Sampling ridiculously low logical error rates via efficient Monte Carlo algorithms

Useful applications of quantum computation will certainly require reaching the teraquops regime. A challenge naturally arises: how to validate the fault-tolerant gadgets and decoders down to such low error rate, and obtain reliable logical error rates for resource estimation?

Logical error rate is usually estimated by directly sampling physical errors. They are then propagated with a Clifford simulation to sample detectors and observables. At low logical error rates, most generated shots are decoded without error while the ones leading to logical errors are extremely rare events, and yet the ones contributing to the precision of the logical error rate estimation. Reaching the teraquops regime that way is impractical.

The usual workaround consists in running Monte Carlo simulations in configurations where the logical error rate remains high enough to gather enough statistics in reasonable amount of time. An ansatz, usually obtained by analytically upper bounding the error rate and turning such bound into a parametrized formula, can then be fitted. As this relies on extrapolation, questions on reliability and precision naturally arise.

In this work, we build on top of advanced Monte Carlo methods developed for statistical physics to efficiently sample rare logical errors, and reconstitute the logical error rate, even when absurdly low. While some questions are left open, we hope those methods to replace ansatz fitting and complement direct sampling of the physical errors' distribution.