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Early fault-tolerant simulations of the Hubbard model

Campbell, Earl T. (2022) Early fault-tolerant simulations of the Hubbard model. Quantum Science and Technology, 7 (1). Art. No. 015007. ISSN 2058-9565. doi:10.1088/2058-9565/ac3110.

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Simulation of the Hubbard model is a leading candidate for the first useful applications of a fault-tolerant quantum computer. A recent study of quantum algorithms for early simulations of the Hubbard model [Kivlichan et al 2019 Quantum 4 296] found that the lowest resource costs were achieved by split-operator Trotterization combined with the fast-fermionic Fourier transform (FFFT) on an L × L lattice with length L = 2^k. On lattices with length L ≠ 2^k, Givens rotations can be used instead of the FFFT but lead to considerably higher resource costs. We present a new analytic approach to bounding the simulation error due to Trotterization that provides much tighter bounds for the split-operator FFFT method, leading to 16× improvement in error bounds. Furthermore, we introduce plaquette Trotterization that works on any size lattice and apply our improved error bound analysis to show competitive resource costs. We consider a phase estimation task and show plaquette Trotterization reduces the number of non-Clifford gates by a factor 5.5× to 9× (depending on the parameter regime) over the best previous estimates for 8 × 8 and 16 × 16 lattices and a much larger factor for other lattice sizes not of the form L = 2^k. In conclusion, we find there is a potentially useful application for fault-tolerant quantum computers using around one million Toffoli gates.

Item Type:Article
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URLURL TypeDescription Paper
Campbell, Earl T.0000-0002-5627-0021
Additional Information:© 2021 IOP Publishing Ltd. Received 4 August 2021; Revised 15 October 2021; Accepted 19 October 2021; Published 18 November 2021. We thank Fernando Brandão for proposing a study of the Hubbard model and useful early discussions. We thank Yuan Su for discussions on commutator bounds and Sam McArdle for detailed feedback on the manuscript.
Group:AWS Center for Quantum Computing
Issue or Number:1
Record Number:CaltechAUTHORS:20211130-210656352
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Official Citation:Earl T Campbell 2022 Quantum Sci. Technol. 7 015007
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:112095
Deposited By: Tony Diaz
Deposited On:30 Nov 2021 21:17
Last Modified:30 Nov 2021 21:17

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