Hybrid quantum linear equation algorithm and its experimental test on IBM Quantum Experience

TL;DR

This paper introduces a hybrid quantum algorithm based on HHL for solving linear equations, reducing circuit depth through classical feed-forward, and demonstrates its improved accuracy on IBM Quantum hardware.

Contribution

A novel hybrid quantum algorithm that simplifies HHL with classical feed-forward and is experimentally validated on IBM Quantum Experience.

Findings

Higher accuracy than HHL on specific linear systems

Successful implementation with four qubits on IBM Quantum

Circuit depth reduction achieved through hybrid approach

Abstract

We propose a hybrid quantum algorithm based on the Harrow-Hassidim-Lloyd (HHL) algorithm for solving a system of linear equations. In our hybrid scheme, a classical information feed-forward is required from the quantum phase estimation algorithm to reduce a circuit depth from the original HHL algorithm. In this paper, we show that this hybrid algorithm is functionally identical to the HHL algorithm under the assumption that the number of qubits used in algorithms is large enough. In addition, it is experimentally examined with four qubits in the IBM Quantum Experience setups, and the experimental results of our algorithm show higher accurate performance on specific systems of linear equations than that of the HHL algorithm.