Fault-tolerant quantum simulation of materials using Bloch orbitals
- URL: http://arxiv.org/abs/2302.05531v1
- Date: Fri, 10 Feb 2023 22:18:27 GMT
- Title: Fault-tolerant quantum simulation of materials using Bloch orbitals
- Authors: Nicholas C. Rubin, Dominic W. Berry, Fionn D. Malone, Alec F. White,
Tanuj Khattar, A. Eugene DePrince III, Sabrina Sicolo, Michael K\"uhn,
Michael Kaicher, Joonho Lee, Ryan Babbush
- Abstract summary: We extend methods for quantum simulation with Bloch orbitals constructed from symmetry-adapted atom-centered orbitals.
We implement qubit encoding using known tensor factorizations and a new Bloch orbital form of tensor hypercontraction.
- Score: 0.3932300766934225
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: The simulation of chemistry is among the most promising applications of
quantum computing. However, most prior work exploring algorithms for
block-encoding, time-evolving, and sampling in the eigenbasis of electronic
structure Hamiltonians has either focused on modeling finite-sized systems, or
has required a large number of plane wave basis functions. In this work, we
extend methods for quantum simulation with Bloch orbitals constructed from
symmetry-adapted atom-centered orbitals so that one can model periodic
\textit{ab initio} Hamiltonians using only a modest number of basis functions.
We focus on adapting existing algorithms based on combining qubitization with
tensor factorizations of the Coulomb operator. Significant modifications of
those algorithms are required to obtain an asymptotic speedup leveraging
translational (or, more broadly, Abelian) symmetries. We implement block
encodings using known tensor factorizations and a new Bloch orbital form of
tensor hypercontraction. Finally, we estimate the resources required to deploy
our algorithms to classically challenging model materials relevant to the
chemistry of Lithium Nickel Oxide battery cathodes within the surface code.
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