Papers
Topics
Authors
Recent
Detailed Answer
Quick Answer
Concise responses based on abstracts only
Detailed Answer
Well-researched responses based on abstracts and relevant paper content.
Custom Instructions Pro
Preferences or requirements that you'd like Emergent Mind to consider when generating responses
Gemini 2.5 Flash
Gemini 2.5 Flash 44 tok/s
Gemini 2.5 Pro 41 tok/s Pro
GPT-5 Medium 13 tok/s Pro
GPT-5 High 15 tok/s Pro
GPT-4o 86 tok/s Pro
Kimi K2 208 tok/s Pro
GPT OSS 120B 447 tok/s Pro
Claude Sonnet 4 36 tok/s Pro
2000 character limit reached

Operational Markovianization in Randomized Benchmarking (2305.04704v2)

Published 8 May 2023 in quant-ph

Abstract: A crucial task to obtain optimal and reliable quantum devices is to quantify their overall performance. The average fidelity of quantum gates is a particular figure of merit that can be estimated efficiently by Randomized Benchmarking (RB). However, the concept of gate-fidelity itself relies on the crucial assumption that noise behaves in a predictable, time-local, or so-called Markovian manner, whose breakdown can naturally become the leading source of errors as quantum devices scale in size and depth. We analytically show that error suppression techniques such as Dynamical Decoupling (DD) and Randomized Compiling (RC) can operationally Markovianize RB: i) fast DD reduces non-Markovian RB to an exponential decay plus longer-time corrections, while on the other hand, ii) RC generally does not affect the average, but iii) it always suppresses the variance of such RB outputs. We demonstrate these effects numerically with a qubit noise model. Our results show that simple and efficient error suppression methods can simultaneously tame non-Markovian noise and allow for standard and reliable gate quality estimation, a fundamentally important task in the path toward fully functional quantum devices.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (83)
  1. J. Eisert, D. Hangleiter, N. Walk, I. Roth, D. Markham, R. Parekh, U. Chabaud,  and E. Kashefi, “Quantum certification and benchmarking,” Nat. Rev. Phys. 2, 382–390 (2020).
  2. M. Kliesch and I. Roth, “Theory of quantum system certification,” PRX Quantum 2, 010201 (2021).
  3. J. Emerson, R. Alicki,  and K. Życzkowski, “Scalable noise estimation with random unitary operators,” J. Optics B: Quantum Semiclass. Opt. 7, S347 (2005).
  4. E. Magesan, J. M. Gambetta,  and J. Emerson, “Characterizing quantum gates via randomized benchmarking,” Phys. Rev. A 85, 042311 (2012).
  5. E. Knill, D. Leibfried, R. Reichle, J. Britton, R. B. Blakestad, J. D. Jost, C. Langer, R. Ozeri, S. Seidelin,  and D. J. Wineland, “Randomized benchmarking of quantum gates,” Phys. Rev. A 77, 012307 (2008).
  6. J. M. Gambetta, A. D. Córcoles, S. T. Merkel, B. R. Johnson, J. A. Smolin, J. M. Chow, C. A. Ryan, C. Rigetti, S. Poletto, T. A. Ohki, M. B. Ketchen,  and M. Steffen, “Characterization of addressability by simultaneous randomized benchmarking,” Phys. Rev. Lett. 109, 240504 (2012).
  7. J. Wallman, C. Granade, R. Harper,  and S. T. Flammia, “Estimating the coherence of noise,” New J. Phys. 17, 113020 (2015).
  8. C. J. Wood and J. M. Gambetta, “Quantification and characterization of leakage errors,” Phys. Rev. A 97, 032306 (2018).
  9. T. Proctor, S. Seritan, K. Rudinger, E. Nielsen, R. Blume-Kohout,  and K. Young, “Scalable randomized benchmarking of quantum computers using mirror circuits,” Phys. Rev. Lett. 129, 150502 (2022).
