Error Suppression for Hamiltonian Quantum Computing in Markovian Environments

TL;DR

This paper extends error suppression techniques in Hamiltonian quantum computing to general Markovian environments, demonstrating that energy penalties can effectively protect encoded ground states with only logarithmic growth in penalty strength.

Contribution

It generalizes the original error suppression results to broader Markovian environments beyond Lindblad form, showing effective protection with minimal energy penalty growth.

Findings

Error suppression holds in general Markovian environments.

Energy penalty strength grows logarithmically with system size.

Protection is effective at fixed temperature.

Abstract

Hamiltonian quantum computing, such as the adiabatic and holonomic models, can be protected against decoherence using an encoding into stabilizer subspace codes for error detection and the addition of energy penalty terms. This method has been widely studied since it was first introduced by Jordan, Farhi, and Shor (JFS) in the context of adiabatic quantum computing. Here we extend the original result to general Markovian environments, not necessarily in Lindblad form. We show that the main conclusion of the original JFS study holds under these general circumstances: assuming a physically reasonable bath model, it is possible to suppress the initial decay out of the encoded ground state with an energy penalty strength that grows only logarithmically in the system size, at a fixed temperature.