Averaged Circuit Eigenvalue Sampling

Author Steven T. Flammia



PDF
Thumbnail PDF

File

LIPIcs.TQC.2022.4.pdf
  • Filesize: 0.71 MB
  • 10 pages

Document Identifiers

Author Details

Steven T. Flammia
  • AWS Center for Quantum Computing, Pasadena, CA, USA
  • California Institute of Technology, Pasadena, CA, USA

Acknowledgements

We thank Laura DeLorenzo, Robin Harper, Robert Huang, Alex Kubica, Ryan O'Donnell, Colm Ryan, Prasahnt Sivarajah, and Giacomo Torlai for discussions.

Cite AsGet BibTex

Steven T. Flammia. Averaged Circuit Eigenvalue Sampling. In 17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 232, pp. 4:1-4:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.TQC.2022.4

Abstract

We introduce ACES, a method for scalable noise metrology of quantum circuits that stands for Averaged Circuit Eigenvalue Sampling. It simultaneously estimates the individual error rates of all the gates in collections of quantum circuits, and can even account for space and time correlations between these gates. ACES strictly generalizes randomized benchmarking (RB), interleaved RB, simultaneous RB, and several other related techniques. However, ACES provides much more information and provably works under strictly weaker assumptions than these techniques. Finally, ACES is extremely scalable: we demonstrate with numerical simulations that it simultaneously and precisely estimates all the Pauli error rates on every gate and measurement in a 100 qubit quantum device using fewer than 20 relatively shallow Clifford circuits and an experimentally feasible number of samples. By learning the detailed gate errors for large quantum devices, ACES opens new possibilities for error mitigation, bespoke quantum error correcting codes and decoders, customized compilers, and more.

Subject Classification

ACM Subject Classification
  • Hardware → Quantum computation
Keywords
  • Quantum noise estimation
  • quantum benchmarking
  • QCVV

