Error suppression and error correction in adiabatic quantum computation I: techniques and challenges

TL;DR

This paper analyzes error suppression techniques in adiabatic quantum computation, showing their limitations and emphasizing the need for error correction to achieve large-scale fault-tolerant quantum computing.

Contribution

It unifies the analysis of energy gap protection and dynamical decoupling within a common formalism and discusses progress and challenges in implementing error correction in AQC.

Findings

Error suppression alone is insufficient for fault-tolerant AQC.

Energy gap protection and dynamical decoupling are closely related techniques.

Critical constraints limit the effectiveness of error suppression methods.

Abstract

Adiabatic quantum computation (AQC) is known to possess some intrinsic robustness, though it is likely that some form of error correction will be necessary for large scale computations. Error handling routines developed for circuit-model quantum computation do not transfer easily to the AQC model since these routines typically require high-quality quantum gates, a resource not generally allowed in AQC. There are two main techniques known to suppress errors during an AQC implementation: energy gap protection and dynamical decoupling. Here we show that both these methods are intimately related and can be analyzed within the same formalism. We analyze the effectiveness of such error suppression techniques and identify critical constraints on the performance of error suppression in AQC, suggesting that error suppression by itself is insufficient for large-scale, fault-tolerant AQC and that a form of error correction is needed. We discuss progress towards implementing error correction in AQC and enumerate several key outstanding problems. This work is a companion paper to "Error suppression and error correction in adiabatic quantum computation II: non-equilibrium dynamics"', which provides a dynamical model perspective on the techniques and limitations of error suppression and error correction in AQC. In this paper we discuss the same results within a quantum information framework, permitting an intuitive discussion of error suppression and correction in encoded AQC.