Simulation of stochastic quantum systems using polynomial chaos expansions.

Area of Science:

• Quantum mechanics
• Computational physics
• Uncertainty quantification

Background:

• Simulating quantum systems driven by classical stochastic processes is computationally challenging.
• Traditional methods like Monte Carlo simulation can be resource-intensive.
• Developing efficient simulation techniques is crucial for advancing quantum research.

Purpose of the Study:

• To present a novel, computationally efficient approach for simulating quantum systems under stochastic influence.
• To leverage polynomial chaos expansion for representing quantum system dynamics.

Main Methods:

• Utilizing polynomial chaos expansion to represent the density matrix.
• Expanding the density matrix in orthogonal polynomials over stochastic process components.
• Deriving a sparsely coupled hierarchy of linear differential equations.
• Employing heuristics from time-dependent perturbation theory for expansion truncation.

Main Results:

• The polynomial chaos technique yields a tractable hierarchy of differential equations.
• Heuristics for truncation provide practical guidelines for computational efficiency.
• Numerical demonstration on a one-qubit system shows significant speedup compared to Monte Carlo methods.

Conclusions:

• The proposed polynomial chaos expansion approach offers a more efficient alternative for simulating quantum systems driven by stochastic processes.
• This method has the potential to accelerate research in quantum dynamics and related fields.
• The technique is validated by an experimentally relevant numerical example.