Improved fault-tolerant quantum simulation of condensed-phase correlated electrons via trotterization

Ian D. Kivlichan*, Craig Gidney, Dominic W. Berry, Nathan Wiebe, Jarrod McClean, Wei Sun, Zhang Jiang, Nicholas Rubin, Austin Fowler, Alán Aspuru-Guzik, Hartmut Neven, Ryan Babbush

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)
3 Downloads (Pure)

Abstract

Recent work has deployed linear combinations of unitaries techniques to reduce the cost of fault-tolerant quantum simulations of correlated electron models. Here, we show that one can sometimes improve upon those results with optimized implementations of Trotter-Suzuki-based product formulas. We show that low-order Trotter methods perform surprisingly well when used with phase estimation to compute relative precision quantities (e.g. energies per unit cell), as is often the goal for condensed-phase systems. In this context, simulations of the Hubbard and plane-wave electronic structure models with N < 105 fermionic modes can be performed with roughly O(1) and O(N2) T complexities. We perform numerics revealing tradeoffs between the error and gate complexity of a Trotter step; e.g., we show that split-operator techniques have less Trotter error than popular alternatives. By compiling to surface code fault-tolerant gates and assuming error rates of one part per thousand, we show that one can error-correct quantum simulations of interesting, classically intractable instances with a few hundred thousand physical qubits.

Original languageEnglish
Article number296
Pages (from-to)1-45
Number of pages45
JournalQuantum
Volume4
DOIs
Publication statusPublished - 13 Jul 2020

Bibliographical note

Copyright © 2020 Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften. All rights reserved. . Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.

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