Applications of the Quantum Phase Difference Estimation Algorithm to the Excitation Energies in Spin Systems on a NISQ Device

TL;DR

This paper demonstrates the implementation of a noise-resilient Quantum Phase Difference Estimation algorithm on NISQ devices to accurately compute energy gaps in spin systems, showcasing its potential for quantum many-body simulations.

Contribution

It introduces a novel fault-tolerant QPDE algorithm optimized for NISQ hardware, applying it to diverse spin systems with high accuracy and noise suppression techniques.

Findings

Achieved 85-93% accuracy in energy gap calculations on IBM quantum processors.

Developed constant-depth quantum circuits leveraging match gate-like structures.

Validated the algorithm's effectiveness across various spin configurations.

Abstract

The Quantum Phase Difference Estimation (QPDE) algorithm, as an extension of the Quantum Phase Estimation (QPE), is a quantum algorithm designed to compute the differences of two eigenvalues of a unitary operator by exploiting the quantum superposition of two eigenstates. Unlike QPE, QPDE is free of controlled-unitary operations, and is suitable for calculations on noisy intermediate-scale quantum (NISQ) devices. We present the implementation and verification of a novel early fault-tolerant QPDE algorithm for determining energy gaps across diverse spin system configurations using NISQ devices. The algorithm is applied to the systems described by two and three-spin Heisenberg Hamiltonians with different geometric arrangements and coupling strengths, including symmetric, asymmetric, spin-frustrated, and non-frustrated configurations. By leveraging the match gate-like structure of the time evolution operator of Heisenberg Hamiltonian, we achieve constant-depth quantum circuits suitable for NISQ hardware implementation. Our results on IBM quantum processors show remarkable accuracy ranging from 85\% to 93\%, demonstrating excellent agreement with classical calculations even in the presence of hardware noise. The methodology incorporates sophisticated quantum noise suppression techniques, including Pauli Twirling and Dynamical Decoupling, and employs an adaptive framework. Our findings demonstrate the practical viability of the QPDE algorithm for quantum many-body simulations on current NISQ hardware, establishing a robust framework for future applications.