Mohan Sarovar, Kevin C. Young
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 dynamical 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 general, we also identify the key challenge to this approach: the requirement of high-weight Hamiltonians. Finally, from a many-body quantum dynamics perspective, our results demonstrate how utilizing the quantum coding formalism can facilitate the dynamical analysis of open, many-body quantum systems. This work is a companion paper to "Error suppression and correction in adiabatic quantum computing: techniques and challenges", 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.
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http://arxiv.org/abs/1307.5892
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