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads

References

  1. S. Aaronson and D. Gottesman. Improved simulation of stabilizer circuits. Phys. Rev. A, 70(5):052328, November 2004. URL: https://doi.org/10.1103/PhysRevA.70.052328.
  2. Frank Arute, Kunal Arya, Ryan Babbush, Dave Bacon, Joseph C. Bardin, Rami Barends, Rupak Biswas, Sergio Boixo, Fernando G. S. L. Brandao, David A. Buell, Brian Burkett, Yu Chen, Zijun Chen, Ben Chiaro, Roberto Collins, William Courtney, Andrew Dunsworth, Edward Farhi, Brooks Foxen, Austin Fowler, Craig Gidney, Marissa Giustina, Rob Graff, Keith Guerin, Steve Habegger, Matthew P. Harrigan, Michael J. Hartmann, Alan Ho, Markus Hoffmann, Trent Huang, Travis S. Humble, Sergei V. Isakov, Evan Jeffrey, Zhang Jiang, Dvir Kafri, Kostyantyn Kechedzhi, Julian Kelly, Paul V. Klimov, Sergey Knysh, Alexander Korotkov, Fedor Kostritsa, David Landhuis, Mike Lindmark, Erik Lucero, Dmitry Lyakh, Salvatore Mandrà, Jarrod R. McClean, Matthew McEwen, Anthony Megrant, Xiao Mi, Kristel Michielsen, Masoud Mohseni, Josh Mutus, Ofer Naaman, Matthew Neeley, Charles Neill, Murphy Yuezhen Niu, Eric Ostby, Andre Petukhov, John C. Platt, Chris Quintana, Eleanor G. Rieffel, Pedram Roushan, Nicholas C. Rubin, Daniel Sank, Kevin J. Satzinger, Vadim Smelyanskiy, Kevin J. Sung, Matthew D. Trevithick, Amit Vainsencher, Benjamin Villalonga, Theodore White, Z. Jamie Yao, Ping Yeh, Adam Zalcman, Hartmut Neven, and John M. Martinis. Quantum supremacy using a programmable superconducting processor. Nature, 574(7779):505-510, October 2019. URL: https://doi.org/10.1038/s41586-019-1666-5.
  3. Stefanie J. Beale, Joel J. Wallman, Mauricio Gutiérrez, Kenneth R. Brown, and Raymond Laflamme. Coherence in quantum error-correcting codes. Phys. Rev. Lett., 121:190501, 2018. URL: https://doi.org/10.1103/PhysRevLett.121.190501.
  4. Robin Blume-Kohout, John King Gamble, Erik Nielsen, Kenneth Rudinger, Jonathan Mizrahi, Kevin Fortier, and Peter Maunz. Demonstration of qubit operations below a rigorous fault tolerance threshold with gate set tomography. Nature Communications, 8:, 2016. URL: https://doi.org/10.1038/ncomms14485.
  5. Sergio Boixo, Sergei V. Isakov, Vadim N. Smelyanskiy, Ryan Babbush, Nan Ding, Zhang Jiang, Michael J. Bremner, John M. Martinis, and Hartmut Neven. Characterizing quantum supremacy in near-term devices. Nature Physics, 14(6):595-600, April 2018. URL: https://doi.org/10.1038/s41567-018-0124-x.
  6. Haoyuan Cai, Qi Ye, and Dong-Ling Deng. Sample complexity of learning quantum circuits, 2021. URL: http://arxiv.org/abs/2107.09078.
  7. Senrui Chen, Wenjun Yu, Pei Zeng, and Steven T. Flammia. Robust shadow estimation, 2020. URL: http://arxiv.org/abs/2011.09636.
  8. Piotr Czarnik, Andrew Arrasmith, Patrick J. Coles, and Lukasz Cincio. Error mitigation with Clifford quantum-circuit data, 2021. URL: http://arxiv.org/abs/2005.10189.
  9. Dripto M. Debroy, Muyuan Li, Michael Newman, and Kenneth R. Brown. Stabilizer slicing: Coherent error cancellations in low-density parity-check stabilizer codes. Phys. Rev. Lett., 121(25):250502, December 2018. URL: https://doi.org/10.1103/physrevlett.121.250502.
  10. Joseph Emerson, Robert Alicki, and Karol Życzkowski. Scalable noise estimation with random unitary operators. J. Opt. B, 7(10):S347, 2005. URL: https://doi.org/10.1088/1464-4266/7/10/021.
  11. Suguru Endo, Simon C. Benjamin, and Ying Li. Practical quantum error mitigation for near-future applications. Phys. Rev. X, 8(3):031027, July 2018. URL: https://doi.org/10.1103/physrevx.8.031027.
  12. Tim J. Evans, Robin Harper, and Steven T. Flammia. Scalable Bayesian Hamiltonian learning, 2019. URL: http://arxiv.org/abs/1912.07636.
  13. S. T. Flammia. ACES. https://github.com/sflammia/ACES, 2021.
  14. Steven Flammia and Joel Wallman. Efficient estimation of Pauli channels. ACM Transactions on Quantum Computing, 1(1):1-32, 2020. URL: https://doi.org/10.1145/3408039.
  15. Steven T. Flammia and Yi-Kai Liu. Direct fidelity estimation from few Pauli measurements. Phys. Rev. Lett., 106(23):230501, June 2011. URL: https://doi.org/10.1103/PhysRevLett.106.230501.
  16. Steven T. Flammia and Ryan O'Donnell. Pauli error estimation via population recovery. Quantum, 5:549, September 2021. URL: https://doi.org/10.22331/q-2021-09-23-549.
  17. Jay M. Gambetta, A. D. Córcoles, S. T. Merkel, B. R. Johnson, John A. Smolin, Jerry M. Chow, Colm A. Ryan, Chad Rigetti, S. Poletto, Thomas A. Ohki, Mark B. Ketchen, and M. Steffen. Characterization of addressability by simultaneous randomized benchmarking. Phys. Rev. Lett., 109:240504, December 2012. URL: https://doi.org/10.1103/PhysRevLett.109.240504.
  18. Michael R. Geller and Zhongyuan Zhou. Efficient error models for fault-tolerant architectures and the Pauli twirling approximation. Phys. Rev. A, 88(1):012314, July 2013. URL: https://doi.org/10.1103/physreva.88.012314.
  19. Robin Harper, Steven T. Flammia, and Joel J. Wallman. Efficient learning of quantum noise. Nature Physics, 16(12):1184-1188, August 2020. URL: https://doi.org/10.1038/s41567-020-0992-8.
  20. Robin Harper, Wenjun Yu, and Steven T. Flammia. Fast estimation of sparse quantum noise. PRX Quantum, 2(1):010322, February 2021. URL: https://doi.org/10.1103/prxquantum.2.010322.
  21. Jonas Helsen, Xiao Xue, Lieven MK Vandersypen, and Stephanie Wehner. A new class of efficient randomized benchmarking protocols. npj Quantum Information, 5(1):71, August 2019. URL: https://doi.org/10.1038/s41534-019-0182-7.
