Loss-tolerant architecture for quantum computing with quantum emitters

Matthias C. Löbl1, Stefano Paesani1,2, and Anders S. Sørensen1

1Center for Hybrid Quantum Networks (Hy-Q), The Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, DK-2100 Copenhagen Ø, Denmark
2NNF Quantum Computing Programme, Niels Bohr Institute, University of Copenhagen, Denmark.

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We develop an architecture for measurement-based quantum computing using photonic quantum emitters. The architecture exploits spin-photon entanglement as resource states and standard Bell measurements of photons for fusing them into a large spin-qubit cluster state. The scheme is tailored to emitters with limited memory capabilities since it only uses an initial non-adaptive (ballistic) fusion process to construct a fully percolated graph state of multiple emitters. By exploring various geometrical constructions for fusing entangled photons from deterministic emitters, we improve the photon loss tolerance significantly compared to similar all-photonic schemes.

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[1] Robert Raussendorf and Hans J. Briegel. ``A one-way quantum computer''. Phys. Rev. Lett. 86, 5188–5191 (2001).

[2] Robert Raussendorf, Daniel E. Browne, and Hans J. Briegel. ``Measurement-based quantum computation on cluster states''. Phys. Rev. A 68, 022312 (2003).

[3] Hans J Briegel, David E Browne, Wolfgang Dür, Robert Raussendorf, and Maarten Van den Nest. ``Measurement-based quantum computation''. Nat. Phys. 5, 19–26 (2009).

[4] K. Kieling, T. Rudolph, and J. Eisert. ``Percolation, renormalization, and quantum computing with nondeterministic gates''. Phys. Rev. Lett. 99, 130501 (2007).

[5] Mercedes Gimeno-Segovia, Pete Shadbolt, Dan E. Browne, and Terry Rudolph. ``From three-photon Greenberger-Horne-Zeilinger states to ballistic universal quantum computation''. Phys. Rev. Lett. 115, 020502 (2015).

[6] Mihir Pant, Don Towsley, Dirk Englund, and Saikat Guha. ``Percolation thresholds for photonic quantum computing''. Nat. Commun. 10, 1070 (2019).

[7] Emanuel Knill, Raymond Laflamme, and Gerald J Milburn. ``A scheme for efficient quantum computation with linear optics''. Nature 409, 46–52 (2001).

[8] Hector Bombin, Isaac H Kim, Daniel Litinski, Naomi Nickerson, Mihir Pant, Fernando Pastawski, Sam Roberts, and Terry Rudolph. ``Interleaving: Modular architectures for fault-tolerant photonic quantum computing'' (2021). url: doi.org/​10.48550/​arXiv.2103.08612.

[9] Sara Bartolucci, Patrick Birchall, Hector Bombin, Hugo Cable, Chris Dawson, Mercedes Gimeno-Segovia, Eric Johnston, Konrad Kieling, Naomi Nickerson, Mihir Pant, et al. ``Fusion-based quantum computation''. Nat. Commun. 14, 912 (2023).

[10] Han-Sen Zhong, Yuan Li, Wei Li, Li-Chao Peng, Zu-En Su, Yi Hu, Yu-Ming He, Xing Ding, Weijun Zhang, Hao Li, Lu Zhang, Zhen Wang, Lixing You, Xi-Lin Wang, Xiao Jiang, Li Li, Yu-Ao Chen, Nai-Le Liu, Chao-Yang Lu, and Jian-Wei Pan. ``12-photon entanglement and scalable scattershot boson sampling with optimal entangled-photon pairs from parametric down-conversion''. Phys. Rev. Lett. 121, 250505 (2018).

[11] S. Paesani, M. Borghi, S. Signorini, A. Maïnos, L. Pavesi, and A. Laing. ``Near-ideal spontaneous photon sources in silicon quantum photonics''. Nat. Commun. 11, 2505 (2020).

