Optimizing Stabilizer Parities for Improved Logical Qubit Memories

TL;DR

This paper introduces variants of Shor's code optimized for correlated idling errors, demonstrating significant improvements in logical qubit memory fidelity, especially in trapped-ion systems, by exploiting stabilizer sign changes and decoherence-free subspaces.

Contribution

It proposes new Shor code variants tailored for correlated errors, showing how stabilizer sign adjustments enhance error correction performance and robustness.

Findings

Achieved a 4-fold improvement in logical memory fidelity.

Demonstrated robustness of even-distance codes to coherent idling noise.

Validated improvements on a trapped-ion quantum computer.

Abstract

We study variants of Shor's code that are adept at handling single-axis correlated idling errors, which are commonly observed in many quantum systems. By using the repetition code structure of the Shor's code basis states, we calculate the logical channel applied to the encoded information when subjected to coherent and correlated single qubit idling errors, followed by stabilizer measurement. Changing the signs of the stabilizer generators allows us to change how the coherent errors interfere, leading to a quantum error correcting code which performs as well as a classical repetition code of equivalent distance against these errors. We demonstrate a factor of 4 improvement of the logical memory in a distance-3 logical qubit implemented on a trapped-ion quantum computer. Even-distance versions of our Shor code variants are decoherence-free subspaces and fully robust to identical and independent coherent idling noise.