  22. Jingzhen Hu, Qingzhong Liang, Narayanan Rengaswamy, and Robert Calderbank. Mitigating coherent noise by balancing weight-2 Z-stabilizers, 2021. URL: http://arxiv.org/abs/2011.00197.
  23. Eric Huang, Andrew C. Doherty, and Steven Flammia. Performance of quantum error correction with coherent errors. Phys. Rev. A, 99:022313, 2019. URL: https://doi.org/10.1103/PhysRevA.99.022313.
  24. Hsin-Yuan Huang, Richard Kueng, and John Preskill. Predicting many properties of a quantum system from very few measurements. Nature Physics, 16(10):1050-1057, June 2020. URL: https://doi.org/10.1038/s41567-020-0932-7.
  25. Hsin-Yuan Huang, Richard Kueng, and John Preskill. Efficient estimation of Pauli observables by derandomization, 2021. URL: http://arxiv.org/abs/2103.07510.
  26. Joseph K Iverson and John Preskill. Coherence in logical quantum channels. New Journal of Physics, 22(7):073066, August 2020. URL: https://doi.org/10.1088/1367-2630/ab8e5c.
  27. Amara Katabarwa and Michael R. Geller. Logical error rate in the Pauli twirling approximation. Scientific Reports, 5(1), September 2015. URL: https://doi.org/10.1038/srep14670.
  28. O. Kern, G. Alber, and D. L. Shepelyansky. Quantum error correction of coherent errors by randomization. Euro. Phys. J. D, 32(1):153-156, January 2005. URL: https://doi.org/10.1140/epjd/e2004-00196-9.
  29. E. Knill. Quantum computing with realistically noisy devices. Nature, 434(7029):39-44, March 2005. URL: https://doi.org/10.1038/nature03350.
  30. Dax Enshan Koh and Sabee Grewal. Classical shadows with noise, 2020. URL: http://arxiv.org/abs/2011.11580.
  31. Richard Kueng, David M. Long, Andrew C. Doherty, and Steven T. Flammia. Comparing experiments to the fault-tolerance threshold. Phys. Rev. Lett., 117:170502, October 2016. URL: https://doi.org/10.1103/PhysRevLett.117.170502.
  32. Ying Li and Simon C. Benjamin. Efficient variational quantum simulator incorporating active error minimization. Phys. Rev. X, 7(2):021050, June 2017. URL: https://doi.org/10.1103/physrevx.7.021050.
  33. Yunchao Liu, Matthew Otten, Roozbeh Bassirianjahromi, Liang Jiang, and Bill Fefferman. Benchmarking near-term quantum computers via random circuit sampling, 2021. URL: http://arxiv.org/abs/2105.05232.
  34. Angus Lowe, Max Hunter Gordon, Piotr Czarnik, Andrew Arrasmith, Patrick J. Coles, and Lukasz Cincio. Unified approach to data-driven quantum error mitigation, 2020. URL: http://arxiv.org/abs/2011.01157.
  35. Easwar Magesan, Jay M. Gambetta, B. R. Johnson, Colm A. Ryan, Jerry M. Chow, Seth T. Merkel, Marcus P. da Silva, George A. Keefe, Mary B. Rothwell, Thomas A. Ohki, Mark B. Ketchen, and M. Steffen. Efficient measurement of quantum gate error by interleaved randomized benchmarking. Phys. Rev. Lett., 109:080505, August 2012. URL: https://doi.org/10.1103/PhysRevLett.109.080505.
  36. John M. Martinis. Qubit metrology for building a fault-tolerant quantum computer. npj Quantum Information, 1:, October 2015. URL: https://doi.org/10.1038/npjqi.2015.5.
  37. Runzhou Tao, Yunong Shi, Jianan Yao, John Hui, Frederic T. Chong, and Ronghui Gu. Gleipnir: Toward practical error analysis for quantum programs. In Proceedings of the 42nd ACM SIGPLAN Conference on Programming Language Design and Implementation (PLDI 2021), 2021. URL: https://doi.org/10.1145/3453483.3454029.
  38. Kristan Temme, Sergey Bravyi, and Jay M. Gambetta. Error mitigation for short-depth quantum circuits. Phys. Rev. Lett., 119(18):180509, November 2017. URL: https://doi.org/10.1103/physrevlett.119.180509.
  39. Giacomo Torlai, Christopher J. Wood, Atithi Acharya, Giuseppe Carleo, Juan Carrasquilla, and Leandro Aolita. Quantum process tomography with unsupervised learning and tensor networks, 2020. URL: http://arxiv.org/abs/2006.02424.
  40. Ewout van den Berg, Zlatko K. Minev, and Kristan Temme. Model-free readout-error mitigation for quantum expectation values, 2021. URL: http://arxiv.org/abs/2012.09738.
  41. Lorenza Viola and Emanuel Knill. Random decoupling schemes for quantum dynamical control and error suppression. Phys. Rev. Lett., 94:060502, February 2005. URL: https://doi.org/10.1103/PhysRevLett.94.060502.
  42. Lorenza Viola, Emanuel Knill, and Seth Lloyd. Dynamical decoupling of open quantum systems. Phys. Rev. Lett., 82:2417-2421, March 1999. URL: https://doi.org/10.1103/PhysRevLett.82.2417.
  43. Joel J. Wallman and Joseph Emerson. Noise tailoring for scalable quantum computation via randomized compiling. Phys. Rev. A, 94:052325, November 2016. URL: https://doi.org/10.1103/PhysRevA.94.052325.
  44. Matthew Ware, Guilhem Ribeill, Diego Ristè, Colm A. Ryan, Blake Johnson, and Marcus P. da Silva. Experimental Pauli-frame randomization on a superconducting qubit. Phys. Rev. A, 103(4):042604, April 2021. URL: https://doi.org/10.1103/physreva.103.042604.
  45. Ming Yuan and Yi Lin. Model selection and estimation in regression with grouped variables. J. R. Statist. Soc. B, 68(1):49-67, 2006. URL: https://doi.org/10.1111/j.1467-9868.2005.00532.x.
  46. Bichen Zhang, Swarnadeep Majumder, Pak Hong Leung, Stephen Crain, Ye Wang, Chao Fang, Dripto M. Debroy, Jungsang Kim, and Kenneth R. Brown. Hidden inverses: Coherent error cancellation at the circuit level, 2021. URL: http://arxiv.org/abs/2104.01119.
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail