Kavli Affiliate: K. Birgitta Whaley
| First 5 Authors: Ian Convy, K. Birgitta Whaley, , ,
| Summary:
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 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 one-term and two-term filters are able to significantly
outperform 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.
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