Gate Set Tomography

Erik Nielsen1, John King Gamble2, Kenneth Rudinger1, Travis Scholten3, Kevin Young1, and Robin Blume-Kohout1

1Quantum Performance Laboratory, Sandia National Laboratories
2Microsoft Research
3IBM Quantum, IBM T.J. Watson Research Center

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Gate set tomography (GST) is a protocol for detailed, predictive characterization of logic operations (gates) on quantum computing processors. Early versions of GST emerged around 2012-13, and since then it has been refined, demonstrated, and used in a large number of experiments. This paper presents the foundations of GST in comprehensive detail. The most important feature of GST, compared to older state and process tomography protocols, is that it is $\textit{calibration-free}$. GST does not rely on pre-calibrated state preparations and measurements. Instead, it characterizes all the operations in a $\textit{gate set}$ simultaneously and self-consistently, relative to each other. Long sequence GST can estimate gates with very high precision and efficiency, achieving Heisenberg scaling in regimes of practical interest. In this paper, we cover GST's intellectual history, the techniques and experiments used to achieve its intended purpose, data analysis, gauge freedom and fixing, error bars, and the interpretation of gauge-fixed estimates of gate sets. Our focus is fundamental mathematical aspects of GST, rather than implementation details, but we touch on some of the foundational algorithmic tricks used in the $\texttt{pyGSTi}$ implementation.

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[1] Gregory A. L. White, "Gate set tomography is not just hyperaccurate, it’s a different way of thinking", Quantum Views 5, 60 (2021).

[2] Antonio A. Gentile, Brian Flynn, Sebastian Knauer, Nathan Wiebe, Stefano Paesani, Christopher E. Granade, John G. Rarity, Raffaele Santagati, and Anthony Laing, "Learning models of quantum systems from experiments", Nature Physics 17 7, 837 (2021).

[3] Matthew Ware, Guilhem Ribeill, Diego Ristè, Colm A. Ryan, Blake Johnson, and Marcus P. da Silva, "Experimental Pauli-frame randomization on a superconducting qubit", Physical Review A 103 4, 042604 (2021).

[4] Gregory A. L. White, Felix A. Pollock, Lloyd C. L. Hollenberg, Kavan Modi, and Charles D. Hill, "Non-Markovian Quantum Process Tomography", arXiv:2106.11722.

[5] Yasunari Suzuki, Suguru Endo, Keisuke Fujii, and Yuuki Tokunaga, "Quantum error mitigation as a universal error-minimization technique: applications from NISQ to FTQC eras", arXiv:2010.03887.

[6] K. Nestmann, V. Bruch, and M. R. Wegewijs, "How Quantum Evolution with Memory is Generated in a Time-Local Way", Physical Review X 11 2, 021041 (2021).

[7] Gregory A. L. White, Felix A. Pollock, Lloyd C. L. Hollenberg, Charles D. Hill, and Kavan Modi, "Diagnosing temporal quantum correlations with compressed non-Markovian calipers", arXiv:2107.13934.

[8] Xiao Xue, Maximilian Russ, Nodar Samkharadze, Brennan Undseth, Amir Sammak, Giordano Scappucci, and Lieven M. K. Vandersypen, "Computing with spin qubits at the surface code error threshold", arXiv:2107.00628.

[9] Robin Blume-Kohout, Kenneth Rudinger, Erik Nielsen, Timothy Proctor, and Kevin Young, "Wildcard error: Quantifying unmodeled errors in quantum processors", arXiv:2012.12231.

[10] Robin Blume-Kohout, Marcus P. da Silva, Erik Nielsen, Timothy Proctor, Kenneth Rudinger, Mohan Sarovar, and Kevin Young, "A taxonomy of small Markovian errors", arXiv:2103.01928.

[11] Salonik Resch and Ulya R. Karpuzcu, "Benchmarking Quantum Computers and the Impact of Quantum Noise", arXiv:1912.00546.

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[13] Kenneth Rudinger, Craig W. Hogle, Ravi K. Naik, Akel Hashim, Daniel Lobser, David I. Santiago, Matthew D. Grace, Erik Nielsen, Timothy Proctor, Stefan Seritan, Susan M. Clark, Robin Blume-Kohout, Irfan Siddiqi, and Kevin C. Young, "Experimental Characterization of Crosstalk Errors with Simultaneous Gate Set Tomography", arXiv:2103.09890.

[14] Ezra Bussmann, Robert E. Butera, James H. G. Owen, John N. Randall, Steven M. Rinaldi, Andrew D. Baczewski, and Shashank Misra, "Atomic-precision advanced manufacturing for Si quantum computing", MRS Bulletin 46 7, 607 (2021).

[15] Yanwu Gu, Rajesh Mishra, Berthold-Georg Englert, and Hui Khoon Ng, "Randomized Linear Gate-Set Tomography", PRX Quantum 2 3, 030328 (2021).

[16] Erik Nielsen, Kenneth Rudinger, Timothy Proctor, Kevin Young, and Robin Blume-Kohout, "Efficient flexible characterization of quantum processors with nested error models", New Journal of Physics 23 9, 093020 (2021).

[17] Violeta N. Ivanova-Rohling, Guido Burkard, and Niklas Rohling, "Quantum state tomography as a numerical optimization problem", arXiv:2012.14494.

[18] Adrien Suau, Jon Nelson, Marc Vuffray, Andrey Y. Lokhov, Lukasz Cincio, and Carleton Coffrin, "Single-Qubit Cross Platform Comparison of Quantum Computing Hardware", arXiv:2108.11334.

[19] Kenneth Rudinger, Guilhem J. Ribeill, Luke C. G. Govia, Matthew Ware, Erik Nielsen, Kevin Young, Thomas A. Ohki, Robin Blume-Kohout, and Timothy Proctor, "Characterizing mid-circuit measurements on a superconducting qubit using gate set tomography", arXiv:2103.03008.

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[21] Ahmed Abid Moueddene, Nader Khammassi, Sebastian Feld, and Said Hamdioui, "A context-aware gate set tomography characterization of superconducting qubits", arXiv:2103.09922.

[22] T. J. Evans, W. Huang, J. Yoneda, R. Harper, T. Tanttu, K. W. Chan, F. E. Hudson, K. M. Itoh, A. Saraiva, C. H. Yang, A. S. Dzurak, and S. D. Bartlett, "Fast Bayesian tomography of a two-qubit gate set in silicon", arXiv:2107.14473.

The above citations are from Crossref's cited-by service (last updated successfully 2021-10-27 17:10:38) and SAO/NASA ADS (last updated successfully 2021-10-27 17:10:40). The list may be incomplete as not all publishers provide suitable and complete citation data.