Simulation of stochastic quantum systems using polynomial chaos expansions

Abstract

We present an approach to the simulation of quantum systems driven by classical stochastic processes that is based on the polynomial chaos expansion, a well-known technique in the field of uncertainty quantification. The polynomial chaos expansion represents the system density matrix as a series of orthogonal polynomials in the principle components of the stochastic process and yields a sparsely coupled hierarchy of linear differential equations. We provide practical heuristics for truncating this expansion based on results from time-dependent perturbation theory and demonstrate, via an experimentally relevant one-qubit numerical example, that our technique can be significantly more computationally efficient than Monte Carlo simulation.

5 pages, 2 figures

References in corpus (5)

• Quantum Computing
• Optimized Dynamical Decoupling in a Model Quantum Memory
• Disentanglement and decoherence from classical non-Markovian noise: Random telegraph noise
• Qubits as spectrometers of dephasing noise
• Reduced equations of motion for quantum systems driven by diffusive Markov processes

Cited by in corpus (1)

• A Unified Stochastic Formulation of Dissipative Quantum Dynamics. I. Generalized Hierarchical Equations