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

Abstract

While adiabatic quantum computing (AQC) has some robustness to noise and decoherence it is widely believed that encoding, error suppression and error correction will be required to scale AQC to large problem sizes. Previous works have established at least two different techniques for error suppression in AQC. In this paper we derive a model for describing the dynamics of encoded AQC and show that previous constructions for error suppression can be unified with this dynamical model. In addition the model clarifies the mechanisms of error suppression and allow identification of its weaknesses. In the second half of the paper we utilize our description of non-equilibrium dynamics in encoded AQC to construct methods for error correction in AQC by cooling local degrees of freedom (qubits). While this is shown to be possible in principle, we also identify the key challenge to this approach: the requirement of high-weight Hamiltonians. Finally, we use our dynamical model to perform a simplified thermal stability analysis of concatenated-stabilizer-code encoded many-body systems for AQC or quantum memories. This work is a companion paper to "\textit{Error suppression and error correction in adiabatic quantum computation I: techniques and challenges}" (Phys. Rev. X, 3, 041013 (2013)), which provides a quantum information perspective on the techniques and limitations of error suppression and correction in AQC. In this paper we couch the same results within a dynamical framework, which allows for detailed analysis of the non-equilibrium dynamics of error suppression and correction in encoded AQC.