Randomized compiling in fault-tolerant quantum computation
- URL: http://arxiv.org/abs/2306.13752v1
- Date: Fri, 23 Jun 2023 19:17:34 GMT
- Title: Randomized compiling in fault-tolerant quantum computation
- Authors: Stefanie J. Beale and Joel J. Wallman
- Abstract summary: We present an algorithm projecting the state of the system onto a logical state with a well-defined error.
The algorithm does not significantly increase the depth of the logical circuit.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Studies of quantum error correction (QEC) typically focus on stochastic Pauli
errors because the existence of a threshold error rate below which stochastic
Pauli errors can be corrected implies that there exists a threshold below which
generic errors can be corrected. However, rigorous estimates of the threshold
for generic errors are typically orders of magnitude worse than the threshold
for stochastic Pauli errors. Specifically, coherent errors have a particularly
harmful impact on the encoded space because they can map encoded states to
superpositions of logical and error states. Further, coherent errors can add up
and interfere over multiple rounds of error correction or between syndrome
measurements, which may result in significantly worse errors than expected
under a stochastic Pauli error model. In this paper, we present an algorithm
which decoheres noise at the logical level, projecting the state of the system
onto a logical state with a well-defined error. The algorithm does not
significantly increase the depth of the logical circuit (and usually does not
lead to any increase in depth), and applies generally to most fault-tolerant
gadgets and error correction steps.
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