin, Panagiotis Giounanlis, Xutong Wu, Anna Koziol, Andrii Sokolov, Imran Bashir, Mike Asker, Dirk Leipold, Reza Nikandish, Teerachot Siriburanon, and Elena Blokhina, "Cryogenic Controller for Electrostatically Controlled Quantum Dots in 22-nm Quantum SoC", IEEE Open Journal of the Solid-State Circuits Society 2, 103 (2022).

[238] Éloi Descamps, Arne Keller, and Pérola Milman, "Gottesman-Kitaev-Preskill Encoding in Continuous Modal Variables of Single Photons", Physical Review Letters 132 17, 170601 (2024).

[239] Davide Castaldo and Markus Reiher, "Utility-Scale Quantum Computational Chemistry", The Journal of Physical Chemistry Letters 17 29, 8140 (2026).

[240] Jonathan Conrad, Jens Eisert, and Steven T. Flammia, "Chasing shadows with Gottesman-Kitaev-Preskill codes", Quantum 10, 1973 (2026).

[241] Hengyue Li, Yusheng Yang, Zhehui Wang, Shuxin Xie, Zilong Zha, Hantao Sun, Jie Chen, Jian Sun, and Shenggang Ying, "Digital Quantum Simulation of Squeezed States via Enhanced Bosonic Encoding and its Demonstration With Superconducting Qubits", Annalen der Physik 538 2, e00333 (2026).

[242] Tomasz Pecyna, Dawid Siera, and Bartosz Bosak, Lecture Notes in Computer Science 15580, 351 (2025) ISBN:978-3-031-85699-0.

[243] Kan Takase, Fumiya Hanamura, Hironari Nagayoshi, J. Eli Bourassa, Rafael N. Alexander, Akito Kawasaki, Warit Asavanant, Mamoru Endo, and Akira Furusawa, "Generation of flying logical qubits using generalized photon subtraction with adaptive Gaussian operations", Physical Review A 110 1, 012436 (2024).

[244] "Time and Frequency Multiplexing for Continuous-Variable Quantum Networks", Sorbonne université (2023).

[245] Yixuan Wang, Jian Zhou, Yanyan Feng, Ye Kang, Guangqiang He, and Jinjing Shi, "The Trojan Horse Attacks on Continuous Variable Quantum Teleportation", Annalen der Physik 538 5, e70216 (2026).

[246] Mohammed Nadir, 2026 International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD) 46 (2026) ISBN:979-8-3315-6344-8.

[247] Nicolas Fabre, "Teleportation-Based Error Correction Protocol of Time–Frequency Qubit States", Applied Sciences 13 16, 9462 (2023).

[248] Satoshi Yoshida, Shiro Tamiya, and Hayata Yamasaki, "Concatenate codes, save qubits", npj Quantum Information 11 1, 88 (2025).

[249] Yanbing Zhang, On-Chip Photonics 337 (2024) ISBN:9780323917650.

[250] Hayder Abdulameer Yousif, Zaid Ghanim Ali, Taif Sami Hassan Ali, Saif Kamil Shnain, and Andrii Petrenko, Communications in Computer and Information Science 3163, 551 (2027) ISBN:978-3-032-39707-2.

[251] Rajveer Nehra, Ryoto Sekine, Luis Ledezma, Qiushi Guo, Robert M. Gray, Arkadev Roy, and Alireza Marandi, "Few-cycle vacuum squeezing in nanophotonics", Science 377 6612, 1333 (2022).

[252] Mohsin Raza, John B. DeBrota, Ariel Shlosberg, Noah Lordi, and Ivan H. Deutsch, "Robust negativity in the quantum-to-classical transition of Kerr dynamics", Physical Review A 114 1, 013708 (2026).

[253] Nicola Montaut, Agnes George, Monika Monika, Farzam Nosrati, Hao Yu, Stefania Sciara, Benjamin Crockett, Ulf Peschel, Zhiming Wang, Rosario Lo Franco, Mario Chemnitz, William J. Munro, David J. Moss, José Azaña, and Roberto Morandotti, "Progress in integrated and fiber optics for time-bin based quantum information processing", Advanced Optical Technologies 14, 1560084 (2025).

