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Efficient learning of quantum noise


Noise is the central obstacle to building large-scale quantum computers. Quantum systems with sufficiently uncorrelated and weak noise could be used to solve computational problems that are intractable with current digital computers. There has been substantial progress towards engineering such systems1,2,3,4,5,6,7,8. However, continued progress depends on the ability to characterize quantum noise reliably and efficiently with high precision9. Here, we describe such a protocol and report its experimental implementation on a 14-qubit superconducting quantum architecture. The method returns an estimate of the effective noise and can detect correlations within arbitrary sets of qubits. We show how to construct a quantum noise correlation matrix allowing the easy visualization of correlations between all pairs of qubits, enabling the discovery of long-range two-qubit correlations in the 14-qubit device that had not previously been detected. Our results are the first implementation of a provably rigorous and comprehensive diagnostic protocol capable of being run on state-of-the-art devices and beyond. These results pave the way for noise metrology in next-generation quantum devices, calibration in the presence of crosstalk, bespoke quantum error-correcting codes10 and customized fault-tolerance protocols11 that can greatly reduce the overhead in a quantum computation.

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Fig. 1: Our algorithm for characterizing the entire averaged probability vector.
Fig. 2: Results from the protocol run in single-qubit mode.
Fig. 3: Results from the protocol run in two-qubit mode.
Fig. 4: Illustration of the applicability of the protocol to larger systems.

Data availability

Source data are available for this paper at All other data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

Code availability

Details of code that was used to analyse the data is available from the corresponding author upon reasonable request.


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We thank S. Bartlett, A. Doherty, J. Emerson and T. Monz for comments on an earlier draft. This work was supported in part by US Army Research Office grant nos. W911NF-14-1-0098 and W911NF-14-1-0103, the Australian Research Council Centre of Excellence for Engineered Quantum Systems (EQUS) CE170100009, the Government of Ontario, and the Government of Canada through the Canada First Research Excellence Fund (CFREF) and Transformative Quantum Technologies (TQT), Natural Sciences and Engineering Research Council (NSERC), Industry Canada.

Author information




R.H., S.T.F. and J.J.W. conceived the experiments, and S.T.F. and J.J.W. conceived the original methodology. The implementation was carried out by R.H. R.H. wrote the initial draft and all authors contributed to the revisions and editing of the manuscript.

Corresponding author

Correspondence to Steven T. Flammia.

Ethics declarations

Competing interests

J.J.W. is the chief technology officer of the company Quantum Benchmark, Inc., and S.T.F. and R.H. were both consultants for it for part of the duration of this project.

Additional information

Peer review information Nature Physics thanks Jonas Bylander, Diego Risté, Marcus da Silva and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary Figs. 1–6, discussion and Tables 1–7.

Source data

Source Data Fig. 2

Correlation matrix data, high and low error bounds.

Source Data Fig. 3

Correlation matrix data, high and low error bounds.

Source Data Fig. 4

Data used for Fig. 4 plot.

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Harper, R., Flammia, S.T. & Wallman, J.J. Efficient learning of quantum noise. Nat. Phys. 16, 1184–1188 (2020).

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