[12] Ravitej Uppu, Freja T Pedersen, Ying Wang, Cecilie T Olesen, Camille Papon, Xiaoyan Zhou, Leonardo Midolo, Sven Scholz, Andreas D Wieck, Arne Ludwig, et al. ``Scalable integrated single-photon source''. Sci. Adv. 6, eabc8268 (2020).

[13] Natasha Tomm, Alisa Javadi, Nadia Olympia Antoniadis, Daniel Najer, Matthias Christian Löbl, Alexander Rolf Korsch, Rüdiger Schott, Sascha René Valentin, Andreas Dirk Wieck, Arne Ludwig, et al. ``A bright and fast source of coherent single photons''. Nat. Nanotechnol. 16, 399–403 (2021).

[14] W. P. Grice. ``Arbitrarily complete bell-state measurement using only linear optical elements''. Phys. Rev. A 84, 042331 (2011).

[15] Fabian Ewert and Peter van Loock. ``$3/​4$-efficient bell measurement with passive linear optics and unentangled ancillae''. Phys. Rev. Lett. 113, 140403 (2014).

[16] Philip Walther, Kevin J Resch, Terry Rudolph, Emmanuel Schenck, Harald Weinfurter, Vlatko Vedral, Markus Aspelmeyer, and Anton Zeilinger. ``Experimental one-way quantum computing''. Nature 434, 169–176 (2005).

[17] K. M. Gheri, C. Saavedra, P. Törmä, J. I. Cirac, and P. Zoller. ``Entanglement engineering of one-photon wave packets using a single-atom source''. Phys. Rev. A 58, R2627–R2630 (1998).

[18] Donovan Buterakos, Edwin Barnes, and Sophia E. Economou. ``Deterministic generation of all-photonic quantum repeaters from solid-state emitters''. Phys. Rev. X 7, 041023 (2017).

[19] Netanel H. Lindner and Terry Rudolph. ``Proposal for pulsed on-demand sources of photonic cluster state strings''. Phys. Rev. Lett. 103, 113602 (2009).

[20] Ido Schwartz, Dan Cogan, Emma R Schmidgall, Yaroslav Don, Liron Gantz, Oded Kenneth, Netanel H Lindner, and David Gershoni. ``Deterministic generation of a cluster state of entangled photons''. Science 354, 434–437 (2016).

[21] Konstantin Tiurev, Pol Llopart Mirambell, Mikkel Bloch Lauritzen, Martin Hayhurst Appel, Alexey Tiranov, Peter Lodahl, and Anders Søndberg Sørensen. ``Fidelity of time-bin-entangled multiphoton states from a quantum emitter''. Phys. Rev. A 104, 052604 (2021).

[22] N. Coste, D.A. Fioretto, N. Belabas, S.C. Wein, P. Hilaire, R. Frantzeskakis, M. Gundin, B. Goes, N. Somaschi, M. Morassi, et al. ``High-rate entanglement between a semiconductor spin and indistinguishable photons''. Nature Photonics 17, 582–587 (2023).

[23] Dan Cogan, Zu-En Su, Oded Kenneth, and David Gershoni. ``Deterministic generation of indistinguishable photons in a cluster state''. Nat. Photon. 17, 324–329 (2023).

[24] M. Arcari, I. Söllner, A. Javadi, S. Lindskov Hansen, S. Mahmoodian, J. Liu, H. Thyrrestrup, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl. ``Near-unity coupling efficiency of a quantum emitter to a photonic crystal waveguide''. Phys. Rev. Lett. 113, 093603 (2014).

[25] L. Scarpelli, B. Lang, F. Masia, D. M. Beggs, E. A. Muljarov, A. B. Young, R. Oulton, M. Kamp, S. Höfling, C. Schneider, and W. Langbein. ``99% beta factor and directional coupling of quantum dots to fast light in photonic crystal waveguides determined by spectral imaging''. Phys. Rev. B 100, 035311 (2019).

