Dynamically Generated Logical Qubits

Matthew B. Hastings1,2 and Jeongwan Haah2

1Station Q, Microsoft Quantum, Santa Barbara, CA 93106-6105, USA
2Microsoft Quantum and Microsoft Research, Redmond, WA 98052, USA

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

Abstract

We present a quantum error correcting code with $\textit{dynamically generated logical qubits}$. When viewed as a subsystem code, the code has no logical qubits. Nevertheless, our measurement patterns generate logical qubits, allowing the code to act as a fault-tolerant quantum memory. Our particular code gives a model very similar to the two-dimensional toric code, but each measurement is a $two$-qubit Pauli measurement.

► BibTeX data

► References

[1] A. Kitaev, ``Fault-tolerant quantum computation by anyons,'' Annals of Physics 303, 2–30 (2003), arXiv:quant-ph/​9707021.
https:/​/​doi.org/​10.1016/​s0003-4916(02)00018-0
arXiv:quant-ph/9707021

[2] D. Poulin, ``Stabilizer formalism for operator quantum error correction,'' Physical Review Letters 95, 230504 (2005), arXiv:quant-ph/​0508131.
https:/​/​doi.org/​10.1103/​physrevlett.95.230504
arXiv:quant-ph/0508131

[3] S. Bravyi, G. Duclos-Cianci, D. Poulin, and M. Suchara, ``Subsystem surface codes with three-qubit check operators,'' Quantum Information and Computation 13, 963–985 (2013), arXiv:1207.1443.
https:/​/​doi.org/​10.26421/​qic13.11-12-4
arXiv:1207.1443

[4] H. Bombin, ``Topological subsystem codes,'' Physical Review A 81, 032301 (2010), arXiv:0908.4246.
https:/​/​doi.org/​10.1103/​physreva.81.032301
arXiv:0908.4246

[5] D. Bacon, ``Operator quantum error-correcting subsystems for self-correcting quantum memories,'' Physical Review A 73, 012340 (2006), arXiv:quant-ph/​0506023.
https:/​/​doi.org/​10.1103/​physreva.73.012340
arXiv:quant-ph/0506023

[6] T. Karzig, C. Knapp, R. M. Lutchyn, P. Bonderson, M. B. Hastings, C. Nayak, J. Alicea, K. Flensberg, S. Plugge, Y. Oreg, C. M. Marcus, and M. H. Freedman, ``Scalable designs for quasiparticle-poisoning-protected topological quantum computation with majorana zero modes,'' Physical Review B 95, 235305 (2017), arXiv:1610.05289.
https:/​/​doi.org/​10.1103/​physrevb.95.235305
arXiv:1610.05289

[7] Y. Li, X. Chen, and M. P. A. Fisher, ``Quantum zeno effect and the many-body entanglement transition,'' Phys. Rev. B 98, 205136 (2018), arXiv:1808.06134.
https:/​/​doi.org/​10.1103/​PhysRevB.98.205136
arXiv:1808.06134

[8] B. Skinner, J. Ruhman, and A. Nahum, ``Measurement-induced phase transitions in the dynamics of entanglement,'' Phys. Rev. X 9, 031009 (2019), arXiv:1808.05953.
https:/​/​doi.org/​10.1103/​PhysRevX.9.031009
arXiv:1808.05953

[9] M. J. Gullans and D. A. Huse, ``Dynamical purification phase transition induced by quantum measurements,'' Physical Review X 10, 041020 (2020), arXiv:1905.05195.
https:/​/​doi.org/​10.1103/​physrevx.10.041020
arXiv:1905.05195

[10] A. Kitaev, ``Anyons in an exactly solved model and beyond,'' Annals of Physics 321, 2–111 (2006), arXiv:cond-mat/​0506438.
https:/​/​doi.org/​10.1016/​j.aop.2005.10.005
arXiv:cond-mat/0506438

[11] K. Kawagoe and M. Levin, ``Microscopic definitions of anyon data,'' Physical Review B 101, 1910.11353 (2020), arXiv:115113.
https:/​/​doi.org/​10.1103/​physrevb.101.115113
arXiv:115113