[254] Takumi Kobori, Yasunari Suzuki, Yosuke Ueno, Teruo Tanimoto, Synge Todo, and Yuuki Tokunaga, 2025 IEEE International Symposium on High Performance Computer Architecture (HPCA) 304 (2025) ISBN:979-8-3315-0647-6.

[255] Yosuke Ueno, Masaaki Kondo, Masamitsu Tanaka, Yasunari Suzuki, and Yutaka Tabuchi, 2022 IEEE International Symposium on High-Performance Computer Architecture (HPCA) 274 (2022) ISBN:978-1-6654-2027-3.

[256] Logan G. Wright, William H. Renninger, Demetri N. Christodoulides, and Frank W. Wise, "Nonlinear multimode photonics: nonlinear optics with many degrees of freedom", Optica 9 7, 824 (2022).

[257] Kosuke Fukui, Takaya Matsuura, and Nicolas C. Menicucci, "Efficient Concatenated Bosonic Code for Additive Gaussian Noise", Physical Review Letters 131 17, 170603 (2023).

[258] A. Alocco, A. Celotto, E. Palumbo, B. Galvano, P. Livreri, L. Fasolo, L. Callegaro, and E. Enrico, "Programmable microwave cluster states via Josephson metamaterials", Nature Communications 17 1, 7700 (2026).

[259] Aneek James, Anthony Rizzo, Yuyang Wang, Asher Novick, Songli Wang, Robert Parsons, Kaylx Jang, Maarten Hattink, and Keren Bergman, "Process Variation-Aware Compact Model of Strip Waveguides for Photonic Circuit Simulation", Journal of Lightwave Technology 1 (2023).

[260] Raphael Dahan, Gefen Baranes, Alexey Gorlach, Ron Ruimy, Nicholas Rivera, and Ido Kaminer, "Creation of Optical Cat and GKP States Using Shaped Free Electrons", Physical Review X 13 3, 031001 (2023).

[261] Akhil Varri, Daniel Wendland, Ravi Pradip, Shabnam Taherinia, Zhe Zhao, Emma Lomonte, Francesco Lenzini, Frank Brückerhoff-Plückelmann, and Wolfram Pernice, "On-chip near 100 dB pump filtering using silicon ion implantation", Optics Express 33 22, 46138 (2025).

[262] Giacomo Pantaleoni, Ben Q. Baragiola, and Nicolas C. Menicucci, "Subsystem analysis of continuous-variable resource states", Physical Review A 104 1, 012430 (2021).

[263] George Watkins, Hoang Minh Nguyen, Keelan Watkins, Steven Pearce, Hoi-Kwan Lau, and Alexandru Paler, "A High Performance Compiler for Very Large Scale Surface Code Computations", Quantum 8, 1354 (2024).

[264] Martin Houde, Liam Beaudoin, Robert Kwolek, Kazuki Hirota, Rajveer Nehra, and Nicolás Quesada, "Ultrashort-pulse-pumped, single-mode type-0 squeezers in lithium niobate nanophotonics", Optica Quantum 3 6, 560 (2025).

[265] Emma Lomonte, Maik Stappers, Linus Krämer, Wolfram H. P. Pernice, and Francesco Lenzini, "Scalable and efficient grating couplers on low-index photonic platforms enabled by cryogenic deep silicon etching", Scientific Reports 14 1, 4256 (2024).

[266] Benjamin Ide, Manoj G. Gowda, Priya J. Nadkarni, and Guillaume Dauphinais, "Fault-Tolerant Logical Measurements via Homological Measurement", Physical Review X 15 2, 021088 (2025).

[267] Leonardo Assis Morais, Till Weinhold, Marcelo Pereira de Almeida, Joshua Combes, Markus Rambach, Adriana Lita, Thomas Gerrits, Sae Woo Nam, Andrew G. White, and Geoff Gillett, "Precisely determining photon-number in real time", Quantum 8, 1355 (2024).

