Non-commuting two-local Hamiltonians for quantum error suppression

TL;DR

This paper demonstrates that non-commuting two-local Hamiltonians derived from subsystem code gauge operators can suppress single-qubit errors, surpassing the limitations of commuting two-local Hamiltonians, thus enhancing near-term quantum error protection.

Contribution

It introduces a method to encode quantum information in non-commuting two-local Hamiltonians using gauge operators from Bacon-Shor codes, overcoming a known no-go theorem.

Findings

Non-commuting two-local Hamiltonians can protect against single-qubit errors.

This approach improves robustness in quantum storage and adiabatic quantum computation.

Reduces the need for higher-order terms in Hamiltonian encoding.

Abstract

Physical constraints make it challenging to implement and control many-body interactions. For this reason, designing quantum information processes with Hamiltonians consisting of only one- and two-local terms is a worthwhile challenge. Enabling error suppression with two-local Hamiltonians is particularly challenging. A no-go theorem of Marvian and Lidar [Physical Review Letters 113(26), 260504 (2014)] demonstrates that, even allowing particles with high Hilbert-space dimension, it is impossible to protect quantum information from single-site errors by encoding in the ground subspace of any Hamiltonian containing only commuting two-local terms. Here, we get around this no-go result by encoding in the ground subspace of a Hamiltonian consisting of non-commuting two-local terms arising from the gauge operators of a subsystem code. Specifically, we show how to protect stored quantum information against single-qubit errors using a Hamiltonian consisting of sums of the gauge generators from Bacon-Shor codes [Physical Review A 73(1), 012340 (2006)] and generalized-Bacon-Shor code [Physical Review A 83(1), 012320 (2011)]. Our results imply that non-commuting two-local Hamiltonians have more error-suppressing power than commuting two-local Hamiltonians. While far from providing full fault tolerance, this approach improves the robustness achievable in near-term implementable quantum storage and adiabatic quantum computations, reducing the number of higher-order terms required to encode commonly used adiabatic Hamiltonians such as the Ising Hamiltonians common in adiabatic quantum optimization and quantum annealing.