[12] S. A. Kivelson, D. S. Rokhsar, and J. P. Sethna, ``2e or not 2e : Flux quantization in the resonating valence bond state,'' Europhysics Letters (EPL) 6, 353–358 (1988).
https:/​/​doi.org/​10.1209/​0295-5075/​6/​4/​013

[13] L. Fidkowski, J. Haah, and M. B. Hastings, ``How dynamical quantum memories forget,'' Quantum 5, 382 (2021), arXiv:2008.10611.
https:/​/​doi.org/​10.22331/​q-2021-01-17-382
arXiv:2008.10611

Cited by

[1] Markus S. Kesselring, Julio C. Magdalena de la Fuente, Felix Thomsen, Jens Eisert, Stephen D. Bartlett, and Benjamin J. Brown, "Anyon Condensation and the Color Code", PRX Quantum 5 1, 010342 (2024).

[2] Andreas Bartschi and Stephan Eidenbenz, 2022 IEEE International Conference on Quantum Computing and Engineering (QCE) 87 (2022) ISBN:978-1-6654-9113-6.

[3] 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).

[4] Basudha Srivastava, Anton Frisk Kockum, and Mats Granath, "The XYZ2 hexagonal stabilizer code", Quantum 6, 698 (2022).

[5] Craig Gidney, "A Pair Measurement Surface Code on Pentagons", Quantum 7, 1156 (2023).

[6] Bowen Yan, Penghua Chen, and Shawn X. Cui, "Generalized Kitaev spin liquid model and emergent twist defect", Annals of Physics 466, 169682 (2024).

[7] Howard M. Wiseman, Eric G. Cavalcanti, and Eleanor G. Rieffel, "A "thoughtful" Local Friendliness no-go theorem: a prospective experiment with new assumptions to suit", Quantum 7, 1112 (2023).

[8] Matthew P.A. Fisher, Vedika Khemani, Adam Nahum, and Sagar Vijay, "Random Quantum Circuits", Annual Review of Condensed Matter Physics 14 1, 335 (2023).

[9] Zhehao Zhang, David Aasen, and Sagar Vijay, "X -cube Floquet code: A dynamical quantum error correcting code with a subextensive number of logical qubits", Physical Review B 108 20, 205116 (2023).

[10] Po-Shen Hsin and Zhenghan Wang, "On topology of the moduli space of gapped Hamiltonians for topological phases", Journal of Mathematical Physics 64 4, 041901 (2023).

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

[12] Bence Hetényi and James R. Wootton, "Tailoring quantum error correction to spin qubits", Physical Review A 109 3, 032433 (2024).

[13] Joseph Sullivan, Rui Wen, and Andrew C. Potter, "Floquet codes and phases in twist-defect networks", Physical Review B 108 19, 195134 (2023).

[14] Alex Townsend-Teague, Julio Magdalena de la Fuente, and Markus Kesselring, "Floquetifying the Colour Code", Electronic Proceedings in Theoretical Computer Science 384, 265 (2023).

[15] Marcin Kalinowski, Nishad Maskara, and Mikhail D. Lukin, "Non-Abelian Floquet Spin Liquids in a Digital Rydberg Simulator", Physical Review X 13 3, 031008 (2023).

[16] Jan Behrends, Florian Venn, and Benjamin Béri, "Surface codes, quantum circuits, and entanglement phases", Physical Review Research 6 1, 013137 (2024).

[17] Zhiyuan Wang and Kaden R. A. Hazzard, "Topological correlations in three-dimensional classical Ising models: An exact solution with a continuous phase transition", Physical Review Research 5 1, 013086 (2023).

[18] Christophe Vuillot, Alessandro Ciani, and Barbara M. Terhal, "Homological Quantum Rotor Codes: Logical Qubits from Torsion", Communications in Mathematical Physics 405 2, 53 (2024).

[19] David Aasen, Zhenghan Wang, and Matthew B. Hastings, "Adiabatic paths of Hamiltonians, symmetries of topological order, and automorphism codes", Physical Review B 106 8, 085122 (2022).

[20] Sergey Bravyi, Oliver Dial, Jay M. Gambetta, Darío Gil, and Zaira Nazario, "The future of quantum computing with superconducting qubits", Journal of Applied Physics 132 16, 160902 (2022).

