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Ngày:

Jeongwan Haah1 và Matthew B. Hastings2,1

1Microsoft Quantum, Redmond, Washington, USA
2Microsoft Quantum, Santa Barbara, California, USA

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Tóm tắt

Magic state distillation uses special codes to suppress errors in input states, which are often tailored to a Clifford-twirled error model. We present detailed measurement sequences for magic state distillation protocols which can suppress arbitrary errors on any part of a protocol, assuming the independence of errors across qubits. Provided with input magic states, our protocol operates on a two-dimensional square grid by measurements of $ZZ$ on horizontal pairs of qubits, $XX$ on vertical pairs, and $Z,X$ on single qubits.

► Dữ liệu BibTeX

► Tài liệu tham khảo

[1] E. Knill, “Fault-tolerant postselected quantum computation: Schemes,” (2004a), arXiv:quant-ph/​0402171v1.
arXiv: quant-ph / 0402171v1

[2] E. Knill, “Fault-tolerant postselected quantum computation: Threshold analysis,” (2004b), arXiv:quant-ph/​0404104v1.
arXiv: quant-ph / 0404104v1

[3] P. Aliferis, D. Gottesman, and J. Preskill, “Quantum accuracy threshold for concatenated distance-3 codes,” Quant. Inf. Comput. 6, 97–165 (2006), arXiv:quant-ph/​0504218.
https: / â € trận / â € doi.org/â $$$ 10.26421 / â € QIC8.3-4
arXiv: quant-ph / 0504218

[4] J. Haah, M. B. Hastings, D. Poulin, and D. Wecker, “Magic state distillation with low space overhead and optimal asymptotic input count,” Quantum 1, 31 (2017), arXiv:1703.07847v1.
https:/​/​doi.org/​10.22331/​q-2017-10-03-31
arXiv: 1703.07847v1

[5] E. T. Campbell and M. Howard, “Unified framework for magic state distillation and multiqubit gate synthesis with reduced resource cost,” Phys. Rev. A 95, 022316 (2017), arXiv:1606.01904v3.
https: / / doi.org/ 10.1103 / PhysRevA.95.022316
arXiv: 1606.01904v3

[6] S. Bravyi and J. Haah, “Magic-state distillation with low overhead,” Phys. Rev. A 86, 052329 (2012), arXiv:1209.2426.
https: / / doi.org/ 10.1103 / PhysRevA.86.052329
arXiv: 1209.2426

[7] B. Eastin, “Distilling one-qubit magic states into Toffoli states,” Phys. Rev. A 87, 032321 (2013), arXiv:1212.4872.
https: / / doi.org/ 10.1103 / PhysRevA.87.032321
arXiv: 1212.4872

[8] C. Jones, “Low-overhead constructions for the fault-tolerant Toffoli gate,” Phys. Rev. A 87, 022328 (2013a), arXiv:1212.5069.
https: / / doi.org/ 10.1103 / PhysRevA.87.022328
arXiv: 1212.5069

[9] T. Jochym-O’Connor, Y. Yu, B. Helou, and R. Laflamme, “The robustness of magic state distillation against errors in clifford gates,” Quant. Inf. Comput. 13, 361–378 (2013), arXiv:1205.6715.
https: / â € trận / â € doi.org/â $$$ 10.26421 / â € QIC13.5-6
arXiv: 1205.6715

[10] P. B. Brooks, Quantum Error Correction with Biased Noise, Ph.D. thesis, California Institute of Technology (2013).
https:/​/​doi.org/​10.7907/​1TVT-J780

[11] D. Litinski, “Magic state distillation: Not as costly as you think,” Quantum 3, 205 (2019), arXiv:1905.06903.
https:/​/​doi.org/​10.22331/​q-2019-12-02-205
arXiv: 1905.06903

[12] C. Chamberland and A. W. Cross, “Fault-tolerant magic state preparation with flag qubits,” Quantum 3, 143 (2019), arXiv:1811.00566.
https:/​/​doi.org/​10.22331/​q-2019-05-20-143
arXiv: 1811.00566

[13] C. Chamberland and K. Noh, “Very low overhead fault-tolerant magic state preparation using redundant ancilla encoding and flag qubits,” npj Quantum Information 6, 91 (2020), arXiv:2003.03049.
https:/​/​doi.org/​10.1038/​s41534-020-00319-5
arXiv: 2003.03049

[14] A. G. Fowler and C. Gidney, “Low overhead quantum computation using lattice surgery,” arXiv:1808.06709.
arXiv: 1808.06709

[15] T. Karzig, C. Knapp, R. M. Lutchyn, P. Bonderson, M. B. Hastings, C. Nayak, J. Alicea, K. Flensberg, S. Plugge, Y. Oreg, et al., “Scalable designs for quasiparticle-poisoning-protected topological quantum computation with majorana zero modes,” Phys. Rev. B 95, 235305 (2017), arXiv:1610.05289.
https: / / doi.org/ 10.1103 / PhysRevB.95.235305
arXiv: 1610.05289

[16] N. Delfosse, B. Reichardt, and K. Svore, “Fault-tolerant cat state preparation with low classical and quantum hardware requirement,” (2020).

[17] C. Jones, “Multilevel distillation of magic states for quantum computing,” Phys. Rev. A 87, 042305 (2013b), arXiv:1210.3388v2.
https: / / doi.org/ 10.1103 / PhysRevA.87.042305
arXiv: 1210.3388v2

[18] J. Haah, “Towers of generalized divisible quantum codes,” Phys. Rev. A 97, 042327 (2018), arXiv:1709.08658.
https: / / doi.org/ 10.1103 / PhysRevA.97.042327
arXiv: 1709.08658

[19] S. Bravyi and A. Kitaev, “Universal quantum computation with ideal Clifford gates and noisy ancillas,” Phys. Rev. A 71, 022316 (2005), arXiv:quant-ph/​0403025.
https: / / doi.org/ 10.1103 / PhysRevA.71.022316
arXiv: quant-ph / 0403025

[20] J. Haah and M. B. Hastings, “Codes and protocols for distilling $T$, controlled-$S$, and Toffoli gates,” Quantum 2, 71 (2018), arXiv:1709.02832.
https:/​/​doi.org/​10.22331/​q-2018-06-07-71
arXiv: 1709.02832

Trích dẫn

Nguồn: https://quantum-journal.org/ con / q-2021 / 01-20-383 /

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