  Quantum error correcting (QEC) stabilizer codes enable protection of quantum
information against errors during storage and processing. Simulation of noisy
QEC codes is used to identify the noise parameters necessary for advantageous
operation of logical qubits in realistic quantum computing architectures.
Typical quantum error correction techniques contain intermediate measurements
and classical feedback that determine the actual noisy circuit sequence in an
instance of performing the protocol. Dynamical subset sampling enables
efficient simulation of such non-deterministic quantum error correcting
protocols for any type of quantum circuit and incoherent noise of low strength.
As an importance sampling technique, dynamical subset sampling allows one to
effectively make use of computational resources to only sample the most
relevant sequences of quantum circuits in order to estimate a protocol's
logical failure rate with well-defined error bars. We demonstrate the
capabilities of dynamical subset sampling with examples from fault-tolerant
(FT) QEC. We show that, in a typical stabilizer simulation with incoherent
Pauli noise of strength $p = 10^{-3}$, our method can reach a required sampling
accuracy on the logical failure rate with two orders of magnitude fewer samples
than direct Monte Carlo simulation. Furthermore, dynamical subset sampling
naturally allows for efficient simulation of realistic multi-parameter noise
models describing faulty quantum processors. It can be applied not only for QEC
in the circuit model but any noisy quantum computing framework with incoherent
fault operators including measurement-based quantum computation and quantum
networks.
