Simulating realizations of quantum computers by solving the time-dependent Schrödinger Equation

Naoki Watanabe, Masaru Tsukada

A fast and stable method is formulated to compute the time evolution of wave functions by numerically solving the time dependent Schrödinger equation. This method is a real space time evolution method implemented by several innovative techniques of computational physics to realize high accuracy, perfect stability and good suitability for vector- and parallel-type supercomputers. Applying this method to some simple electron dynamics, we confirmed the efficiency and the accuracy of the method.

Erik Lötstedt, Takanori Nishi, Kaoru Yamanouchi

Erik Lötstedt, Kaoru Yamanouchi

Qiming Chen, Re-Bing Wu

This paper proposes a numerical method for solving time-dependent Schrodinger equations with finite spectral bandwidth, which applies to both periodic and non-periodic cases. We introduce the concept of Pulse Width Modulation (PWM), which is broadly used in classical control engineering, to simulate time-dependent quantum dynamics by switching between a finite number of constant Hamiltonians. The switching timings can be programmed to improve the precision and save computational resources. The effectiveness of the PWM method is demonstrated by numerical simulations, which shows that it is faster and more robust than the standard piecewise constant control systems. Moreover, we also propose the realization of PWM method for potential implementation in experimental systems.

Giuliano Benenti, G. Strini

The nature of a quantum computer is described in the concrete context of a quantum simulator of the single-particle Schrödinger equation. We show that a register of 6–10 qubits is sufficient to realize a useful quantum simulator capable of efficiently solving standard quantum mechanical problems.

LEVI, Benjamin, Bertrand Georgeot