Error suppression and error correction in adiabatic quantum computation II: non-equilibrium dynamics

摘要

While adiabatic quantum computing (AQC) has some robustness to noise anddecoherence it is widely believed that encoding, error suppression and errorcorrection will be required to scale AQC to large problem sizes. Previous workshave established at least two different techniques for error suppression inAQC. In this paper we derive a model for describing the dynamics of encoded AQCand show that previous constructions for error suppression can be unified withthis dynamical model. In addition the model clarifies the mechanisms of errorsuppression and allow identification of its weaknesses. In the second half ofthe paper we utilize our description of non-equilibrium dynamics in encoded AQCto construct methods for error correction in AQC by cooling local degrees offreedom (qubits). While this is shown to be possible in principle, we alsoidentify the key challenge to this approach: the requirement of high-weightHamiltonians. Finally, we use our dynamical model to perform a simplifiedthermal stability analysis of concatenated-stabilizer-code encoded many-bodysystems for AQC or quantum memories. This work is a companion paper to "\textit{Error suppression and errorcorrection in adiabatic quantum computation I: techniques and challenges}"(Phys. Rev. X, 3, 041013 (2013)), which provides a quantum informationperspective on the techniques and limitations of error suppression andcorrection in AQC. In this paper we couch the same results within a dynamicalframework, which allows for detailed analysis of the non-equilibrium dynamicsof error suppression and correction in encoded AQC.