  10. A. Erhard, J. J. Wallman, L. Postler, M. Meth, R. Stricker, E. A. Martinez, P. Schindler, T. Monz, J. Emerson,  and R. Blatt, “Characterizing large-scale quantum computers via cycle benchmarking,” Nat. Commun. 10 (2019), 10.1038/s41467-019-13068-7.
  11. J. Helsen, M. Ioannou, J. Kitzinger, E. Onorati, A. H. Werner, J. Eisert,  and I. Roth, “Shadow estimation of gate-set properties from random sequences,” Nature Communications 14, 5039 (2023).
  12. S. T. Flammia, “Averaged circuit eigenvalue sampling,”  (2021), arXiv:2108.05803 [quant-ph] .
  13. R. Harper and S. T. Flammia, “Learning correlated noise in a 39-qubit quantum processor,” PRX Quantum 4, 040311 (2023).
  14. J. Chen, D. Ding,  and C. Huang, “Randomized benchmarking beyond groups,” PRX Quantum 3, 030320 (2022).
  15. J. Helsen, I. Roth, E. Onorati, A. Werner,  and J. Eisert, “General framework for randomized benchmarking,” PRX Quantum 3, 020357 (2022).
  16. A. Rivas, S. F. Huelga,  and M. B. Plenio, “Quantum non-Markovianity: characterization, quantification and detection,” Rep. Prog. Phys. 77, 094001 (2014).
  17. H.-P. Breuer, E.-M. Laine, J. Piilo,  and B. Vacchini, “Colloquium: Non-Markovian dynamics in open quantum systems,” Rev. Mod. Phys. 88, 021002 (2016).
  18. I. de Vega and D. Alonso, “Dynamics of non-Markovian open quantum systems,” Rev. Mod. Phys. 89, 015001 (2017).
  19. F. A. Pollock, C. Rodríguez-Rosario, T. Frauenheim, M. Paternostro,  and K. Modi, “Non-Markovian quantum processes: Complete framework and efficient characterization,” Phys. Rev. A 97, 012127 (2018a).
  20. F. A. Pollock, C. Rodríguez-Rosario, T. Frauenheim, M. Paternostro,  and K. Modi, “Operational markov condition for quantum processes,” Phys. Rev. Lett. 120, 040405 (2018b).
  21. S. Milz and K. Modi, “Quantum stochastic processes and quantum non-Markovian phenomena,” PRX Quantum 2, 030201 (2021).
  22. J. M. Epstein, A. W. Cross, E. Magesan,  and J. M. Gambetta, “Investigating the limits of randomized benchmarking protocols,” Phys. Rev. A 89, 062321 (2014).
  23. H. Ball, T. M. Stace, S. T. Flammia,  and M. J. Biercuk, “Effect of noise correlations on randomized benchmarking,” Phys. Rev. A 93, 022303 (2016).
  24. P. Figueroa-Romero, K. Modi, R. J. Harris, T. M. Stace,  and M.-H. Hsieh, “Randomized benchmarking for non-markovian noise,” PRX Quantum 2, 040351 (2021).
  25. P. Figueroa-Romero, K. Modi,  and M.-H. Hsieh, “Towards a general framework of Randomized Benchmarking incorporating non-Markovian Noise,” Quantum 6, 868 (2022).
  26. A. Ceasura, P. Iyer, J. J. Wallman,  and H. Pashayan, “Non-exponential behaviour in logical randomized benchmarking,”  (2022), arXiv:2212.05488 [quant-ph] .
  27. Y.-Q. Chen, K.-L. Ma, Y.-C. Zheng, J. Allcock, S. Zhang,  and C.-Y. Hsieh, “Non-Markovian noise characterization with the transfer tensor method,” Phys. Rev. Appl. 13, 034045 (2020).
  28. G. A. L. White, C. D. Hill, F. A. Pollock, L. C. L. Hollenberg,  and K. Modi, “Demonstration of non-Markovian process characterisation and control on a quantum processor,” Nat. Commun. 11, 6301 (2020).
  29. K. Goswami, C. Giarmatzi, C. Monterola, S. Shrapnel, J. Romero,  and F. Costa, “Experimental characterization of a non-markovian quantum process,” Phys. Rev. A 104, 022432 (2021).
  30. G. White, F. Pollock, L. Hollenberg, K. Modi,  and C. Hill, “Non-markovian quantum process tomography,” PRX Quantum 3, 020344 (2022).
  31. M. Papič and I. de Vega, “Neural-network-based qubit-environment characterization,” Phys. Rev. A 105, 022605 (2022).
  32. C. Guo, “Quantifying non-Markovianity in open quantum dynamics,” SciPost Phys. 13, 028 (2022).