[268] Grégoire de Gliniasty, Paul Hilaire, Pierre-Emmanuel Emeriau, Stephen C. Wein, Alexia Salavrakos, and Shane Mansfield, "A Spin-Optical Quantum Computing Architecture", Quantum 8, 1423 (2024).

[269] M. Sloan, A. Viola, M. Liscidini, and J. E. Sipe, "High-gain squeezing in lossy resonators: An asymptotic-field approach", Physical Review A 111 6, 063502 (2025).

[270] Margarita Davydova, Nathanan Tantivasadakarn, Shankar Balasubramanian, and David Aasen, "Quantum computation from dynamic automorphism codes", Quantum 8, 1448 (2024).

[271] Muhammad AbuGhanem, "Toward scalable fault-tolerant photonic quantum computers", The Journal of Supercomputing 82 2, 51 (2026).

[272] Liang DONG, Linyu CHEN, Xingchang WANG, Xinyun LIANG, Ying ZUO, and Jiefei CHEN, "Optical quantum storage of cold atomic ensemble controlled by magnetic field", Acta Physica Sinica 75 4, 040302 (2026).

[273] Manuel H. Muñoz-Arias, Kevin J. Randles, Nils T. Otterstrom, Paul S. Davids, Michael Gehl, and Mohan Sarovar, "Modeling integrated frequency shifters and beam splitters", Physical Review Applied 26 2, 024045 (2026).

[274] M. Sloan and J. E. Sipe, "Squeezing enhancement through resonant interference in multiring resonators", Physical Review A 114 4, 043735 (2026).

[275] Joaquin Medina Dueñas, Gabriel O'Ryan Pérez, Carla Hermann-Avigliano, and Luis E. F. Foa Torres, "Quadrature protection of squeezed states in a one-dimensional photonic topological insulator", Quantum 5, 526 (2021).

[276] Matthew A. Steinberg, Sebastian Feld, Carmen G. Almudever, Michael Marthaler, and Jan-Michael Reiner, "Topological-Graph Dependencies and Scaling Properties of a Heuristic Qubit-Assignment Algorithm", IEEE Transactions on Quantum Engineering 3, 1 (2022).

[277] Huihui Zhu, Tian Chen, Haoran Ma, Zichao Zhao, Jia Guo, Qishen Liang, Yawen Tu, Tao He, Wei Luo, Bo Wang, Qinghua Song, Chaoyuan Jin, Feng Liu, Yihao Yang, Yuehai Wang, Kwek Chuan Leong, Dawei Wang, and Jianyi Yang, "Recent progress towards large-scale integrated photonic quantum computation", npj Nanophotonics 3 1, 20 (2026).

[278] Hengyun Zhou, Madelyn Cain, and Mikhail D. Lukin, "Opportunities in full-stack design of low-overhead fault-tolerant quantum computation", Nature Computational Science 5 12, 1110 (2025).

[279] Andrei Aralov, Émilie Gillet, Viet Nguyen, Andrea Cosentino, Mattia Walschaers, and Massimo Frigerio, "Photon Catalysis for General Multimode Multi-Photon Quantum State Preparation", PRX Quantum 7 2, 020323 (2026).

[280] Jonathan Conrad, Jens Eisert, and Jean-Pierre Seifert, "Good Gottesman-Kitaev-Preskill codes from the NTRU cryptosystem", Quantum 8, 1398 (2024).

[281] Yujin Kang, Jonghyun Lee, Jinyoung Ha, and Jun Heo, "Fault-tolerant quantum computation using low-cost joint measurements", Quantum Information Processing 23 5, 190 (2024).

[282] John R. Scott and Krishna C. Balram, "Timing Constraints Imposed by Classical Digital Control Systems on Photonic Implementations of Measurement-Based Quantum Computing", IEEE Transactions on Quantum Engineering 3, 1 (2022).

[283] Guo Zheng, Wenhao He, Gideon Lee, Kyungjoo Noh, and Liang Jiang, "Performance and Achievable Rates of the Gottesman-Kitaev-Preskill Code for Pure-Loss and Amplification Channels", PRX Quantum 6 3, 030314 (2025).

