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Journal of Applied Computer Science

Quantum simulations of particle scattered by a rectangular potential

Marcin Ostrowski

Published Jan 1, 2012• 1 citation
OpenAlex

Abstract

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).

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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).
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.
This paper investigates whether a quantum computer can efficiently simulate the non-elastic scattering of the Schrödinger particle on a stationary excitable shield. The return of the shield to the ground state is caused by photon emission. An algorithm is presented for simulating the time evolution of such a process, implemented on standard two-input gates. The algorithm is used for the computation of elastic and non-elastic scattering probabilities. The results obtained by our algorithm are compared with those obtained using the standard Cayley’s method.