  33. G. White, “Characterization and control of non-Markovian quantum noise,” Nat. Rev. Phys. 4, 287 (2022).
  34. N. Ezzell, B. Pokharel, L. Tewala, G. Quiroz,  and D. A. Lidar, “Dynamical decoupling for superconducting qubits: A performance survey,” Phys. Rev. Appl. 20, 064027 (2023).
  35. A. Winick, J. J. Wallman, D. Dahlen, I. Hincks, E. Ospadov,  and J. Emerson, “Concepts and conditions for error suppression through randomized compiling,”  (2022), arXiv:2212.07500 [quant-ph] .
  36. G. D. Berk, S. Milz, F. A. Pollock,  and K. Modi, “Extracting quantum dynamical resources: consumption of non-markovianity for noise reduction,” npj Quantum Information 9, 104 (2023).
  37. H. K. Ng, D. A. Lidar,  and J. Preskill, “Combining dynamical decoupling with fault-tolerant quantum computation,” Phys. Rev. A 84, 012305 (2011).
  38. B. Pokharel, N. Anand, B. Fortman,  and D. A. Lidar, “Demonstration of fidelity improvement using dynamical decoupling with superconducting qubits,” Phys. Rev. Lett. 121, 220502 (2018).
  39. M. Ware, G. Ribeill, D. Ristè, C. A. Ryan, B. Johnson,  and M. P. da Silva, “Experimental Pauli-frame randomization on a superconducting qubit,” Phys. Rev. A 103, 042604 (2021).
  40. A. Hashim, R. K. Naik, A. Morvan, J.-L. Ville, B. Mitchell, J. M. Kreikebaum, M. Davis, E. Smith, C. Iancu, K. P. O’Brien, I. Hincks, J. J. Wallman, J. Emerson,  and I. Siddiqi, “Randomized compiling for scalable quantum computing on a noisy superconducting quantum processor,” Phys. Rev. X 11, 041039 (2021).
  41. J. Kelly, R. Barends, B. Campbell, Y. Chen, Z. Chen, B. Chiaro, A. Dunsworth, A. G. Fowler, I.-C. Hoi, E. Jeffrey, A. Megrant, J. Mutus, C. Neill, P. J. J. O’Malley, C. Quintana, P. Roushan, D. Sank, A. Vainsencher, J. Wenner, T. C. White, A. N. Cleland,  and J. M. Martinis, “Optimal Quantum Control using Randomized Benchmarking,” Phys. Rev. Lett. 112, 240504 (2014).
  42. A. M. Souza, R. S. Sarthour, I. S. Oliveira,  and D. Suter, “High-fidelity gate operations for quantum computing beyond dephasing time limits,” Phys. Rev. A 92, 062332 (2015).
  43. We point out that the average gate-fidelity of a quantum channel 𝒢~~𝒢\tilde{\mathcal{G}}over~ start_ARG caligraphic_G end_ARG with respect to a gate 𝒢𝒢\mathcal{G}caligraphic_G, is a measure of their “average orthogonality”, rather than their distinguishability (which albeit related, are not quite the same thing): F𝖺𝗏𝗀:=∫\ilimits@⁢𝑑ψ⁢tr⁡[𝒢~⁢(ψ)⁢𝒢⁢(ψ)]assignsubscriptF𝖺𝗏𝗀\ilimits@differential-d𝜓tr~𝒢𝜓𝒢𝜓\mathrm{F}_{\mathsf{avg}}:=\intop\ilimits@{d}\psi\operatorname{tr}[\tilde{% \mathcal{G}}(\psi)\mathcal{G}(\psi)]roman_F start_POSTSUBSCRIPT sansserif_avg end_POSTSUBSCRIPT := ∫ italic_d italic_ψ roman_tr [ over~ start_ARG caligraphic_G end_ARG ( italic_ψ ) caligraphic_G ( italic_ψ ) ], where ψ𝜓\psiitalic_ψ are (uniformly distributed) pure states.
  44. G. A. L. White, K. Modi,  and C. D. Hill, “Filtering crosstalk from bath non-markovianity via spacetime classical shadows,” Phys. Rev. Lett. 130, 160401 (2023).
  45. S. Milz, F. Sakuldee, F. A. Pollock,  and K. Modi, “Kolmogorov extension theorem for (quantum) causal modelling and general probabilistic theories,” Quantum 4, 255 (2020).
  46. K. Khodjasteh and D. A. Lidar, “Performance of deterministic dynamical decoupling schemes: Concatenated and periodic pulse sequences,” Phys. Rev. A 75, 062310 (2007).
  47. C. Arenz, D. Burgarth,  and R. Hillier, “Dynamical decoupling and homogenization of continuous variable systems,” J. Phys. A: Math. Theor. 50, 135303 (2017).
