Quantum Mechanical Search and Harmonic Perturbation

Abstract

Perturbation theory in quantum mechanics studies how quantum systems interact with their environmental perturbations. Harmonic perturbation is a rare special case of time-dependent perturbations in which exact analysis exists. Some important technology advances, such as masers, lasers, nuclear magnetic resonance, etc., originated from it. Here we add quantum computation to this list with a theoretical demonstration. Based on harmonic perturbation, a quantum mechanical algorithm is devised to search the ground state of a given Hamiltonian. The intrinsic complexity of the algorithm is continuous and parametric in both time T and energy E. More precisely, the probability of locating a search target of a Hamiltonian in N-dimensional vector space is shown to be 1/(1+ c N E^{-2} T^{-2}) for some constant c. This result is optimal. As harmonic perturbation provides a different computation mechanism, the algorithm may suggest new directions in realizing quantum computers.

6 pages, 4 figures, revtex4

References in corpus (9)

• Strengths and Weaknesses of Quantum Computing
• Tight bounds on quantum searching
• Quantum Search by Local Adiabatic Evolution
• Experimental implementation of an adiabatic quantum optimization algorithm
• How Powerful is Adiabatic Quantum Computation?
• Quantum Computing: Pro and Con
• Implementation of a three-quantum-bit search algorithm
• Experimental Implementation of Hogg's Algorithm on a Three-Quantum-bit NMR Quantum Computer
• Quantum search with resonances