Error suppression for Hamiltonian-based quantum computation using subsystem codes

TL;DR

This paper introduces a general framework for suppressing errors in Hamiltonian-based quantum computation using subsystem codes, including stabilizer codes, with performance bounds and practical 2-local constructions.

Contribution

It develops a unified error suppression scheme for Hamiltonian quantum computing employing subsystem codes and demonstrates concrete 2-local implementations.

Findings

Complete error suppression achieved in large penalty limit

Performance bounds for error suppression schemes

Explicit 2-local constructions for specific quantum gates

Abstract

We present general conditions for quantum error suppression for Hamiltonian-based quantum computation using subsystem codes. This involves encoding the Hamiltonian performing the computation using an error detecting subsystem code and the addition of a penalty term that commutes with the encoded Hamiltonian. The scheme is general and includes the stabilizer formalism of both subspace and subsystem codes as special cases. We derive performance bounds and show that complete error suppression results in the large penalty limit. To illustrate the power of subsystem-based error suppression, we introduce fully 2-local constructions for protection of the swap gate of adiabatic gate teleportation and the Ising chain in a transverse field.