[284] Antonio deMarti iOlius, Josu Etxezarreta Martinez, Patricio Fuentes, Pedro M. Crespo, and Javier Garcia-Frias, "Performance of surface codes in realistic quantum hardware", Physical Review A 106 6, 062428 (2022).

[285] S. Ismailzadeh and B. Abedi Ravan, "Multioutcome circuit optimization for enhanced non-Gaussian state generation", Physical Review A 114 4, 043511 (2026).

[286] Shikai Liu, Oliver August Dall’Alba Sandberg, Ming Lai Chan, Björn Schrinski, Yiouli Anyfantaki, Rasmus B. Nielsen, Robert G. Larsen, Andrei Skalkin, Ying Wang, Leonardo Midolo, Sven Scholz, Andreas D. Wieck, Arne Ludwig, Anders S. Sørensen, Alexey Tiranov, and Peter Lodahl, "Violation of Bell inequality by photon scattering on a two-level emitter", Nature Physics 20 9, 1429 (2024).

[287] Takaya Matsuura, Springer Theses 103 (2023) ISBN:978-981-19-8287-3.

[288] Yujin Kang, Youshin Chung, and Jun Heo, "Space‐Efficient Logical Qubit Architecture with a Bus for Magic State Consumption", Advanced Quantum Technologies 9 4, e00505 (2026).

[289] Jahan Claes, J. Eli Bourassa, and Shruti Puri, "Tailored cluster states with high threshold under biased noise", npj Quantum Information 9 1, 9 (2023).

[290] Tummas Napoleon Arge, Seongmin Jo, Huy Quang Nguyen, Francesco Lenzini, Jens Arnbak Holbøll Nielsen, Wolfram Pernice, Jonas Schou Neergaard-Nielsen, Tobias Gehring, and Ulrik Lund Andersen, Quantum 2.0 Conference and Exhibition QW2A.2 (2024) ISBN:978-1-55752-518-5.

[291] Shang Yu, Zhian Jia, Aonan Zhang, Ewan Mer, Zhenghao Li, Valerio Crescimanna, Kuan‐Cheng Chen, Raj B. Patel, Ian A. Walmsley, and Dagomir Kaszlikowski, "Shedding Light on the Future: Exploring Quantum Neural Networks through Optics", Advanced Quantum Technologies 8 12, 2400074 (2025).

[292] S. Sempere-Llagostera, R. B. Patel, I. A. Walmsley, and W. S. Kolthammer, "Experimentally Finding Dense Subgraphs Using a Time-Bin Encoded Gaussian Boson Sampling Device", Physical Review X 12 3, 031045 (2022).

[293] Ruilin Liu, Sebastián V. Romero, Izaskun Oregi, Eneko Osaba, Esther Villar-Rodriguez, and Yue Ban, "Digital Quantum Simulation and Circuit Learning for the Generation of Coherent States", Entropy 24 11, 1529 (2022).

[294] Jeremy C. Adcock and Yunhong Ding, "Quantum prospects for hybrid thin-film lithium niobate on silicon photonics", Frontiers of Optoelectronics 15 1, 7 (2022).

[295] Hideyuki Miyahara, Yiyou Chen, Vwani Roychowdhury, and Louis-Serge Bouchard, "Decoherence mitigation by embedding a logical qubit in a qudit", Quantum Information Processing 22 7, 278 (2023).

[296] Niklas Euler, Monika Monika, Ulf Peschel, and Martin Gärttner, "Detecting high-dimensional time-bin entanglement in fiber-loop systems", Physical Review A 112 1, 012410 (2025).

[297] Robert I. Booth, Ulysse Chabaud, and Pierre-Emmanuel Emeriau, "Contextuality and Wigner Negativity Are Equivalent for Continuous-Variable Quantum Measurements", Physical Review Letters 129 23, 230401 (2022).

[298] Antonio F. Aguiar, Orleans C. V. Gomes, and João Batista R. Silva, "Photonic QPU With Coherent States for Reversible Quantum Logic", Annalen der Physik 538 2, e00635 (2026).

[299] Baptiste Royer, Shraddha Singh, and S.M. Girvin, "Encoding Qubits in Multimode Grid States", PRX Quantum 3 1, 010335 (2022).

