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Generalized Quantum Search Hamiltonian

Joonwoo Bae·Younghun Kwon
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Abstract

There are hamiltonians that solve a search problem of finding one of $N$ items in $O(\sqrt{N})$ steps. They are hamiltonians to describe an oscillation between two states. In this paper we propose a generalized search hamiltonian, $H_{g}$. Then the known search hamiltonians become special cases of $H_{g}$. From the generalized search hamiltonian, we present remarkable results that searching with 100% is subject only to the phase factor in $H_{g}$ and independent to the number of states or initialization.

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Joonwoo Bae, Younghun Kwon. 2002-02-03. Generalized Quantum Search Hamiltonian. https://doi.org/10.1103/physreva.66.012314

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