4.6 Article

Optimizing quantum phase estimation for the simulation of Hamiltonian eigenstates

期刊

QUANTUM SCIENCE AND TECHNOLOGY
卷 5, 期 4, 页码 -

出版社

IOP Publishing Ltd
DOI: 10.1088/2058-9565/abaa2c

关键词

quantum phase estimation; digital quantum simulation; classical post-processing; noisy intermediate-scale quantum; quantum many-body problem

资金

  1. Fundacao para a Ciencia e a Tecnologia (FCT) [SFRH/BD/138806/2018, PTDC/FIS-NAN/4662/2014 (016656)]

向作者/读者索取更多资源

We revisit quantum phase estimation algorithms for the purpose of obtaining the energy levels of many-body Hamiltonians and pay particular attention to the statistical analysis of their outputs. We introduce the mean phase direction of the parent distribution associated with eigenstate inputs as a new post-processing tool. By connecting it with the unknown phase, we find that if used as its direct estimator, it exceeds the accuracy of the standard majority rule using one less bit of resolution, making evident that it can also be inverted to provide unbiased estimation. Moreover, we show how to directly use this quantity to accurately find the energy levels when the initialized state is an eigenstate of the simulated propagator during the whole time evolution, which allows for shallower algorithms. We then use IBM Q hardware to carry out the digital quantum simulation of three toy models: a two-level system, a two-spin Ising model and a two-site Hubbard model at half-filling. Methodologies are provided to implement Trotterization and reduce the variability of results in noisy intermediate scale quantum computers.

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