[300] Andreas Pfenning, Sebastian Krüger, Fauzia Jabeen, Lukas Worschech, Fabian Hartmann, and Sven Höfling, "Single-Photon Counting with Semiconductor Resonant Tunneling Devices", Nanomaterials 12 14, 2358 (2022).

[301] Jiawei Zhang and Koji Sugioka, "Basics and applications of optical interferometers integrated by femtosecond laser", Applied Research 1 3, e202200002 (2022).

[302] V. G. Matsos, C. H. Valahu, M. J. Millican, T. Navickas, X. C. Kolesnikow, M. J. Biercuk, and T. R. Tan, "Universal quantum gate set for Gottesman–Kitaev–Preskill logical qubits", Nature Physics 21 10, 1664 (2025).

[303] Fariba Hosseinynejad, Pavithran Iyer, Guillaume Dauphinais, and David L. Feder, "Realistic Gottesman-Kitaev-Preskill Stabilizer States Enable Universal Quantum Computation", Physical Review Letters 136 15, 150602 (2026).

[304] Matthew P. Stafford and Nicolas C. Menicucci, "Biased Gottesman-Kitaev-Preskill repetition code", Physical Review A 108 5, 052428 (2023).

[305] Jack Davis, Nicolas Fabre, and Ulysse Chabaud, "Identifying quantum resources in encoded computations", npj Quantum Information 12 1, 140 (2026).

[306] Takato Yoshida, Daichi Okuno, Takahiro Kashiwazaki, Takeshi Umeki, Shigehito Miki, Fumihiro China, Masahiro Yabuno, Hirotaka Terai, and Shuntaro Takeda, "Sequential and Programmable Squeezing Gates for Optical Non-Gaussian Input States", PRX Quantum 6 1, 010311 (2025).

[307] Kosuke Fukui, Mamoru Endo, Warit Asavanant, Atsushi Sakaguchi, Jun-ichi Yoshikawa, and Akira Furusawa, "Generating the Gottesman-Kitaev-Preskill qubit using a cross-Kerr interaction between squeezed light and Fock states in optics", Physical Review A 105 2, 022436 (2022).

[308] Harashta Tatimma Larasati and Byung-Soo Choi, "Towards fault-tolerant distributed quantum computation (FT-DQC): Taxonomy, recent progress, and challenges", ICT Express 11 3, 417 (2025).

[309] Juan Li, Peng Liu, Xinghua Li, Xueying Yang, Tao Liu, Ruifang Dong, and Shougang Zhang, "Resource-efficient generation of continuous-variable Greenberger–Horne–Zeilinger entanglement based on a quantum frequency comb", Quantum Review Letters 2, 111 (2026).

[310] Noa Feldman and Moshe Goldstein, "Noisy quantum computation modeled by quantum walk: universality without ancillas", Quantum Science and Technology 7 4, 045032 (2022).

[311] Arsalan Motamedi, Yuan Yao, Kasper Nielsen, Ulysse Chabaud, J. Eli Bourassa, Rafael N. Alexander, and Filippo M. Miatto, "The stellar decomposition of Gaussian quantum states", Quantum 10, 1971 (2026).

[312] Chan Roh, Geunhee Gwak, Young-Do Yoon, and Young-Sik Ra, "Generation of three-dimensional cluster entangled state", Nature Photonics 19 5, 526 (2025).

[313] Samuel J Sheldon, Pieter Kok, and Callum W Duncan, "A quantum Gate Architecture via Teleportation and entanglement", Quantum Science and Technology 11 4, 045056 (2026).

[314] Kosuke Fukui, Shuntaro Takeda, Mamoru Endo, Warit Asavanant, Jun-ichi Yoshikawa, Peter van Loock, and Akira Furusawa, "Efficient Backcasting Search for Optical Quantum State Synthesis", Physical Review Letters 128 24, 240503 (2022).

