Measuring and Suppressing Error Correlations in Quantum Circuits

TL;DR

This paper experimentally investigates error correlations in quantum circuits using a trapped ion qubit, demonstrating that dynamically corrected gates significantly suppress correlated errors, thus improving quantum error correction assumptions.

Contribution

The study introduces a method to identify and quantify error correlations in quantum circuits and shows that virtual dynamically corrected gates effectively suppress these correlations.

Findings

Error correlations can be detected via end-of-circuit measurements.

Dynamically corrected gates reduce correlated errors by over 270 times.

Error correlations become indistinguishable from uncorrelated noise with DCGs.

Abstract

Quantum error correction provides a path to large-scale quantum computers, but is built on challenging assumptions about the characteristics of the underlying errors. In particular, the mathematical assumption of independent errors in quantum logic operations is at odds with realistic environments where error-sources may exhibit strong temporal correlations. We present experiments enabling the identification of error correlations between operations in quantum circuits, using only projective measurements at the end of the circuit. Using a single trapped ion qubit and engineered noise with tunable temporal correlations, we identify a clear signature of error correlations between sequential gates in randomly composed quantum circuits, and extract quantitative measures linked to the underlying noise correlation length. By replacing all gates in these circuits with "virtual" dynamically corrected gates (DCGs), we demonstrate that even in the presence of strongly correlated noise the signatures of error correlations between sequential gates appear similar to standard gates exposed to uncorrelated noise. A theoretical model applied to our experiments reveals that common DCGs suppress the correlated error component by over $270\times$ with $95\%$ confidence. Using block-correlated noise, we explore the scaling of the effective error correlation length at the virtual level, and show that DCGs exhibit error correlations indistinguishable from those arising from uncorrelated noise.