Quantum Error Transmutation

TL;DR

This paper generalizes quantum error correction to allow for error transmutation, enabling recovery up to a set of admissible errors, which benefits noisy quantum system simulation and error-robust algorithms.

Contribution

It introduces the concept of quantum error transmuting codes, providing algebraic conditions and demonstrating existing and new codes with this property.

Findings

Derived algebraic conditions for error transmutation

Identified existing codes with error transmuting properties

Discovered new low-qubit, translation-invariant codes

Abstract

We introduce a generalisation of quantum error correction, relaxing the requirement that a code should identify and correct a set of physical errors on the Hilbert space of a quantum computer exactly, instead allowing recovery up to a pre-specified admissible set of errors on the code space. We call these quantum error transmuting codes. They are of particular interest for the simulation of noisy quantum systems, and for use in algorithms inherently robust to errors of a particular character. Necessary and sufficient algebraic conditions on the set of physical and admissible errors for error transmutation are derived, generalising the Knill-Laflamme quantum error correction conditions. We demonstrate how some existing codes, including fermionic encodings, have error transmuting properties to interesting classes of admissible errors. Additionally, we report on the existence of some new codes, including low-qubit and translation invariant examples.