Fundamental thresholds of realistic quantum error correction circuits from classical spin models

TL;DR

This paper develops a method to map realistic, faulty quantum error correction circuits to classical spin models, enabling the study of their error thresholds and robustness without relying on specific decoding strategies.

Contribution

It extends the classical-quantum mapping to include multi-parameter circuit noise, providing a new way to evaluate quantum error correction thresholds and hardware performance.

Findings

Monte-Carlo simulations reveal phase diagrams of the spin models

Results benchmark against minimum-weight perfect matching decoder

Method assesses thresholds independent of decoding strategies

Abstract

Mapping quantum error correcting codes to classical disordered statistical mechanics models and studying the phase diagram of the latter has proven a powerful tool to study the fundamental error robustness and associated critical error thresholds of leading quantum error correcting codes under phenomenological noise models. In this work, we extend this mapping to admit realistic, multi-parameter faulty quantum circuits in the description of quantum error correcting codes. Based on the underlying microscopic circuit noise model, we first systematically derive the associated strongly correlated classical spin models. We illustrate this approach in detail for the example of a quantum repetition code in which faulty stabilizer readout circuits are periodically applied. Finally, we use Monte-Carlo simulations to study the resulting phase diagram of the associated interacting spin model and benchmark our results against a minimum-weight perfect matching decoder. The presented method provides an avenue to assess the fundamental thresholds of QEC codes and associated readout circuitry, independent of specific decoding strategies, and can thereby help guiding the development of near-term QEC hardware.