A Logarithmic Bayesian Approach to Quantum Error Detection

Ian Convy; K. Birgitta Whaley

doi:10.22331/q-2022-04-04-680

A Logarithmic Bayesian Approach to Quantum Error Detection

Department of Chemistry, University of California, Berkeley, CA 94720, USA
Berkeley Quantum Information and Computation Center, University of California, Berkeley, CA 94720, USA

Published:	2022-04-04, volume 6, page 680
Eprint:	arXiv:2110.10732v3
Doi:	https://doi.org/10.22331/q-2022-04-04-680
Citation:	Quantum 6, 680 (2022).

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Abstract

We consider the problem of continuous quantum error correction from a Bayesian perspective, proposing a pair of digital filters using logarithmic probabilities that are able to achieve near-optimal performance on a three-qubit bit-flip code, while still being reasonable to implement on low-latency hardware. These practical filters are approximations of an optimal filter that we derive explicitly for finite time steps, in contrast with previous work that has relied on stochastic differential equations such as the Wonham filter. By utilizing logarithmic probabilities, we are able to eliminate the need for explicit normalization and can reduce the Gaussian noise distribution to a simple quadratic expression. The state transitions induced by the bit-flip errors are modeled using a Markov chain, which for log-probabilties must be evaluated using a LogSumExp function. We develop the two versions of our filter by constraining this LogSumExp to have either one or two inputs, which favors either simplicity or accuracy, respectively. Using simulated data, we demonstrate that the single-term and two-term filters are able to significantly outperform both a double threshold scheme and a linearized version of the Wonham filter in tests of error detection under a wide variety of error rates and time steps.

Featured image: Simulated signal readout from a continuous measurement. (a) Signals averaged over a long time interval, showing an obvious change in the syndrome values after each error. (b) Signals averaged over a shorter time interval, where the measurement noise now obscures the change in the syndrome values. (c) The underlying syndrome values without noise, along with the averages across three integration periods.

► BibTeX data

@article{Convy2022logarithmicbayesian,
  doi = {10.22331/q-2022-04-04-680},
  url = {https://doi.org/10.22331/q-2022-04-04-680},
  title = {A {L}ogarithmic {B}ayesian {A}pproach to {Q}uantum {E}rror {D}etection},
  author = {Convy, Ian and Whaley, K. Birgitta},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {6},
  pages = {680},
  month = apr,
  year = {2022}
}

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Cited by

[1] Ian Convy, Haoran Liao, Song Zhang, Sahil Patel, William P Livingston, Ho Nam Nguyen, Irfan Siddiqi, and K Birgitta Whaley, "Machine learning for continuous quantum error correction on superconducting qubits", New Journal of Physics 24 6, 063019 (2022).

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