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General error estimate for adiabatic quantum computing

Gernot Schaller·Sarah Mostame·Ralf Schützhold
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Abstract

Most investigations devoted to the conditions for adiabatic quantum computing are based on the first-order correction ${\bra{Ψ_{\rm ground}(t)}\dot H(t)\ket{Ψ_{\rm excited}(t)} /ΔE^2(t)\ll1}$. However, it is demonstrated that this first-order correction does not yield a good estimate for the computational error. Therefore, a more general criterion is proposed, which includes higher-order corrections as well and shows that the computational error can be made exponentially small -- which facilitates significantly shorter evolution times than the above first-order estimate in certain situations. Based on this criterion and rather general arguments and assumptions, it can be demonstrated that a run-time $T$ of order of the inverse minimum energy gap $ΔE_{\rm min}$ is sufficient and necessary, i.e., $T=\ord(ΔE_{\rm min}^{-1})$. For some examples, these analytical investigations are confirmed by numerical simulations. PACS: 03.67.Lx, 03.67.-a.

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Gernot Schaller, Sarah Mostame, Ralf Schützhold. 2006-04-07. General error estimate for adiabatic quantum computing. https://doi.org/10.1103/physreva.73.062307

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