Unification and limitations of error suppression techniques for adiabatic quantum computing

TL;DR

This paper examines error suppression techniques in adiabatic quantum computing, revealing their fundamental relationship, limitations, and the necessity for error correction for scalable fault-tolerant quantum computation.

Contribution

It unifies the analysis of energy gap protection and dynamical decoupling within a common formalism and highlights their limitations, emphasizing the need for error correction methods.

Findings

Energy gap protection and dynamical decoupling are fundamentally related.

Error suppression alone is insufficient for fault-tolerance in large-scale AQC.

Critical constraints limit the effectiveness of current error suppression techniques.

Abstract

While adiabatic quantum computation (AQC) possesses some intrinsic robustness to noise, it is expected that a form of error control will be necessary for large scale computations. Error control ideas developed for circuit-model quantum computation do not transfer easily to the AQC model and to date there have been two main proposals to suppress errors during an AQC implementation: energy gap protection and dynamical decoupling. Here we show that these two methods are fundamentally related and may 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 fault-tolerant, large-scale AQC and that a form of error correction is needed. This manuscript has been superseded by the articles, "Error suppression and error correction in adiabatic quantum computation I: techniques and challenges," arXiv:1307.5893, and "Error suppression and error correction in adiabatic quantum computation II: non-equilibrium dynamics," arXiv:1307.5892.