  48. C. Arenz, D. Burgarth, P. Facchi,  and R. Hillier, “Dynamical decoupling of unbounded hamiltonians,” J. Math. Phys. 59 (2018), 10.1063/1.5016495.
  49. I. A. Luchnikov, S. V. Vintskevich, H. Ouerdane,  and S. N. Filippov, “Simulation complexity of open quantum dynamics: Connection with tensor networks,” Phys. Rev. Lett. 122, 160401 (2019).
  50. D. Burgarth, P. Facchi, M. Fraas,  and R. Hillier, “Non-Markovian noise that cannot be dynamically decoupled by periodic spin echo pulses,” SciPost Phys. 11, 027 (2021a).
  51. J. Qi, X. Xu, D. Poletti,  and H. K. Ng, “Efficacy of noisy dynamical decoupling,” Phys. Rev. A 107, 032615 (2023).
  52. A. Hashim, S. Seritan, T. Proctor, K. Rudinger, N. Goss, R. K. Naik, J. M. Kreikebaum, D. I. Santiago,  and I. Siddiqi, “Benchmarking quantum logic operations relative to thresholds for fault tolerance,” npj Quantum Information 9 (2023), 10.1038/s41534-023-00764-y.
  53. J. J. Wallman and J. Emerson, “Noise tailoring for scalable quantum computation via randomized compiling,” Phys. Rev. A 94, 052325 (2016).
  54. Y. R. Sanders, J. J. Wallman,  and B. C. Sanders, “Bounding quantum gate error rate based on reported average fidelity,” New J. Phys. 18, 012002 (2015).
  55. The statement in Eq. (11\@@italiccorr) holds more generally for fmsubscriptf𝑚\mathrm{f}_{m}roman_f start_POSTSUBSCRIPT italic_m end_POSTSUBSCRIPT being noisy expectation values.
  56. B. Dirkse, J. Helsen,  and S. Wehner, “Efficient unitarity randomized benchmarking of few-qubit clifford gates,” Phys. Rev. A 99, 012315 (2019).
  57. L. V. Abdurakhimov, I. Mahboob, H. Toida, K. Kakuyanagi, Y. Matsuzaki,  and S. Saito, “Identification of different types of high-frequency defects in superconducting qubits,” PRX Quantum 3, 040332 (2022).
  58. C. Addis, F. Ciccarello, M. Cascio, G. M. Palma,  and S. Maniscalco, “Dynamical decoupling efficiency versus quantum non-markovianity,” New Journal of Physics 17, 123004 (2015).
  59. A. D’Arrigo, G. Falci,  and E. Paladino, “Quantum zeno and anti-zeno effect on a two-qubit gate by dynamical decoupling,” The European Physical Journal Special Topics 227, 2189 (2019).
  60. D. Burgarth, P. Facchi, M. Ligabò,  and D. Lonigro, “Hidden non-markovianity in open quantum systems,” Phys. Rev. A 103, 012203 (2021b).
  61. D. Burgarth, P. Facchi, D. Lonigro,  and K. Modi, “Quantum non-markovianity elusive to interventions,” Phys. Rev. A 104, L050404 (2021c).
  62. J. Claes, E. Rieffel,  and Z. Wang, “Character randomized benchmarking for non-multiplicity-free groups with applications to subspace, leakage, and matchgate randomized benchmarking,” PRX Quantum 2, 010351 (2021).
  63. D. Chruściński and A. Kossakowski, “Multipartite invariant states. i. unitary symmetry,” Phys. Rev. A 73, 062314 (2006).
  64. G. Chiribella, G. M. D’Ariano,  and P. Perinotti, “Quantum circuit architecture,” Phys. Rev. Lett. 101, 060401 (2008).
  65. G. Chiribella, G. M. D’Ariano,  and P. Perinotti, “Theoretical framework for quantum networks,” Phys. Rev. A 80, 022339 (2009).
  66. C. Portmann, C. Matt, U. Maurer, R. Renner,  and B. Tackmann, “Causal boxes: Quantum information-processing systems closed under composition,” IEEE Trans. Inf. Theory , 1–1 (2017).
  67. H. I. Nurdin and J. Gough, “From the heisenberg to the schrödinger picture: Quantum stochastic processes and process tensors,” 2021 60th IEEE Conference on Decision and Control (CDC)  (2021), 10.1109/cdc45484.2021.9683765.
  68. F. Costa and S. Shrapnel, “Quantum causal modelling,” New J. Phys. 18, 063032 (2016).
