From quantum circuits to adiabatic algorithms

Details From quantum circuits to adiabatic algorithms From quantum circuits to adiabatic algorithms

2004-09-03

arxiv.org/abs/quant-ph/0409024v7

Physics

Quantum Physics

Version accepted by and to appear in Phys. Rev. A

Scientific paper

10.1103/PhysRevA.71.062314

This paper explores several aspects of the adiabatic quantum computation model. We first show a way that directly maps any arbitrary circuit in the standard quantum computing model to an adiabatic algorithm of the same depth. Specifically, we look for a smooth time-dependent Hamiltonian whose unique ground state slowly changes from the initial state of the circuit to its final state. Since this construction requires in general an n-local Hamiltonian, we will study whether approximation is possible using previous results on ground state entanglement and perturbation theory. Finally we will point out how the adiabatic model can be relaxed in various ways to allow for 2-local partially adiabatic algorithms as well as 2-local holonomic quantum algorithms.

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