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

• URL: http://arxiv.org/abs/2105.05018v1
• Date: Fri, 7 May 2021 21:41:08 GMT
• Title: Optimizing the Phase Estimation Algorithm Applied to the Quantum Simulation of Heisenberg-Type Hamiltonians
• Authors: Scott Johnstun and Jean-Fran\c{c}ois Van Huele
• Abstract summary: 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. We introduce three optimizations to the algorithm: circular, iterative, and Bayesian.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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