Quantum Error Transmutation

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.