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Energy and Efficiency of Adiabatic Quantum Search Algorithms

Saurya Das·Randy Kobes·Gabor Kunstatter
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Abstract

We present the results of a detailed analysis of a general, unstructured adiabatic quantum search of a data base of $N$ items. In particular we examine the effects on the computation time of adding energy to the system. We find that by increasing the lowest eigenvalue of the time dependent Hamiltonian {\it temporarily} to a maximum of $\propto \sqrt{N}$, it is possible to do the calculation in constant time. This leads us to derive the general theorem which provides the adiabatic analogue of the $\sqrt{N}$ bound of conventional quantum searches. The result suggests that the action associated with the oracle term in the time dependent Hamiltonian is a direct measure of the resources required by the adiabatic quantum search.

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Saurya Das, Randy Kobes, Gabor Kunstatter. 2003-02-26. Energy and Efficiency of Adiabatic Quantum Search Algorithms. https://doi.org/10.1088/0305-4470%2F36%2F11%2F313

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