Adiabatic Quantum Counting by Geometric Phase Estimation

Details Adiabatic Quantum Counting by Geometric Phase Estimation Adiabatic Quantum Counting by Geometric Phase Estimation

2008-05-09

arxiv.org/abs/0805.1387v2

Physics

Quantum Physics

9 pages

Scientific paper

We design an adiabatic quantum algorithm for the counting problem, i.e., approximating the proportion, $\alpha$, of the marked items in a given database. As the quantum system undergoes a designed cyclic adiabatic evolution, it acquires a Berry phase $2\pi\alpha$. By estimating the Berry phase, we can approximate $\alpha$, and solve the problem. For an error bound $\epsilon$, the algorithm can solve the problem with cost of order $(\frac{1}{\epsilon})^{3/2}$, which is not as good as the optimal algorithm in the quantum circuit model, but better than the classical random algorithm. Moreover, since the Berry phase is a purely geometric feature, the result may be robust to decoherence and resilient to certain noise.

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