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

[22] Jianxin Chen, Dawei Ding, Cupjin Huang, and Linghang Kong, "Linear cross-entropy benchmarking with Clifford circuits", Physical Review A 108 5, 052613 (2023).

[23] Adam Paetznick, Christina Knapp, Nicolas Delfosse, Bela Bauer, Jeongwan Haah, Matthew B. Hastings, and Marcus P. da Silva, "Performance of Planar Floquet Codes with Majorana-Based Qubits", PRX Quantum 4 1, 010310 (2023).

[24] Adithya Sriram, Tibor Rakovszky, Vedika Khemani, and Matteo Ippoliti, "Topology, criticality, and dynamically generated qubits in a stochastic measurement-only Kitaev model", Physical Review B 108 9, 094304 (2023).

[25] Jeongwan Haah and Matthew B. Hastings, "Boundaries for the Honeycomb Code", Quantum 6, 693 (2022).

[26] Tyler D. Ellison, Yu-An Chen, Arpit Dua, Wilbur Shirley, Nathanan Tantivasadakarn, and Dominic J. Williamson, "Pauli topological subsystem codes from Abelian anyon theories", Quantum 7, 1137 (2023).

[27] Tyler D. Ellison, Yu-An Chen, Arpit Dua, Wilbur Shirley, Nathanan Tantivasadakarn, and Dominic J. Williamson, "Pauli Stabilizer Models of Twisted Quantum Doubles", PRX Quantum 3 1, 010353 (2022).

[28] Manuel H. Muñoz-Arias, "Statistical complexity and the road to equilibrium in many-body chaotic quantum systems", Physical Review E 106 4, 044103 (2022).

[29] Benjamin A. Cordier, Nicolas P. D. Sawaya, Gian Giacomo Guerreschi, and Shannon K. McWeeney, "Biology and medicine in the landscape of quantum advantages", Journal of The Royal Society Interface 19 196, 20220541 (2022).

[30] Hossein Dehghani, Ali Lavasani, Mohammad Hafezi, and Michael J. Gullans, "Neural-network decoders for measurement induced phase transitions", Nature Communications 14 1, 2918 (2023).

[31] Margarita Davydova, Nathanan Tantivasadakarn, and Shankar Balasubramanian, "Floquet Codes without Parent Subsystem Codes", PRX Quantum 4 2, 020341 (2023).

[32] Armands Strikis, Simon C. Benjamin, and Benjamin J. Brown, "Quantum Computing is Scalable on a Planar Array of Qubits with Fabrication Defects", Physical Review Applied 19 6, 064081 (2023).

[33] Vaibhav Sharma, Chao-Ming Jian, and Erich J. Mueller, "Subsystem symmetry, spin-glass order, and criticality from random measurements in a two-dimensional Bacon-Shor circuit", Physical Review B 108 2, 024205 (2023).

[34] Ryohei Kobayashi and Guanyu Zhu, "Cross-Cap Defects and Fault-Tolerant Logical Gates in the Surface Code and the Honeycomb Floquet Code", PRX Quantum 5 2, 020360 (2024).

[35] Héctor Bombín, Chris Dawson, Ryan V. Mishmash, Naomi Nickerson, Fernando Pastawski, and Sam Roberts, "Logical Blocks for Fault-Tolerant Topological Quantum Computation", PRX Quantum 4 2, 020303 (2023).

[36] Craig Gidney, Michael Newman, and Matt McEwen, "Benchmarking the Planar Honeycomb Code", Quantum 6, 813 (2022).

[37] Arpit Dua, Nathanan Tantivasadakarn, Joseph Sullivan, and Tyler D. Ellison, "Engineering 3D Floquet Codes by Rewinding", PRX Quantum 5 2, 020305 (2024).

[38] Ali Lavasani, Zhu-Xi Luo, and Sagar Vijay, "Monitored quantum dynamics and the Kitaev spin liquid", Physical Review B 108 11, 115135 (2023).

[39] Craig Gidney, Michael Newman, Austin Fowler, and Michael Broughton, "A Fault-Tolerant Honeycomb Memory", Quantum 5, 605 (2021).

[40] Andreas Bauer, "Topological error correcting processes from fixed-point path integrals", Quantum 8, 1288 (2024).

