Error mitigation for universal gates on encoded qubits

TL;DR

This paper proposes a hybrid approach combining error correction and error mitigation to implement fault-tolerant Clifford+T circuits efficiently, reducing overhead and enabling near-term quantum advantage.

Contribution

It introduces a method to protect Clifford gates with error correction and mitigate T-gate errors via quasi-probability, avoiding magic state distillation.

Findings

Clifford+T circuits with fewer T-gates are feasible on small error-corrected devices.

The approach reduces hardware overhead compared to traditional magic state distillation.

Such circuits are challenging for classical simulation algorithms.

Abstract

The Eastin-Knill theorem states that no quantum error correcting code can have a universal set of transversal gates. For CSS codes that can implement Clifford gates transversally it suffices to provide one additional non-Clifford gate, such as the T-gate, to achieve universality. Common methods to implement fault-tolerant T-gates like magic state distillation generate a significant hardware overhead that will likely prevent their practical usage in the near-term future. Recently methods have been developed to mitigate the effect of noise in shallow quantum circuits that are not protected by error correction. Error mitigation methods require no additional hardware resources but suffer from a bad asymptotic scaling and apply only to a restricted class of quantum algorithms. In this work, we combine both approaches and show how to implement encoded Clifford+T circuits where Clifford gates are protected from noise by error correction while errors introduced by noisy encoded T-gates are mitigated using the quasi-probability method. As a result, Clifford+T circuits with a number of T-gates inversely proportional to the physical noise rate can be implemented on small error-corrected devices without magic state distillation. We argue that such circuits can be out of reach for state-of-the-art classical simulation algorithms.