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Open Systems & Information Dynamics

Quantum Simulation of Two Interacting Schrödinger Particles

Marcin Ostrowski

Published Dec 1, 2016• 4 citations
Publisher

Abstract

In this paper, we examine whether a quantum computer can efficiently simulate time evolution of two Schrödinger particles. We consider particles interacting with each other and with an external potential. In order to solve the Schrödinger equation in the quantum register, we use an algorithm based on the quantum Fourier transform.
DOI
10.1142/s1230161216500207

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This paper examines whether a quantum computer can efficiently simulate the evolution of the Schrödinger particle in a one-dimensional infinite potential well.The present study involves simulation of the change of the particle's state due to instant enlarging of the well's size.In order to solve the Schrödinger equation in the quantum register, an algorithm based on the Quantum Fourier Transform is applied.The paper presents an algorithm for simulating time evolution of such a system, implemented on standard two-input gates.
In this paper we examine whether a quantum computer can efficiently simulate time evolution of a one dimensional Schrödinger particle. Two cases are considered: free particle and particle dispersed on a rectangular potential. In order to simulate the Schrödinger particle, we use a quantum algorithm based on the procedure of diagonalisation of time evolution operator. The procedure of diagonalisation is based on the Quantum Fourier Transform (QFT) algorithm. The effects of simulation are presented in the form of figures. We also compare the results obtained from quantum algorithm with the results of classical simulations (Cayley's method).
The simulation of quantum systems on a quantum computer using the Zalka–Wiesner algorithm including quantum noise has been considered. The efficiency of developed methods and algorithms has been demonstrated by example of the solution of the time-dependent Schrödinger equation for a particle in the Pöschl–Teller potential. The developed analytical theory of the effect of quantum noise on the accuracy of simulation has been compared with Monte Carlo simulations. The accuracy of the solution of the Schrödinger equation for a many-electron system has been forecasted as a function of the number of electrons and for different levels of noise.