Quantum Circuit Design for Solving Linear Systems of Equations

TL;DR

This paper reviews the quantum algorithm for solving linear systems, designs a small-scale 2x2 quantum circuit implementation, and demonstrates its potential for experimental realization through simulation.

Contribution

It provides a detailed quantum circuit design for solving linear systems and demonstrates its feasibility with a small 2x2 system and numerical simulations.

Findings

Quantum circuit for 2x2 system implemented with 4 qubits

Numerical simulations show effective performance

Potential for experimental realization

Abstract

Recently, it is shown that quantum computers can be used for obtaining certain information about the solution of a linear system Ax=b exponentially faster than what is possible with classical computation. Here we first review some key aspects of the algorithm from the standpoint of finding its efficient quantum circuit implementation using only elementary quantum operations, which is important for determining the potential usefulness of the algorithm in practical settings. Then we present a small-scale quantum circuit that solves a 2x2 linear system. The quantum circuit uses only 4 qubits, implying a tempting possibility for experimental realization. Furthermore, the circuit is numerically simulated and its performance under different circuit parameter settings is demonstrated.