Quantum circuits for solving one-dimensional Schr\"odinger equations

TL;DR

This paper presents quantum circuits designed to solve one-dimensional Schrödinger equations, demonstrating their effectiveness through simulations of common quantum systems using only eight qubits.

Contribution

It introduces simple quantum circuits capable of solving standard quantum mechanical problems, validated by simulation results.

Findings

Accurate results for harmonic oscillator, square-well, and Coulomb potential.

Effective solution with only eight qubits.

Quantum circuits can handle typical quantum systems.

Abstract

We construct quantum circuits for solving one-dimensional Schr\"odinger equations. Simulations of three typical examples, i.e., harmonic oscillator, square-well and Coulomb potential, show that reasonable results can be obtained with eight qubits. Our simulations show that simple quantum circuits can solve the standard quantum mechanical problems.