Automated searching for quantum subsystem codes

TL;DR

This paper introduces a computational algorithm to find optimal quantum subsystem codes based on measurement operators, enabling systematic analysis of codes in lattice systems with 2-body interactions.

Contribution

It presents a novel algorithm for computing optimal quantum subsystem codes from arbitrary measurement sets, shifting from theoretical to computational analysis.

Findings

Identified optimal codes for 2-body interaction systems on various lattice geometries.

Demonstrated the algorithm's effectiveness through systematic code investigations.

Provided insights into the structure of quantum subsystem codes in lattice models.

Abstract

Quantum error correction allows for faulty quantum systems to behave in an effectively error free manner. One important class of techniques for quantum error correction is the class of quantum subsystem codes, which are relevant both to active quantum error correcting schemes as well as to the design of self-correcting quantum memories. Previous approaches for investigating these codes have focused on applying theoretical analysis to look for interesting codes and to investigate their properties. In this paper we present an alternative approach that uses computational analysis to accomplish the same goals. Specifically, we present an algorithm that computes the optimal quantum subsystem code that can be implemented given an arbitrary set of measurement operators that are tensor products of Pauli operators. We then demonstrate the utility of this algorithm by performing a systematic investigation of the quantum subsystem codes that exist in the setting where the interactions are limited to 2-body interactions between neighbors on lattices derived from the convex uniform tilings of the plane.