Driving Hamiltonian in a Quantum Search Problem

Kazuto Oshima

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Driving Hamiltonian in a Quantum Search Problem

Kazuto Oshima

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Abstract

We examine the driving Hamiltonian in the analog analogue of Grover's algorithm by Farhi and Gutmann. For a quantum system with a given Hamiltonian $E|w> < w|$, we explicitly show that while the driving Hamiltonian $E|s> < s|$ optimally produces the state $|w>$ from an initial state $|s>$, the driving Hamiltonian $E^{\prime}|s> < s|(E^{\prime} \ne E)$ does not provide any speedup compared even with a classical computation.

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Kazuto Oshima. 2001-11-04. Driving Hamiltonian in a Quantum Search Problem. https://arxiv.org/abs/quant-ph/0111021

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