[315] Tiphaine Kouadou, Elie Gozlan, Loïc Garcia, David Polizzi, David Fainsin, Iris Paparelle, R L Rincón Celis, Bastien Oriot, Anthony Abi Aad, Peter Namdar, Ganaël Roland, Nicolas Treps, Bérengère Argence, and Valentina Parigi, "Homodyne detection for pulse-by-pulse squeezing measurement", New Journal of Physics 28 5, 054509 (2026).

[316] Takaya Matsuura, Nicolas C. Menicucci, and Hayata Yamasaki, "Continuous-variable fault-tolerant quantum computation under general noise", Nature Communications 17 1, 1709 (2026).

[317] N. Quesada, L. G. Helt, M. Menotti, M. Liscidini, and J. E. Sipe, "Beyond photon pairs—nonlinear quantum photonics in the high-gain regime: a tutorial", Advances in Optics and Photonics 14 3, 291 (2022).

[318] Sara Bartolucci, Patrick Birchall, Hector Bombin, Hugo Cable, Chris Dawson, Mercedes Gimeno-Segovia, Eric Johnston, Konrad Kieling, Naomi Nickerson, Mihir Pant, Fernando Pastawski, Terry Rudolph, and Chris Sparrow, "Fusion-based quantum computation", arXiv:2101.09310, (2021).

[319] Blayney W. Walshe, Ben Q. Baragiola, Rafael N. Alexander, and Nicolas C. Menicucci, "Continuous-variable gate teleportation and bosonic-code error correction", Physical Review A 102 6, 062411 (2020).

[320] Giacomo Corrielli, Andrea Crespi, and Roberto Osellame, "Femtosecond laser micromachining for integrated quantum photonics", Nanophotonics 10 15, 419 (2021).

[321] Ulysse Chabaud, Ganaël Roeland, Mattia Walschaers, Frédéric Grosshans, Valentina Parigi, Damian Markham, and Nicolas Treps, "Certification of Non-Gaussian States with Operational Measurements", PRX Quantum 2 2, 020333 (2021).

[322] Victor V. Albert, "Bosonic coding: introduction and use cases", arXiv:2211.05714, (2022).

[323] Axel Dahlberg, Bart van der Vecht, Carlo Delle Donne, Matthew Skrzypczyk, Ingmar te Raa, Wojciech Kozlowski, and Stephanie Wehner, "NetQASM-a low-level instruction set architecture for hybrid quantum-classical programs in a quantum internet", Quantum Science and Technology 7 3, 035023 (2022).

[324] Nicolas Fabre, "Teleportation-based error correction protocol of time-frequency qubits states", arXiv:2302.06940, (2023).

[325] Shikha Bangar, Leanto Sunny, Kubra Yeter-Aydeniz, and George Siopsis, "Experimentally Realizable Continuous-variable Quantum Neural Networks", arXiv:2306.02525, (2023).

[326] Namrata Shukla, Stefan Nimmrichter, and Barry C. Sanders, "Squeezed comb states", Physical Review A 103 1, 012408 (2021).

[327] Ivan H. Deutsch, "Harnessing the Power of the Second Quantum Revolution", arXiv:2010.10283, (2020).

[328] Matteo Cherchi, Arijit Bera, Antti Kemppinen, Jaani Nissilä, Kirsi Tappura, Marco Caputo, Lauri Lehtimäki, Janne Lehtinen, Joonas Govenius, Tomi Hassinen, Mika Prunnila, and Timo Aalto, "Supporting quantum technologies with an ultralow-loss silicon photonics platform", Advanced Photonics Nexus 2, 024002 (2023).

[329] Dong-Woo Ko, Q. Salman Ahmed, James W. Field, James C. Gates, and Peter Horak, "Out-of-plane beam shaping with UV-written tilted Bragg gratings for beam delivery on quantum chips", Optics Express 30 25, 44628 (2022).

[330] Ming Lai Chan, Aliki Anna Capatos, Peter Lodahl, Anders Søndberg Sørensen, and Stefano Paesani, "Practical blueprint for low-depth photonic quantum computing with quantum dots", arXiv:2507.16152, (2025).

