Discrete Approximation of Quantum Stochastic Models

Abstract

We develop a general technique for proving convergence of repeated quantum interactions to the solution of a quantum stochastic differential equation. The wide applicability of the method is illustrated in a variety of examples. Our main theorem, which is based on the Trotter-Kato theorem, is not restricted to a specific noise model and does not require boundedness of the limit coefficients.

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• Implementing quantum stochastic differential equations on a quantum computer
• Quantum simulating an experiment: Light interference from single ions and their mirror images
• Strong convergence of quantum random walks via semigroup decomposition
• On The Scattering Process in Quantum Optics
• Quantum random walk approximation on locally compact quantum groups
• Discrete Quantum Control - State Preparation