Mitigating errors in logical qubits

TL;DR

This paper introduces exclusive decoders combined with post-selection for surface code quantum error correction, achieving high thresholds, reduced resource requirements, and demonstrating potential for scalable quantum computing.

Contribution

It develops a novel family of exclusive decoders with post-selection, quantifies their performance, and applies them to improve magic state distillation and other quantum error correction tasks.

Findings

Achieves a 50% threshold under depolarizing noise with exclusive decoders.

Demonstrates up to quadratic improvement in logical failure rates below threshold.

Reports 75% reduction in physical qubits for magic state distillation.

Abstract

Quantum error correcting codes protect quantum information, allowing for large quantum computations provided that physical error rates are sufficiently low. We combine post-selection with surface code error correction through the use of a parameterized family of exclusive decoders, which are able to abort on decoding instances that are deemed too difficult. We develop new numerical sampling methods to quantify logical failure rates with exclusive decoders as well as the trade-off in terms of the amount of post-selection required. For the most discriminating of exclusive decoders, we demonstrate a threshold of 50\% under depolarizing noise for the surface code (or $32(1)\%$ for the fault-tolerant case with phenomenological measurement errors), and up to a quadratic improvement in logical failure rates below threshold. Furthermore, surprisingly, with a modest exclusion criterion, we identify a regime at low error rates where the exclusion rate decays with code distance, providing a pathway for scalable and time-efficient quantum computing with post-selection. We apply our exclusive decoder to the 15-to-1 magic state distillation protocol, and report a $75\%$ reduction in the number of physical qubits required, and a $60\%$ reduction in the total spacetime volume required, including accounting for repetitions required for post-selection. We also consider other applications, as an error mitigation technique, and in concatenated schemes. Our work highlights the importance of post-selection as a powerful tool in quantum error correction.