Dynamically Generated Logical Qubits

Matthew B. Hastings; Jeongwan Haah

doi:10.22331/q-2021-10-19-564

Dynamically Generated Logical Qubits

Matthew B. Hastings^1,2 and Jeongwan Haah²

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

Published:	2021-10-19, volume 5, page 564
Eprint:	arXiv:2107.02194v2
Doi:	https://doi.org/10.22331/q-2021-10-19-564
Citation:	Quantum 5, 564 (2021).

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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

@article{Hastings2021dynamically,
  doi = {10.22331/q-2021-10-19-564},
  url = {https://doi.org/10.22331/q-2021-10-19-564},
  title = {Dynamically {G}enerated {L}ogical {Q}ubits},
  author = {Hastings, Matthew B. and Haah, Jeongwan},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {5},
  pages = {564},
  month = oct,
  year = {2021}
}

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

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

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

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

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

[6] 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).

[7] 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).

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

[9] 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).

[10] 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).

[11] 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).

[12] 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).

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

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

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

[16] 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).

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

[18] 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).

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

[20] 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).

[21] 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).

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

[23] Yaodong Li and Matthew P. A. Fisher, "Robust decoding in monitored dynamics of open quantum systems with Z_2 symmetry", arXiv:2108.04274, (2021).

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

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

[26] 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).

[27] Matt McEwen, Dave Bacon, and Craig Gidney, "Relaxing Hardware Requirements for Surface Code Circuits using Time-dynamics", arXiv:2302.02192, (2023).

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

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

[30] Jacob C. Bridgeman, Aleksander Kubica, and Michael Vasmer, "Lifting topological codes: Three-dimensional subsystem codes from two-dimensional anyon models", arXiv:2305.06365, (2023).

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

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

[33] Guillaume Dauphinais, David W. Kribs, and Michael Vasmer, "Stabilizer Formalism for Operator Algebra Quantum Error Correction", arXiv:2304.11442, (2023).

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

[35] Andreas Bauer, "Topological error correcting processes from fixed-point path integrals", arXiv:2303.16405, (2023).

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

The above citations are from Crossref's cited-by service (last updated successfully 2023-05-29 21:27:56) and SAO/NASA ADS (last updated successfully 2023-05-29 21:27:57). The list may be incomplete as not all publishers provide suitable and complete citation data.

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