Impact of correlations and heavy-tails on quantum error correction

TL;DR

This paper demonstrates that heavy-tailed, correlated errors in quantum systems can cause a breakdown of quantum error correction, highlighting the need for new noise characterization and mitigation strategies.

Contribution

It reveals how heavy-tailed, correlated errors impact quantum error correction and emphasizes the importance of developing detection and mitigation protocols.

Findings

Heavy-tailed errors can cause high-weight errors in quantum circuits.

Correlated errors reduce or eliminate logical qubit protection.

Current noise models may overlook heavy-tailed phenomena.

Abstract

We show that space- and time-correlated single-qubit rotation errors can lead to high-weight errors in a quantum circuit when the rotation angles are drawn from heavy-tailed distributions. This leads to a breakdown of quantum error correction, yielding reduced or in some cases no protection of the encoded logical qubits. While heavy-tailed phenomena are prevalent in the natural world, there is very little research as to whether noise with these statistics exist in current quantum processing devices. Furthermore, it is an open problem to develop tomographic or noise spectroscopy protocols that could test for the existence of noise with such statistics. These results suggest the need for quantum characterization methods that can reliably detect or reject the presence of such errors together with continued first-principles studies of the origins of space- and time-correlated noise in quantum processors. If such noise does exist, physical or control-based mitigation protocols must be developed to mitigate this noise as it would severely hinder the performance of fault-tolerant quantum computers.