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Quantum error correcting (QEC) stabilizer codes enable protection of quantuminformation against errors during storage and processing. Simulation of noisyQEC codes is used to identify the noise parameters necessary for advantageousoperation of logical qubits in realistic quantum computing architectures.Typical quantum error correction techniques contain intermediate measurementsand classical feedback that determine the actual noisy circuit sequence in aninstance of performing the protocol. Dynamical subset sampling enablesefficient simulation of such non-deterministic quantum error correctingprotocols for any type of quantum circuit and incoherent noise of low strength.As an importance sampling technique, dynamical subset sampling allows one toeffectively make use of computational resources to only sample the mostrelevant sequences of quantum circuits in order to estimate a protocol'slogical failure rate with well-defined error bars. We demonstrate thecapabilities of dynamical subset sampling with examples from fault-tolerant(FT) QEC. We show that, in a typical stabilizer simulation with incoherentPauli noise of strength $p = 10^{-3}$, our method can reach a required samplingaccuracy on the logical failure rate with two orders of magnitude fewer samplesthan direct Monte Carlo simulation. Furthermore, dynamical subset samplingnaturally allows for efficient simulation of realistic multi-parameter noisemodels describing faulty quantum processors. It can be applied not only for QECin the circuit model but any noisy quantum computing framework with incoherentfault operators including measurement-based quantum computation and quantumnetworks.

Dynamical subset sampling of quantum error correcting protocols