Efficient unitary method for simulation of driven quantum dot systems

Abstract

Density matrices evolved according the von Neumann equation are commonly used to simulate the dynamics of driven quantum systems. However, computational methods using density matrices are often too slow to explore the large parameter spaces of solid state quantum systems. Here we develop a unitary computation method to quickly perform simulations for closed quantum systems, where dissipation to the environment can be ignored. We use three techniques to optimize simulations, apply them to six time-dependent pulses for a semiconductor quantum dot qubit system, and predict the dynamic evolutions. We compare computational times between our unitary method and the density matrix method for a variety of image sizes. As an example, we implement our unitary method for a realistic four-state system [Z. Shi, et al., Nat. Commun. 5, 3020 (2014)], and find that it is over two orders of magnitude faster than the corresponding density matrix method implemented in the popular quantum simulation software QuTiP.

9 pages, 6 figues

References in corpus (6)

• Quantum Computing
• QuTiP 2: A Python framework for the dynamics of open quantum systems
• Real time evolution using the density matrix renormalization group
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• Noise enhancement due to quantum coherence in coupled quantum dots
• Exponential propagators for the Schrödinger equation with a time-dependent potential