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

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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.

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► 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", arXiv:2108.10457.

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

[3] Christophe Vuillot, "Planar Floquet Codes", arXiv:2110.05348.

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

[5] James R. Wootton, "Hexagonal matching codes with 2-body measurements", arXiv:2109.13308.

[6] 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", arXiv:2110.04285.

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

[8] Jeongwan Haah and Matthew B. Hastings, "Boundaries for the Honeycomb Code", arXiv:2110.09545.

[9] Julia Wildeboer, Thomas Iadecola, and Dominic J. Williamson, "Symmetry-Protected Infinite-Temperature Quantum Memory from Subsystem Codes", arXiv:2110.05710.

[10] 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.

The above citations are from SAO/NASA ADS (last updated successfully 2021-12-07 23:29:36). The list may be incomplete as not all publishers provide suitable and complete citation data.

On Crossref's cited-by service no data on citing works was found (last attempt 2021-12-07 23:29:34).