[26] Philip Thomas, Leonardo Ruscio, Olivier Morin, and Gerhard Rempe. ``Efficient generation of entangled multi-photon graph states from a single atom''. Nature 608, 677–681 (2022).

[27] Aymeric Delteil, Zhe Sun, Wei-bo Gao, Emre Togan, Stefan Faelt, and Ataç Imamoğlu. ``Generation of heralded entanglement between distant hole spins''. Nat. Phys. 12, 218–223 (2016).

[28] R. Stockill, M. J. Stanley, L. Huthmacher, E. Clarke, M. Hugues, A. J. Miller, C. Matthiesen, C. Le Gall, and M. Atatüre. ``Phase-tuned entangled state generation between distant spin qubits''. Phys. Rev. Lett. 119, 010503 (2017).

[29] Martin Hayhurst Appel, Alexey Tiranov, Simon Pabst, Ming Lai Chan, Christian Starup, Ying Wang, Leonardo Midolo, Konstantin Tiurev, Sven Scholz, Andreas D. Wieck, Arne Ludwig, Anders Søndberg Sørensen, and Peter Lodahl. ``Entangling a hole spin with a time-bin photon: A waveguide approach for quantum dot sources of multiphoton entanglement''. Phys. Rev. Lett. 128, 233602 (2022).

[30] Daniel E. Browne and Terry Rudolph. ``Resource-efficient linear optical quantum computation''. Phys. Rev. Lett. 95, 010501 (2005).

[31] Richard J Warburton. ``Single spins in self-assembled quantum dots''. Nat. Mater. 12, 483–493 (2013).

[32] Peter Lodahl, Sahand Mahmoodian, and Søren Stobbe. ``Interfacing single photons and single quantum dots with photonic nanostructures''. Rev. Mod. Phys. 87, 347–400 (2015).

[33] Hannes Bernien, Bas Hensen, Wolfgang Pfaff, Gerwin Koolstra, Machiel S Blok, Lucio Robledo, Tim H Taminiau, Matthew Markham, Daniel J Twitchen, Lilian Childress, et al. ``Heralded entanglement between solid-state qubits separated by three metres''. Nature 497, 86–90 (2013).

[34] Sam Morley-Short, Sara Bartolucci, Mercedes Gimeno-Segovia, Pete Shadbolt, Hugo Cable, and Terry Rudolph. ``Physical-depth architectural requirements for generating universal photonic cluster states''. Quantum Sci. Technol. 3, 015005 (2017).

[35] Leon Zaporski, Noah Shofer, Jonathan H Bodey, Santanu Manna, George Gillard, Martin Hayhurst Appel, Christian Schimpf, Saimon Filipe Covre da Silva, John Jarman, Geoffroy Delamare, et al. ``Ideal refocusing of an optically active spin qubit under strong hyperfine interactions''. Nat. Nanotechnol. 18, 257–263 (2023).

[36] Giang N. Nguyen, Clemens Spinnler, Mark R. Hogg, Liang Zhai, Alisa Javadi, Carolin A. Schrader, Marcel Erbe, Marcus Wyss, Julian Ritzmann, Hans-Georg Babin, Andreas D. Wieck, Arne Ludwig, and Richard J. Warburton. ``Enhanced electron-spin coherence in a gaas quantum emitter''. Phys. Rev. Lett. 131, 210805 (2023).

[37] Xiaodong Xu, Yanwen Wu, Bo Sun, Qiong Huang, Jun Cheng, D. G. Steel, A. S. Bracker, D. Gammon, C. Emary, and L. J. Sham. ``Fast spin state initialization in a singly charged inas-gaas quantum dot by optical cooling''. Phys. Rev. Lett. 99, 097401 (2007).

[38] Nadia O Antoniadis, Mark R Hogg, Willy F Stehl, Alisa Javadi, Natasha Tomm, Rüdiger Schott, Sascha R Valentin, Andreas D Wieck, Arne Ludwig, and Richard J Warburton. ``Cavity-enhanced single-shot readout of a quantum dot spin within 3 nanoseconds''. Nat. Commun. 14, 3977 (2023).

