Bayesian ACRONYM Tuning

Authors John Gamble, Christopher Granade, Nathan Wiebe

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Author Details

John Gamble
  • Quantum Architectures and Computing Group, Microsoft Research, Redmond WA, USA
Christopher Granade
  • Quantum Architectures and Computing Group, Microsoft Research, Redmond WA, USA
Nathan Wiebe
  • Quantum Architectures and Computing Group, Microsoft Research, Redmond WA, USA


This project was prepared using a reproducible workflow [Granade, 2017].

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John Gamble, Christopher Granade, and Nathan Wiebe. Bayesian ACRONYM Tuning. In 14th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 135, pp. 7:1-7:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


We provide an algorithm that uses Bayesian randomized benchmarking in concert with a local optimizer, such as SPSA, to find a set of controls that optimizes that average gate fidelity. We call this method Bayesian ACRONYM tuning as a reference to the analogous ACRONYM tuning algorithm. Bayesian ACRONYM distinguishes itself in its ability to retain prior information from experiments that use nearby control parameters; whereas traditional ACRONYM tuning does not use such information and can require many more measurements as a result. We prove that such information reuse is possible under the relatively weak assumption that the true model parameters are Lipschitz-continuous functions of the control parameters. We also perform numerical experiments that demonstrate that over-rotation errors in single qubit gates can be automatically tuned from 88% to 99.95% average gate fidelity using less than 1kB of data and fewer than 20 steps of the optimizer.

Subject Classification

ACM Subject Classification
  • Hardware → Quantum computation
  • Quantum Computing
  • Randomized Benchmarking


