Optimizing Quantum Adiabatic Algorithm

Abstract

In quantum adiabatic algorithm, as the adiabatic parameter $s(t)$ changes slowly from zero to one with finite rate, a transition to excited states inevitably occurs and this induces an intrinsic computational error. We show that this computational error depends not only on the total computation time $T$ but also on the time derivatives of the adiabatic parameter $s(t)$ at the beginning and the end of evolution. Previous work (Phys. Rev. A \textbf{82}, 052305) also suggested this result. With six typical paths, we systematically demonstrate how to optimally design an adiabatic path to reduce the computational errors. Our method has a clear physical picture and also explains the pattern of computational error. In this paper we focus on quantum adiabatic search algorithm although our results are general.

8 pages, 9 figures

References in corpus (5)

• Adiabatic Theory of Nonlinear Evolution of Quantum States
• Quantum Adiabatic Brachistochrone
• Adiabatic approximation with exponential accuracy for many-body systems and quantum computation
• Accuracy vs run time in adiabatic quantum search
• Hierarchical Theory of Quantum Adiabatic Evolution

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• Quantum annealing sampling with a bias field
• Accelerated spin-adapted ground state preparation with non-variational quantum algorithms