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arXiv · 2105.05018

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

Scott Johnstun·Jean-François Van Huele
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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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Scott Johnstun, Jean-François Van Huele. 2021-05-07. Optimizing the Phase Estimation Algorithm Applied to the Quantum Simulation of Heisenberg-Type Hamiltonians. https://arxiv.org/abs/2105.05018

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