Energy and Efficiency of Adiabatic Quantum Search Algorithms

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.

6 pages, Revtex, 1 figure. Theorem modified, references and comments added, sections introduced, typos corrected. Version to appear in J. Phys. A

References in corpus (1)

• Robustness of adiabatic quantum computation

Cited by in corpus (9)

• General error estimate for adiabatic quantum computing
• Energetic cost of superadiabatic quantum computation
• Non adiabatic quantum search algorithms
• On models of nonlinear evolution paths in adiabatic quantum algorithms
• Optimizing adiabaticity in quantum mechanics
• Reply to Andrew Hodges
• Quantum Adiabatic Computation and the Travelling Salesman Problem
• Hilbert Space Average Method and adiabatic quantum search
• Entanglement and Adiabatic Quantum Computation