An integrity measure to benchmark quantum error correcting memories

TL;DR

This paper introduces the integrity measure for benchmarking quantum error correction memories, demonstrating its experimental simplicity and comparing various codes through simulations to identify optimal strategies under different noise conditions.

Contribution

It presents the integrity measure as a practical benchmarking tool and provides a comparative analysis of different quantum codes for memory performance.

Findings

Integrity correlates with logical fidelity and pseudo-threshold.

Certain codes outperform others depending on noise characteristics.

Fault-tolerant implementations show improved robustness.

Abstract

Rapidly developing experiments across multiple platforms now aim to realise small quantum codes, and so demonstrate a memory within which a logical qubit can be protected from noise. There is a need to benchmark the achievements in these diverse systems, and to compare the inherent power of the codes they rely upon. We describe a recently-introduced performance measure called integrity, which relates to the probability that an ideal agent will successfully 'guess' the state of a logical qubit after a period of storage in the memory. Integrity is straightforward to evaluate experimentally without state tomography and it can be related to various established metrics such as the logical fidelity and the pseudo-threshold. We offer a set of experimental milestones that are steps towards demonstrating unconditionally superior encoded memories. Using intensive numerical simulations we compare memories based on the five-qubit code, the seven-qubit Steane code, and a nine-qubit code which is the smallest instance of a surface code; we assess both the simple and fault-tolerant implementations of each. While the 'best' code upon which to base a memory does vary according to the nature and severity of the noise, nevertheless certain trends emerge.