Dynamical subset sampling of quantum error correcting protocols

TL;DR

This paper introduces dynamical subset sampling, an importance sampling method that efficiently simulates non-deterministic quantum error correction protocols, significantly reducing computational resources needed for accurate logical failure rate estimation.

Contribution

The paper presents a novel importance sampling technique, dynamical subset sampling, for efficient simulation of noisy quantum error correction protocols with fewer samples than traditional methods.

Findings

Achieves two orders of magnitude reduction in samples for logical failure rate estimation.

Effectively simulates realistic multi-parameter noise models.

Applicable to various quantum computing frameworks beyond circuit-based QEC.

Abstract

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.