Optimizing the Phase Estimation Algorithm Applied to the Quantum Simulation of Heisenberg-Type Hamiltonians

TL;DR

This paper enhances the phase estimation algorithm for quantum simulation of Heisenberg Hamiltonians by introducing three optimizations and testing them on classical and real quantum computers, improving performance.

Contribution

It presents three novel optimizations—circular, iterative, and Bayesian—for the phase estimation algorithm applied to quantum simulations of Heisenberg systems.

Findings

Optimizations improve algorithm performance.

Successful implementation on IBM's quantum platform.

Enhanced understanding of iterative and update-based quantum algorithms.

Abstract

The phase estimation algorithm is a powerful quantum algorithm with applications in cryptography, number theory, and simulation of quantum systems. We use this algorithm to simulate the time evolution of a system of two spin-1/2 particles under a Heisenberg Hamiltonian. The evolution is performed through both classical simulations of quantum computers and real quantum computers via IBM's Qiskit platform. We also introduce three optimizations to the algorithm: circular, iterative, and Bayesian. We apply these optimizations to our simulations and investigate how the performance improves. We also discuss the paradigms of iterative and update-based algorithms, which are attributes of these optimizations that can improve quantum algorithms generally.