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Article overview
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Quantum Sequential Hamiltonian Algorithm | | Hongye Yu
; Yuliang Huang
; Biao Wu
; | | Date: |
23 Jun 2017 | | Abstract: | We propose a generic quantum algorithm, sequential Hamiltonian algorithm, and
prove rigorously that our algorithm is as efficient as quantum circuit
algorithm. Our quantum algorithm consists of a series of Hamiltonians, $H_0,
H_1, H_2, cdots, H_j, H_{j+1}, cdots, H_fl$, where $H_0$ has a simple and
easy-to-construct ground state and the ground state of $H_fl$ is the solution.
The algorithm works by adiabatically switching on and off the Hamiltonians in
sequence. The time complexity of our algorithm is determined by both the number
of Hamiltonians $fl$ and the minimum energy gap during the adiabatic
switchings. We give an analytical example where our algorithm has an
exponential speed-up over the usual quantum adiabatic algorithm
$H(s)=(1-s)H_0+sH_fl$. A heuristic understanding of this speed-up is offered. | | Source: | arXiv, 1706.7646 | | Services: | Forum | Review | PDF | Favorites | |
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