Quantum Mechanical Search and Harmonic Perturbation.pdf

Quantum Mechanical Search and Harmonic Perturbation Jie-Hong R. Jiang,1 Dah-Wei Chiou,2 and Cheng-En Wu3 1Department of Electrical Engineering, National Taiwan University, Taipei 10617, Taiwan∗ 2Department of Physics, University of California, Berkeley, CA 94720, USA 3Department of Physics, National Tsing Hua University, Hsinchu 30013, Taiwan Perturbation theory in quantum mechanics studies how quantum systems interact with their environmental perturbations. Harmonic perturbation is a rare special case of time-dependent per- turbations 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 7 probability of locating a search target of a Hamiltonian in N-dimensional vector space is shown 0 −2 −2 0 to be 1/(1 + cNE T ) for some constant c. This result is optimal. As harmonic perturbation 2 provides a different computation mechanism, the algorithm may suggest new directions in realizing quantum computers. p e PACS numbers: 03.67.Lx S Keywords: Quantum Computation, Complexity, Grover D