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  1. 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, 2017. Google Scholar
  2. Robert J. Chapman, Christopher Ferrie, and Alberto Peruzzo. Experimental Demonstration of Self-Guided Quantum Tomography. Physical Review Letters, 117(4):040402, July 2016. URL:
  3. Joshua Combes, Christopher Granade, Christopher Ferrie, and Steven T. Flammia. Logical Randomized Benchmarking. arXiv:1702.03688 [quant-ph], February 2017. URL:
  4. Andrew W Cross, David P DiVincenzo, and Barbara M Terhal. A Comparative Code Study for Quantum Fault-Tolerance. arXiv:0711.1556, November 2007. URL:
  5. Christoph Dankert, Richard Cleve, Joseph Emerson, and Etera Livine. Exact and Approximate Unitary 2-Designs: Constructions and Applications. arXiv:quant-ph/0606161, June 2006. Physical Review A 80, 012304 (2009). URL:
  6. Arnaud Doucet and Adam M. Johansen. A Tutorial on Particle Filtering and Smoothing: Fifteen Years Later, 2011. Google Scholar
  7. D. J. Egger and F. K. Wilhelm. Adaptive Hybrid Optimal Quantum Control for Imprecisely Characterized Systems. Physical Review Letters, 112(24):240503, June 2014. URL:
  8. Joseph Emerson, Robert Alicki, and Karol Zyczkowski. Scalable Noise Estimation with Random Unitary Operators. Journal of Optics B: Quantum and Semiclassical Optics, 7(10):S347-S352, 2005. Google Scholar
  9. Edward Farhi, Jeffrey Goldstone, and Sam Gutmann. A quantum approximate optimization algorithm. arXiv preprint arXiv:1411.4028, 2014. URL:
  10. Christopher Ferrie. Self-Guided Quantum Tomography. Physical Review Letters, 113(19):190404, November 2014. URL:
  11. Christopher Ferrie and Osama Moussa. Robust and Efficient in Situ Quantum Control. Physical Review A, 91(5):052306, May 2015. URL:
  12. Austin G Fowler, Ashley M Stephens, and Peter Groszkowski. High-threshold universal quantum computation on the surface code. Physical Review A, 80(5):052312, 2009. Google Scholar
  13. Christopher Granade, Christopher Ferrie, and D. G. Cory. Accelerated Randomized Benchmarking. New Journal of Physics, 17(1):013042, January 2015. URL:
  14. Christopher Granade, Christopher Ferrie, Ian Hincks, Steven Casagrande, Thomas Alexander, Jonathan Gross, Michal Kononenko, and Yuval Sanders. QInfer: Statistical inference software for quantum applications. Quantum, 1:5, 2017. Google Scholar
  15. Christopher Granade and Nathan Wiebe. Structured filtering. New Journal of Physics, 19(8):083014, 2017. Google Scholar
  16. Christopher E Granade. Software Tools for Writing Reproducible Papers., May 2017.
  17. Reinier W. Heeres, Philip Reinhold, Nissim Ofek, Luigi Frunzio, Liang Jiang, Michel H. Devoret, and Robert J. Schoelkopf. Implementing a Universal Gate Set on a Logical Qubit Encoded in an Oscillator. arXiv:1608.02430 [quant-ph], August 2016. URL:
  18. I. Hincks. personal communications. Google Scholar
  19. Ian Hincks, Joel J. Wallman, Chris Ferrie, Chris Granade, and David G. Cory. Bayesian Inference for Randomized Benchmarking Protocols. arXiv:1802.00401 [quant-ph], February 2018. URL:
  20. Ian Hincks, Joel J Wallman, Chris Ferrie, Chris Granade, and David G Cory. Bayesian Inference for Randomized Benchmarking Protocols. arXiv preprint arXiv:1802.00401, 2018. URL:
  21. Michał Horodecki, Paweł Horodecki, and Ryszard Horodecki. General Teleportation Channel, Singlet Fraction, and Quasidistillation. Physical Review A, 60(3):1888-1898, September 1999. URL:
  22. Julian Kelly, R Barends, B Campbell, Y Chen, Z Chen, B Chiaro, A Dunsworth, Austin G Fowler, I-C Hoi, E Jeffrey, et al. Optimal quantum control using randomized benchmarking. Physical review letters, 112(24):240504, 2014. Google Scholar
  23. Shelby Kimmel, Marcus P. da Silva, Colm A. Ryan, Blake R. Johnson, and Thomas Ohki. Robust Extraction of Tomographic Information via Randomized Benchmarking. Physical Review X, 4(1):011050, March 2014. URL:
  24. Jane Liu and Mike West. Combined Parameter and State Estimation in Simulation-Based Filtering. In De Freitas and NJ Gordon, editors, Sequential Monte Carlo Methods in Practice. Springer-Verlag, New York, 2001. Google Scholar
  25. Easwar Magesan, Jay M. Gambetta, and Joseph Emerson. Characterizing Quantum Gates via Randomized Benchmarking. Physical Review A, 85(4), April 2012. URL:
  26. 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. Physical Review Letters, 109(8):080505, August 2012. URL:
  27. Seth T Merkel, Jay M Gambetta, John A Smolin, Stefano Poletto, Antonio D Córcoles, Blake R Johnson, Colm A Ryan, and Matthias Steffen. Self-consistent quantum process tomography. Physical Review A, 87(6):062119, 2013. Google Scholar
  28. Michael A Nielsen. A Simple Formula for the Average Gate Fidelity of a Quantum Dynamical Operation. quant-ph/0205035, May 2002. Phys. Lett. A 303 (4): 249-252 (2002). URL:
  29. Alberto Peruzzo, Jarrod McClean, Peter Shadbolt, Man-Hong Yung, Xiao-Qi Zhou, Peter J Love, Alán Aspuru-Guzik, and Jeremy L O’brien. A variational eigenvalue solver on a photonic quantum processor. Nature communications, 5:4213, 2014. Google Scholar
  30. Timothy Proctor, Kenneth Rudinger, Kevin Young, Mohan Sarovar, and Robin Blume-Kohout. What Randomized Benchmarking Actually Measures. arXiv:1702.01853 [quant-ph], February 2017. URL:
  31. Łukasz Rudnicki, Zbigniew Puchała, and Karol Zyczkowski. Gauge Invariant Information Concerning Quantum Channels. arXiv:1707.06926 [quant-ph], July 2017. URL:
  32. Maria Schuld, Alex Bocharov, Krysta Svore, and Nathan Wiebe. Circuit-centric quantum classifiers. arXiv preprint arXiv:1804.00633, 2018. URL:
  33. J.C. Spall. Multivariate Stochastic Approximation Using a Simultaneous Perturbation Gradient Approximation. IEEE Transactions on Automatic Control, 37(3):332-341, March 1992. URL:
  34. Joel Wallman, Chris Granade, Robin Harper, and Steven T. Flammia. Estimating the Coherence of Noise. New Journal of Physics, 17(11):113020, 2015. URL:
  35. Joel J. Wallman. Randomized Benchmarking with Gate-Dependent Noise. arXiv:1703.09835 [quant-ph], March 2017. URL:
  36. John Watrous. The Theory of Quantum Information. Cambridge University Press, Cambridge, United Kingdom, 1 edition edition, April 2018. Google Scholar
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