[41] Oscar Higgott, "PyMatching: A Python Package for Decoding Quantum Codes with Minimum-Weight Perfect Matching", ACM Transactions on Quantum Computing 3 3, 1 (2022).

[42] Jason Gavriel, Daniel Herr, Alexis Shaw, Michael J. Bremner, Alexandru Paler, and Simon J. Devitt, 2023 IEEE International Conference on Quantum Computing and Engineering (QCE) 910 (2023) ISBN:979-8-3503-4323-6.

[43] Oscar Higgott, Thomas C. Bohdanowicz, Aleksander Kubica, Steven T. Flammia, and Earl T. Campbell, "Improved Decoding of Circuit Noise and Fragile Boundaries of Tailored Surface Codes", Physical Review X 13 3, 031007 (2023).

[44] Ammar Jahin, Andy C. Y. Li, Thomas Iadecola, Peter P. Orth, Gabriel N. Perdue, Alexandru Macridin, M. Sohaib Alam, and Norm M. Tubman, "Fermionic approach to variational quantum simulation of Kitaev spin models", Physical Review A 106 2, 022434 (2022).

[45] Grace M. Sommers, David A. Huse, and Michael J. Gullans, "Crystalline Quantum Circuits", PRX Quantum 4 3, 030313 (2023).

[46] Nathanan Tantivasadakarn, Ashvin Vishwanath, and Ruben Verresen, "Hierarchy of Topological Order From Finite-Depth Unitaries, Measurement, and Feedforward", PRX Quantum 4 2, 020339 (2023).

[47] Matthew Brooks and Charles Tahan, "Quantum computation by spin-parity measurements with encoded spin qubits", Physical Review B 108 3, 035206 (2023).

[48] Gözde Üstün, Andrea Morello, and Simon Devitt, "Single-step parity check gate set for quantum error correction", Quantum Science and Technology 9 3, 035037 (2024).

[49] Arpit Dua, Aleksander Kubica, Liang Jiang, Steven T. Flammia, and Michael J. Gullans, "Clifford-Deformed Surface Codes", PRX Quantum 5 1, 010347 (2024).

[50] Craig Gidney, "Stability Experiments: The Overlooked Dual of Memory Experiments", Quantum 6, 786 (2022).

[51] Oliver Lunt, Jonas Richter, and Arijeet Pal, Quantum Science and Technology 251 (2022) ISBN:978-3-031-03997-3.

[52] Yaodong Li and Matthew P. A. Fisher, "Decodable hybrid dynamics of open quantum systems with Z2 symmetry", Physical Review B 108 21, 214302 (2023).

[53] Edward H. Chen, Theodore J. Yoder, Youngseok Kim, Neereja Sundaresan, Srikanth Srinivasan, Muyuan Li, Antonio D. Córcoles, Andrew W. Cross, and Maika Takita, "Calibrated Decoders for Experimental Quantum Error Correction", Physical Review Letters 128 11, 110504 (2022).

[54] Matt McEwen, Dave Bacon, and Craig Gidney, "Relaxing Hardware Requirements for Surface Code Circuits using Time-dynamics", Quantum 7, 1172 (2023).

[55] Jacob C. Bridgeman, Aleksander Kubica, and Michael Vasmer, "Lifting Topological Codes: Three-Dimensional Subsystem Codes from Two-Dimensional Anyon Models", PRX Quantum 5 2, 020310 (2024).

[56] DinhDuy Vu, Ali Lavasani, Jong Yeon Lee, and Matthew P. A. Fisher, "Stable Measurement-Induced Floquet Enriched Topological Order", Physical Review Letters 132 7, 070401 (2024).

[57] James R Wootton, "Hexagonal matching codes with two-body measurements", Journal of Physics A: Mathematical and Theoretical 55 29, 295302 (2022).

[58] Da-Chuan Lu, Zhengdi Sun, and Yi-Zhuang You, "Realizing triality and $p$-ality by lattice twisted gauging in (1+1)d quantum spin systems", arXiv:2405.14939, (2024).

[59] David Aasen, Jeongwan Haah, Zhi Li, and Roger S. K. Mong, "Measurement Quantum Cellular Automata and Anomalies in Floquet Codes", arXiv:2304.01277, (2023).