[39] David Press, Thaddeus D Ladd, Bingyang Zhang, and Yoshihisa Yamamoto. ``Complete quantum control of a single quantum dot spin using ultrafast optical pulses''. Nature 456, 218–221 (2008).

[40] Sean D. Barrett and Pieter Kok. ``Efficient high-fidelity quantum computation using matter qubits and linear optics''. Phys. Rev. A 71, 060310(R) (2005).

[41] Yuan Liang Lim, Almut Beige, and Leong Chuan Kwek. ``Repeat-until-success linear optics distributed quantum computing''. Phys. Rev. Lett. 95, 030505 (2005).

[42] L.-M. Duan and R. Raussendorf. ``Efficient quantum computation with probabilistic quantum gates''. Phys. Rev. Lett. 95, 080503 (2005).

[43] Hyeongrak Choi, Mihir Pant, Saikat Guha, and Dirk Englund. ``Percolation-based architecture for cluster state creation using photon-mediated entanglement between atomic memories''. npj Quantum Information 5, 104 (2019).

[44] Emil V. Denning, Dorian A. Gangloff, Mete Atatüre, Jesper Mørk, and Claire Le Gall. ``Collective quantum memory activated by a driven central spin''. Phys. Rev. Lett. 123, 140502 (2019).

[45] Matteo Pompili, Sophie LN Hermans, Simon Baier, Hans KC Beukers, Peter C Humphreys, Raymond N Schouten, Raymond FL Vermeulen, Marijn J Tiggelman, Laura dos Santos Martins, Bas Dirkse, et al. ``Realization of a multinode quantum network of remote solid-state qubits''. Science 372, 259–264 (2021).

[46] Mercedes Gimeno-Segovia. ``Towards practical linear optical quantum computing''. PhD thesis. Imperial College London. (2016). url: doi.org/​10.25560/​43936.

[47] Daniel Herr, Alexandru Paler, Simon J Devitt, and Franco Nori. ``A local and scalable lattice renormalization method for ballistic quantum computation''. npj Quantum Information 4, 27 (2018).

[48] M. F. Sykes and John W. Essam. ``Exact critical percolation probabilities for site and bond problems in two dimensions''. Journal of Mathematical Physics 5, 1117–1127 (1964).

[49] M. Hein, J. Eisert, and H. J. Briegel. ``Multiparty entanglement in graph states''. Phys. Rev. A 69, 062311 (2004).

[50] Marc Hein, Wolfgang Dür, Jens Eisert, Robert Raussendorf, M Nest, and H-J Briegel. ``Entanglement in graph states and its applications'' (2006). url: doi.org/​10.48550/​arXiv.quant-ph/​0602096.

[51] Steven C Van der Marck. ``Calculation of percolation thresholds in high dimensions for fcc, bcc and diamond lattices''. Int J Mod Phys C 9, 529–540 (1998).

[52] Łukasz Kurzawski and Krzysztof Malarz. ``Simple cubic random-site percolation thresholds for complex neighbourhoods''. Rep. Math. Phys. 70, 163–169 (2012).

[53] Matthias C. Löbl, Stefano Paesani, and Anders S. Sørensen. ``Efficient algorithms for simulating percolation in photonic fusion networks'' (2023). url: doi.org/​10.48550/​arXiv.2312.04639.

[54] Krzysztof Malarz and Serge Galam. ``Square-lattice site percolation at increasing ranges of neighbor bonds''. Phys. Rev. E 71, 016125 (2005).

[55] Zhipeng Xun and Robert M. Ziff. ``Bond percolation on simple cubic lattices with extended neighborhoods''. Phys. Rev. E 102, 012102 (2020).

[56] Stefano Paesani and Benjamin J. Brown. ``High-threshold quantum computing by fusing one-dimensional cluster states''. Phys. Rev. Lett. 131, 120603 (2023).

