Lattice quantum algorithm for the Schrodinger wave equation in 2+1 dimensions with a demonstration by modeling soliton instabilities

作     者：Yepez, Jeffrey Vahala, George Vahala, Linda 

作者机构：USAF Res Lab Bedford MA 01731 USA Coll William & Mary Dept Phys Williamsburg VA 23187 USA Old Dominion Univ Coll Engn & Technol Norfolk VA 23529 USA 

出 版 物：《QUANTUM INFORMATION PROCESSING》 (量子信息处理)

年 卷 期：2005年第4卷第6期

页      面：457-469页

核心收录：

学科分类：07[理学] 070201[理学-理论物理] 0702[理学-物理学] 

基　　金：Air Force Office of Scientific Research  AFOSR 

主　　题：non-linear Schrodinger wave equation quantum algorithm soliton dynamics non-linear quantum mechanical instability quantum computing computational physics 

摘      要：A lattice-based quantum algorithm is presented to model the non-linear Schrodinger-like equations in 2 + 1 dimensions. In this lattice-based model, using only 2 qubits per node, a sequence of unitary collide (qubit-qubit interaction) and stream (qubit translation) operators locally evolve a discrete field of probability amplitudes that in the long-wavelength limit accurately approximates a non-relativistic scalar wave function. The collision operator locally entangles pairs of qubits followed by a streaming operator that spreads the entanglement throughout the two dimensional lattice. The quantum algorithmic scheme employs a non-linear potential that is proportional to the moduli square of the wave function. The model is tested on the transverse modulation instability of a one dimensional soliton wave train, both in its linear and non-linear stages. In the integrable cases where analytical solutions are available, the numerical predictions are in excellent agreement with the theory.