[60] Linnea Grans-Samuelsson, Ryan V. Mishmash, David Aasen, Christina Knapp, Bela Bauer, Brad Lackey, Marcus P. da Silva, and Parsa Bonderson, "Improved Pairwise Measurement-Based Surface Code", arXiv:2310.12981, (2023).

[61] Ryohei Kobayashi and Guanyu Zhu, "Cross-cap defects and fault-tolerant logical gates in the surface code and the honeycomb Floquet code", arXiv:2310.06917, (2023).

[62] Christopher A. Pattison, Michael E. Beverland, Marcus P. da Silva, and Nicolas Delfosse, "Improved quantum error correction using soft information", arXiv:2107.13589, (2021).

[63] Daniel Gottesman, "Opportunities and Challenges in Fault-Tolerant Quantum Computation", arXiv:2210.15844, (2022).

[64] Margarita Davydova, Nathanan Tantivasadakarn, Shankar Balasubramanian, and David Aasen, "Quantum computation from dynamic automorphism codes", arXiv:2307.10353, (2023).

[65] Michael Liaofan Liu, Nathanan Tantivasadakarn, and Victor V. Albert, "Subsystem CSS codes, a tighter stabilizer-to-CSS mapping, and Goursat's Lemma", arXiv:2311.18003, (2023).

[66] Oskar Novak and Narayanan Rengaswamy, "GNarsil: Splitting Stabilizers into Gauges", arXiv:2404.18302, (2024).

[67] Takuya Okuda, Aswin Parayil Mana, and Hiroki Sukeno, "Anomaly inflow for CSS and fractonic lattice models and dualities via cluster state measurement", arXiv:2405.15853, (2024).

[68] Christophe Vuillot, "Planar Floquet Codes", arXiv:2110.05348, (2021).

[69] Julia Wildeboer, Thomas Iadecola, and Dominic J. Williamson, "Symmetry-Protected Infinite-Temperature Quantum Memory from Subsystem Codes", PRX Quantum 3 2, 020330 (2022).

[70] Alex Townsend-Teague, Julio Magdalena de la Fuente, and Markus Kesselring, "Floquetifying the Colour Code", arXiv:2307.11136, (2023).

[71] M. B. Hastings, "Quantum Codes on Graphs", arXiv:2308.10264, (2023).

[72] Benjamin A. Cordier, Nicolas P. D. Sawaya, Gian G. Guerreschi, and Shannon K. McWeeney, "Biology and medicine in the landscape of quantum advantages", arXiv:2112.00760, (2021).

[73] Andrew J. Landahl and Benjamin C. A. Morrison, "Logical fermions for fault-tolerant quantum simulation", arXiv:2110.10280, (2021).

[74] David Aasen, Jeongwan Haah, Parsa Bonderson, Zhenghan Wang, and Matthew Hastings, "Fault-Tolerant Hastings-Haah Codes in the Presence of Dead Qubits", arXiv:2307.03715, (2023).

[75] Yuanjie Ren and Peter Shor, "Topological quantum computation assisted by phase transitions", arXiv:2311.00103, (2023).

[76] Andreas Bärtschi and Stephan Eidenbenz, "Short-Depth Circuits for Dicke State Preparation", arXiv:2207.09998, (2022).

[77] Andreas Bauer, "Low-overhead non-Clifford topological fault-tolerant circuits for all non-chiral abelian topological phases", arXiv:2403.12119, (2024).

[78] Michael E. Beverland, Shilin Huang, and Vadym Kliuchnikov, "Fault tolerance of stabilizer channels", arXiv:2401.12017, (2024).

[79] Craig Gidney and Dave Bacon, "Less Bacon More Threshold", arXiv:2305.12046, (2023).

[80] Matthew Buican and Rajath Radhakrishnan, "Qudit Stabilizer Codes, CFTs, and Topological Surfaces", arXiv:2311.13680, (2023).

The above citations are from Crossref's cited-by service (last updated successfully 2024-06-18 05:35:25) and SAO/NASA ADS (last updated successfully 2024-06-18 05:35:27). The list may be incomplete as not all publishers provide suitable and complete citation data.