[57] Michael Newman, Leonardo Andreta de Castro, and Kenneth R Brown. ``Generating fault-tolerant cluster states from crystal structures''. Quantum 4, 295 (2020).

[58] Peter Kramer and Martin Schlottmann. ``Dualisation of voronoi domains and klotz construction: a general method for the generation of proper space fillings''. Journal of Physics A: Mathematical and General 22, L1097 (1989).

[59] Thomas J. Bell, Love A. Pettersson, and Stefano Paesani. ``Optimizing graph codes for measurement-based loss tolerance''. PRX Quantum 4, 020328 (2023).

[60] Sophia E. Economou, Netanel Lindner, and Terry Rudolph. ``Optically generated 2-dimensional photonic cluster state from coupled quantum dots''. Phys. Rev. Lett. 105, 093601 (2010).

[61] Cathryn P Michaels, Jesús Arjona Martínez, Romain Debroux, Ryan A Parker, Alexander M Stramma, Luca I Huber, Carola M Purser, Mete Atatüre, and Dorian A Gangloff. ``Multidimensional cluster states using a single spin-photon interface coupled strongly to an intrinsic nuclear register''. Quantum 5, 565 (2021).

[62] Bikun Li, Sophia E Economou, and Edwin Barnes. ``Photonic resource state generation from a minimal number of quantum emitters''. Npj Quantum Inf. 8, 11 (2022).

[63] Thomas M. Stace, Sean D. Barrett, and Andrew C. Doherty. ``Thresholds for topological codes in the presence of loss''. Phys. Rev. Lett. 102, 200501 (2009).

[64] 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, 030301(R) (2018).

[65] Matthew B. Hastings, Grant H. Watson, and Roger G. Melko. ``Self-correcting quantum memories beyond the percolation threshold''. Phys. Rev. Lett. 112, 070501 (2014).

[66] Barbara M. Terhal. ``Quantum error correction for quantum memories''. Rev. Mod. Phys. 87, 307–346 (2015).

[67] Nikolas P Breuckmann, Kasper Duivenvoorden, Dominik Michels, and Barbara M Terhal. ``Local decoders for the 2d and 4d toric code'' (2016). url: doi.org/​10.48550/​arXiv.1609.00510.

[68] Nikolas P. Breuckmann and Jens Niklas Eberhardt. ``Quantum low-density parity-check codes''. PRX Quantum 2, 040101 (2021).

[69] Konstantin Tiurev, Martin Hayhurst Appel, Pol Llopart Mirambell, Mikkel Bloch Lauritzen, Alexey Tiranov, Peter Lodahl, and Anders Søndberg Sørensen. ``High-fidelity multiphoton-entangled cluster state with solid-state quantum emitters in photonic nanostructures''. Phys. Rev. A 105, L030601 (2022).

[70] Maarten Van den Nest, Jeroen Dehaene, and Bart De Moor. ``Graphical description of the action of local clifford transformations on graph states''. Phys. Rev. A 69, 022316 (2004).

[71] Shiang Yong Looi, Li Yu, Vlad Gheorghiu, and Robert B. Griffiths. ``Quantum-error-correcting codes using qudit graph states''. Phys. Rev. A 78, 042303 (2008).

[72] Hussain A. Zaidi, Chris Dawson, Peter van Loock, and Terry Rudolph. ``Near-deterministic creation of universal cluster states with probabilistic bell measurements and three-qubit resource states''. Phys. Rev. A 91, 042301 (2015).

[73] Adán Cabello, Lars Eirik Danielsen, Antonio J. López-Tarrida, and José R. Portillo. ``Optimal preparation of graph states''. Phys. Rev. A 83, 042314 (2011).

[74] Jeremy C Adcock, Sam Morley-Short, Axel Dahlberg, and Joshua W Silverstone. ``Mapping graph state orbits under local complementation''. Quantum 4, 305 (2020).

[75] Pieter Kok and Brendon W. Lovett. ``Introduction to optical quantum information processing''. Cambridge university press. (2010).

