# Fionn Malone

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Quantum computation of stopping power for inertial fusion target design

Dominic Berry

Alina Kononov

Alec White

Joonho Lee

Andrew Baczewski

arXiv preprint (2023)

Preview abstract
Stopping power is the rate at which a material absorbs the kinetic energy of a charged particle passing through it - one of many properties needed over a wide range of thermodynamic conditions in modeling inertial fusion implosions. First-principles stopping calculations are classically challenging because they involve the dynamics of large electronic systems far from equilibrium, with accuracies that are particularly difficult to constrain and assess in the warm-dense conditions preceding ignition. Here, we describe a protocol for using a fault-tolerant quantum computer to calculate stopping power from a first-quantized representation of the electrons and projectile. Our approach builds upon the electronic structure block encodings of Su et al. [PRX Quantum 2, 040332 2021], adapting and optimizing those algorithms to estimate observables of interest from the non-Born-Oppenheimer dynamics of multiple particle species at finite temperature. We also work out the constant factors associated with a novel implementation of a high order Trotter approach to simulating a grid representation of these systems. Ultimately, we report logical qubit requirements and leading-order Toffoli costs for computing the stopping power of various projectile/target combinations relevant to interpreting and designing inertial fusion experiments. We estimate that scientifically interesting and classically intractable stopping power calculations can be quantum simulated with
roughly the same number of logical qubits and about one hundred times more Toffoli gates than is required for state-of-the-art quantum simulations of industrially relevant molecules such as FeMoCo or P450.
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Purification-Based Quantum Error Mitigation of Pair-Correlated Electron Simulations

Thomas E O'Brien

Gian-Luca R. Anselmetti

Fotios Gkritsis

Vincent Elfving

Stefano Polla

William J. Huggins

Oumarou Oumarou

Kostyantyn Kechedzhi

Dmitry Abanin

Rajeev Acharya

Igor Aleiner

Richard Ross Allen

Trond Ikdahl Andersen

Kyle Anderson

Markus Ansmann

Frank Carlton Arute

Kunal Arya

Juan Atalaya

Michael Blythe Broughton

Bob Benjamin Buckley

Alexandre Bourassa

Leon Brill

Tim Burger

Nicholas Bushnell

Jimmy Chen

Yu Chen

Benjamin Chiaro

Desmond Chun Fung Chik

Josh Godfrey Cogan

Roberto Collins

Paul Conner

William Courtney

Alex Crook

Ben Curtin

Ilya Drozdov

Andrew Dunsworth

Daniel Eppens

Lara Faoro

Edward Farhi

Reza Fatemi

Ebrahim Forati

Brooks Riley Foxen

William Giang

Dar Gilboa

Alejandro Grajales Dau

Steve Habegger

Michael C. Hamilton

Sean Harrington

Jeremy Patterson Hilton

Trent Huang

Ashley Anne Huff

Sergei Isakov

Justin Thomas Iveland

Cody Jones

Pavol Juhas

Marika Kieferova

Andrey Klots

Alexander Korotkov

Fedor Kostritsa

John Mark Kreikebaum

Dave Landhuis

Pavel Laptev

Kim Ming Lau

Lily MeeKit Laws

Joonho Lee

Kenny Lee

Alexander T. Lill

Wayne Liu

Orion Martin

Trevor Johnathan Mccourt

Anthony Megrant

Xiao Mi

Masoud Mohseni

Shirin Montazeri

Alexis Morvan

Ramis Movassagh

Wojtek Mruczkiewicz

Charles Neill

Ani Nersisyan

Michael Newman

Jiun How Ng

Murray Nguyen

Alex Opremcak

Andre Gregory Petukhov

Rebecca Potter

Kannan Aryaperumal Sankaragomathi

Christopher Schuster

Mike Shearn

Aaron Shorter

Vladimir Shvarts

Jindra Skruzny

Vadim Smelyanskiy

Clarke Smith

Rolando Diego Somma

Doug Strain

Marco Szalay

Alfredo Torres

Guifre Vidal

Jamie Yao

Ping Yeh

Juhwan Yoo

Grayson Robert Young

Yaxing Zhang

Ningfeng Zhu

Christian Gogolin

Nature Physics (2023)

Preview abstract
An important measure of the development of quantum computing platforms has been the simulation of increasingly complex physical systems. Prior to fault-tolerant quantum computing, robust error mitigation strategies are necessary to continue this growth. Here, we study physical simulation within the seniority-zero electron pairing subspace, which affords both a computational stepping stone to a fully correlated model, and an opportunity to validate recently introduced ``purification-based'' error-mitigation strategies. We compare the performance of error mitigation based on doubling quantum resources in time (echo verification) or in space (virtual distillation), on up to 20 qubits of a superconducting qubit quantum processor. We observe a reduction of error by one to two orders of magnitude below less sophisticated techniques (e.g. post-selection); the gain from error mitigation is seen to increase with the system size. Employing these error mitigation strategies enables the implementation of the largest variational algorithm for a correlated chemistry system to-date. Extrapolating performance from these results allows us to estimate minimum requirements for a beyond-classical simulation of electronic structure. We find that, despite the impressive gains from purification-based error mitigation, significant hardware improvements will be required for classically intractable variational chemistry simulations.
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Fault-Tolerant Quantum Simulation of Materials Using Bloch Orbitals

Dominic Berry

Alec White

Eugene DePrince III

Sabrina Sicolo

Michael Kuehn

Michael Kaicher

Joonho Lee

PRX Quantum, vol. 4 (2023), pp. 040303

Preview 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 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. We find that even with these improvements, the quantum runtime of these algorithms is on the order of thousands of days and further algorithmic improvements are required to make realistic quantum simulation of materials practical.
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