[331] Daan Camps, Ermal Rrapaj, Katherine Klymko, Hyeongjin Kim, Kevin Gott, Siva Darbha, Jan Balewski, Brian Austin, and Nicholas J. Wright, "Quantum Computing Technology Roadmaps and Capability Assessment for Scientific Computing -- An analysis of use cases from the NERSC workload", arXiv:2509.09882, (2025).

[332] Victor V. Albert and Philippe Faist, "Handbook of Error-Correcting Codes", arXiv:2606.11484, (2026).

[333] Julio Abraham Mendoza Fierro, Luis Manuel Arévalo Aguilar, and Marcela Maribel Méndez Otero, "Probability and fidelity of teleportation in a two-mode continuous variable cluster state via an insufficiently selective measurement", arXiv:2407.09921, (2024).

[334] Takumi Kobori, Yasunari Suzuki, Yosuke Ueno, Teruo Tanimoto, Synge Todo, and Yuuki Tokunaga, "LSQCA: Resource-Efficient Load/Store Architecture for Limited-Scale Fault-Tolerant Quantum Computing", arXiv:2412.20486, (2024).

[335] Jintae Kim, Jung Hoon Han, and Isaac H. Kim, "Fault-tolerant Quantum Error Correction Using a Linear Array of Emitters", arXiv:2403.01376, (2024).

[336] Alexandre C. Ricardo, Gubio G. de Lima, Amanda G. Valério, Tiago de S. Farias, and Celso J. Villas-Boas, "Quantum computation over the vibrational modes of a single trapped ion", arXiv:2412.15025, (2024).

[337] Jonatan Piasetzky, Amit Rotem, Yuval Warshavsky, Yehonatan Drori, Khen Cohen, Yaron Oz, and Haim Suchowski, "High fidelity CNOT gates in photonic integrated circuits using composite segmented directional couplers", arXiv:2509.25505, (2025).

[338] Spiro Gicev, Ben Harper, Haiyue Kang, Muhammad Usman, and Martin Sevior, "Crosstalk In Contemporary Quantum Devices", arXiv:2605.26528, (2026).

[339] Zoltán Kolarovszki, Dániel T. R. Nagy, and Zoltán Zimborás, "On the learning abilities of photonic continuous-variable Born machines", arXiv:2410.11785, (2024).

[340] Léo Monbroussou, Maniraman Periyasamy, Viacheslav Kuzmin, Pavel Sekatski, Viktoria Patapovich, Asel Sagingalieva, and Alexey Melnikov, "Hybrid Quantum Neural Networks: Theory, Implementations, and Applications", arXiv:2608.01194, (2026).

[341] Jaroslav Kysela, Katharina Ludwig, Nitica Sakharwade, Anette Messinger, and Wolfgang Lechner, "YZ-plane measurement-based quantum computation: Universality and Parity Architecture implementation", arXiv:2603.29379, (2026).

[342] Simanshu Kumar and Nandan S Bisht, "OAM-Induced Lattice Rotation Reveals a Fractional Optimum in Fault-Tolerant GKP Quantum Sensing", arXiv:2605.13271, (2026).

[343] Timo Hillmann, Jens Eisert, and Francesco Arzani, "Quantum low-density lattice codes", arXiv:2609.03021, (2026).

[344] Wei Wang, Menglong Fang, Hao Yu, Sijin Li, Zan Tang, Hong Cai, Lip-Ket Chin, Peter van Loock, Daiqin Su, and Ai-Qun Liu, "Photonic Chips for Universal Quantum Computing: Retrospective and Prospective", arXiv:2610.11321, (2026).

[345] Éloi Descamps, "PhD thesis: Modes, States, and Symmetries in quantum Optics for quantum Information and Metrology", arXiv:2607.26761, (2026).

The above citations are from Crossref's cited-by service (last updated successfully 2026-10-28 23:49:11) and SAO/NASA ADS (last updated successfully 2026-10-28 23:49:13). The list may be incomplete as not all publishers provide suitable and complete citation data.

This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.

Blueprint for a Scalable Photonic Fault-Tolerant Quantum Computer

Abstract

Popular summary

► BibTeX data

► References

Cited by

2 thoughts on “Blueprint for a Scalable Photonic Fault-Tolerant Quantum Computer”