[76] Scott Aaronson and Daniel Gottesman. ``Improved simulation of stabilizer circuits''. Phys. Rev. A 70, 052328 (2004).

[77] Austin G. Fowler, Ashley M. Stephens, and Peter Groszkowski. ``High-threshold universal quantum computation on the surface code''. Phys. Rev. A 80, 052312 (2009).

[78] Daniel Gottesman. ``Theory of fault-tolerant quantum computation''. Phys. Rev. A 57, 127–137 (1998).

[79] Matthias C. Löbl et al. ``perqolate''. https:/​/​github.com/​nbi-hyq/​perqolate (2023).

[80] John H. Conway and Neil J. A. Sloane. ``Low–dimensional lattices. vii. coordination sequences''. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 453, 2369–2389 (1997).

[81] Krzysztof Malarz. ``Percolation thresholds on a triangular lattice for neighborhoods containing sites up to the fifth coordination zone''. Phys. Rev. E 103, 052107 (2021).

[82] Krzysztof Malarz. ``Random site percolation on honeycomb lattices with complex neighborhoods''. Chaos: An Interdisciplinary Journal of Nonlinear Science 32, 083123 (2022).

[83] B. Derrida and D. Stauffer. ``Corrections to scaling and phenomenological renormalization for 2-dimensional percolation and lattice animal problems''. Journal de Physique 46, 1623–1630 (1985).

[84] Stephan Mertens and Cristopher Moore. ``Percolation thresholds and fisher exponents in hypercubic lattices''. Phys. Rev. E 98, 022120 (2018).

[85] Xiaomei Feng, Youjin Deng, and Henk W. J. Blöte. ``Percolation transitions in two dimensions''. Phys. Rev. E 78, 031136 (2008).

[86] Xiao Xu, Junfeng Wang, Jian-Ping Lv, and Youjin Deng. ``Simultaneous analysis of three-dimensional percolation models''. Frontiers of Physics 9, 113–119 (2014).

[87] 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 (1998).

[88] Zhipeng Xun and Robert M. Ziff. ``Precise bond percolation thresholds on several four-dimensional lattices''. Phys. Rev. Res. 2, 013067 (2020).

[89] Yi Hu and Patrick Charbonneau. ``Percolation thresholds on high-dimensional ${D}_{n}$ and ${E}_{8}$-related lattices''. Phys. Rev. E 103, 062115 (2021).

[90] Sam Morley-Short, Mercedes Gimeno-Segovia, Terry Rudolph, and Hugo Cable. ``Loss-tolerant teleportation on large stabilizer states''. Quantum Science and Technology 4, 025014 (2019).

Cited by

[1] Philip Thomas, Leonardo Ruscio, Olivier Morin, and Gerhard Rempe, "Fusion of deterministically generated photonic graph states", Nature 629 8012, 567 (2024).

[2] Grégoire de Gliniasty, Paul Hilaire, Pierre-Emmanuel Emeriau, Stephen C. Wein, Alexia Salavrakos, and Shane Mansfield, "A Spin-Optical Quantum Computing Architecture", arXiv:2311.05605, (2023).

[3] Yijian Meng, Carlos F. D. Faurby, Ming Lai Chan, Patrik I. Sund, Zhe Liu, Ying Wang, Nikolai Bart, Andreas D. Wieck, Arne Ludwig, Leonardo Midolo, Anders S. Sørensen, Stefano Paesani, and Peter Lodahl, "Photonic fusion of entangled resource states from a quantum emitter", arXiv:2312.09070, (2023).

[4] Shuang Xu, Wei-Jiang Gong, H. Z. Shen, and X. X. Yi, "Fault-tolerant fusing of repeater graph states and its application", Quantum Science and Technology 9 3, 035009 (2024).

[5] Matthias C. Löbl, Stefano Paesani, and Anders S. Sørensen, "Efficient algorithms for simulating percolation in photonic fusion networks", arXiv:2312.04639, (2023).

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