Two Variations of Quantum Phase Estimation for Reducing Circuit Error Rates: Application to the Harrow--Hassidim--Lloyd Algorithm

TL;DR

This paper proposes two novel variations of quantum phase estimation to reduce circuit errors, integrating them into the HHL algorithm, and demonstrates their effectiveness on IBM hardware for solving linear systems.

Contribution

Introduces quantum shifted and punctured phase estimation methods that streamline circuits and reduce errors in quantum algorithms.

Findings

Reduced qubit and gate counts in HHL algorithm implementations.

Experimental validation on IBM hardware shows lower error rates.

Hybrid quantum-classical approach effectively mitigates circuit errors.

Abstract

We introduce two variations of the quantum phase estimation algorithm: quantum shifted phase estimation and quantum punctured phase estimation. The shifted method employs a bit-string left shift to discard the most significant bit and focus on lower-order phase components, and the punctured method removes qubits corresponding to known phase bits, thereby streamlining the circuit. To demonstrate the effectiveness of the two variations, we integrate them into a hybrid quantum-classical implementation of the Harrow--Hassidim--Lloyd algorithm for solving linear systems. The hybrid method leverages both quantum and classical processors to identify and remove unnecessary qubits and gates. As a result, our method reduces qubit and gate counts compared to previous implementations, leading to lower overall circuit error rates on current hardware. Experimental demonstrations on IBM superconducting hardware confirm the error-mitigation effectiveness of the proposed hybrid method.