Bulletin of the American Physical Society
APS March Meeting 2023
Volume 68, Number 3
Las Vegas, Nevada (March 5-10)
Virtual (March 20-22); Time Zone: Pacific Time
Session A64: Algorithms for Hamiltionian Simulations
8:00 AM–11:00 AM,
Monday, March 6, 2023
Room: Room 415
Sponsoring
Unit:
DQI
Chair: William Munizzi, Arizona State University
Abstract: A64.00007 : Efficient calculation of energy derivatives on a Fault-Tolerant Quantum Computer
9:36 AM–9:48 AM
Presenter:
Raffaele Santagati
(Boehringer-Ingelheim Quantum Lab)
Authors:
Raffaele Santagati
(Boehringer-Ingelheim Quantum Lab)
Thomas E O'Brien
(Google LLC)
Michael Streif
(Boehringer Ingelheim)
Nicholas C Rubin
(Google)
Yuan Su
(Google)
William J Huggins
(Google)
Joshua Goings
(Google)
Nikolaj Moll
(Boehringer Ingelheim)
Elica Kyoseva
(Boehringer-Ingelheim)
Matthias Degroote
(Boehringer-Ingelheim)
Christofer Tautermann
(Boehringer-Ingelheim)
Joonho Lee
(Columbia University)
Dominic W Berry
(Macquarie University)
Nathan Wiebe
(University of Toronto)
Ryan Babbush
(Google)
Here, we present new algorithms for efficiently calculating energy derivatives on fault-tolerant quantum computers, exploiting existing state-of-the-art techniques, including block encoding of fermionic operators, use of higher order finite difference formula, and Heisenberg-limited expectation value estimation methods. We optimize the algorithms' parameters to reduce their computational cost and discuss their asymptotic scalings. We show how these approaches can achieve Heisenberg's limited scaling of the errors and compare their different performance, supporting the results with numerical simulations. We will discuss the limits of such techniques and their direct dependence on the cost of state preparation and the calculation of the expectation value of the energy. We will finally explore their applicability to problems of practical relevance, such as the geometry optimization of molecules.
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