  69. D. Kretschmann and R. F. Werner, “Quantum channels with memory,” Phys. Rev. A 72, 062323 (2005).
  70. G. Gutoski and J. Watrous, “Toward a general theory of quantum games,” STOC ’07 , 565–574 (2007).
  71. S. Milz, F. A. Pollock,  and K. Modi, “An introduction to operational quantum dynamics,” Open Syst. Inf. Dyn. 24, 1740016 (2017).
  72. P. Taranto, “Memory effects in quantum processes,” Int. J. Quantum Inf. 18, 1941002 (2020).
  73. S. Milz, M. S. Kim, F. A. Pollock,  and K. Modi, “Completely positive divisibility does not mean Markovianity,” Phys. Rev. Lett. 123, 040401 (2019).
  74. R. Blume-Kohout, M. P. da Silva, E. Nielsen, T. Proctor, K. Rudinger, M. Sarovar,  and K. Young, “A taxonomy of small markovian errors,” PRX Quantum 3, 020335 (2022).
  75. A unitary t𝑡titalic_t-design is an ensemble of unitary matrices that reproduce up to the t𝑡titalic_tth statistical moment of the unitary group with the uniform, so-called Haar measure; see e.g. [4].
  76. S. Milz, C. Spee, Z.-P. Xu, F. Pollock, K. Modi,  and O. Gühne, “Genuine multipartite entanglement in time,” SciPost Phys. 10 (2021), 10.21468/scipostphys.10.6.141.
  77. L. Kong, “A framework for randomized benchmarking over compact groups,”  (2021), arXiv:2111.10357 [quant-ph] .
  78. J. Helsen, X. Xue, L. M. K. Vandersypen,  and S. Wehner, “A new class of efficient randomized benchmarking protocols,” npj Quantum Inf. 5, 71 (2019).
  79. J. E. Gough and H. I. Nurdin, “Can quantum Markov evolutions ever be dynamically decoupled?” in 2017 IEEE 56th Annual Conference on Decision and Control (CDC) (IEEE, 2017) pp. 6155–6160.
  80. Equivalently a unitary 2-design; the projectors are 𝒫^1=Ψsubscript^𝒫1Ψ\hat{\mathcal{P}}_{1}=\Psiover^ start_ARG caligraphic_P end_ARG start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT = roman_Ψ and 𝒫^2=𝟙−Ψsubscript^𝒫21Ψ\hat{\mathcal{P}}_{2}=\mathds{1}-\Psiover^ start_ARG caligraphic_P end_ARG start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT = blackboard_1 - roman_Ψ where Ψ:=\sum@⁢\slimits@⁢|i⁢i⟩⁢⟨j⁢j|/d𝖲assignΨ\sum@\slimits@ket𝑖𝑖bra𝑗𝑗subscript𝑑𝖲\Psi:=\sum@\slimits@|ii\rangle\!\langle{jj}|/d_{\mathsf{S}}roman_Ψ := | italic_i italic_i ⟩ ⟨ italic_j italic_j | / italic_d start_POSTSUBSCRIPT sansserif_S end_POSTSUBSCRIPT. See e.g. [67]. For details on the particular case of the Average Sequence Fidelity (ASF) in the Clifford case, see [25].
  81. M. F. Sacchi, “Optimal discrimination of quantum operations,” Phys. Rev. A 71, 062340 (2005).
  82. J. J. Wallman and S. T. Flammia, “Randomized benchmarking with confidence,” New J. Phys. 16, 103032 (2014).
  83. O. Kern, G. Alber,  and D. L. Shepelyansky, “Quantum error correction of coherent errors by randomization,” Eur. Phys. J. D. 32, 153–156 (2005).
Citations (7)
View on Semantic Scholar

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now
List To Do Tasks Checklist Streamline Icon: https://streamlinehq.com

Collections

Sign up for free to add this paper to one or more collections.

User Circle Single Streamline Icon: https://streamlinehq.com Sign Up
Lightbulb On Streamline Icon: https://streamlinehq.com

Continue Learning

We haven't generated follow-up questions for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Generate Now
X Twitter Logo Streamline Icon: https://streamlinehq.com

Tweets

Don't miss out on important new AI/ML research

See which papers are being discussed right now on X, Reddit, and more:

Explore Trending Papers

“Emergent Mind helps me see which AI papers have caught fire online.”

Philip

Philip

Creator, AI Explained on YouTube