Quantum circuit design for solving linear systems of equations

Abstract

Recently, it has been demonstrated that quantum computers can be used for solving linear systems of algebraic equations with exponential speedup compared with classical computers. Here, we present an efficient and generic quantum circuit design for implementing the algorithm for solving linear systems. In particular, we show the detailed construction of a quantum circuit which solves a 4 × 4 linear system with seven qubits. It consists of only the basic quantum gates that can be realized with present physical devices, implying great possibility for experimental implementation. Furthermore, the performance of the circuit is numerically simulated and its ability to solve the intended linear system is verified.

Keywords:

• quantum algorithm
• quantum computing
• linear systems

Acknowledgement

This work is dedicated to professor Dudley Herschbach in appreciation of his contribution to science and celebration of his 80th birthday. Also we thank the NSF Center for Quantum Information and Computation for Chemistry, Award number CHE-1037992.