# Ryan Babbush

Ryan is the director of the Quantum Algorithm & Applications Team at Google. The mandate of this research team is to develop new and more efficient quantum algorithms, discovery and analyze new applications of quantum computers, build and open source tools for accelerating quantum algorithms research, and to design algorithms experiments to demonstrate on existing quantum devices.

Authored Publications

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Analyzing Prospects for Quantum Advantage in Topological Data Analysis

Dominic W. Berry

Yuan Su

Casper Gyurik

Robbie King

Joao Basso

Abhishek Rajput

Nathan Wiebe

Vedran Djunko

PRX Quantum, 5(2024), pp. 010319

Preview abstract
Lloyd et al. were first to demonstrate the promise of quantum algorithms for computing Betti numbers in persistent homology (a way of characterizing topological features of data sets). Here, we propose, analyze, and optimize an improved quantum algorithm for topological data analysis (TDA) with reduced scaling, including a method for preparing Dicke states based on inequality testing, a more efficient amplitude estimation algorithm using Kaiser windows, and an optimal implementation of eigenvalue projectors based on Chebyshev polynomials. We compile our approach to a fault-tolerant gate set and estimate constant factors in the Toffoli complexity. Our analysis reveals that super-quadratic quantum speedups are only possible for this problem when targeting a multiplicative error approximation and the Betti number grows asymptotically. Further, we propose a dequantization of the quantum TDA algorithm that shows that having exponentially large dimension and Betti number are necessary, but insufficient conditions, for super-polynomial advantage. We then introduce and analyze specific problem examples for which super-polynomial advantages may be achieved, and argue that quantum circuits with tens of billions of Toffoli gates can solve some seemingly classically intractable instances.
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Drug Design on Quantum Computers

Raffaele Santagati

Alán Aspuru-Guzik

Matthias Degroote

Leticia Gonzalez

Elica Kyoseva

Nikolaj Moll

Markus Oppel

Robert Parrish

Michael Streif

Christofer Tautermann

Horst Weiss

Nathan Wiebe

Clemens Utschig-Utschig

Nature Physics(2024)

Preview abstract
The promised industrial applications of quantum computers often rest on their anticipated ability to perform accurate, efficient quantum chemical calculations. Computational drug discovery relies on accurate predictions of how candidate drugs interact with their targets in a cellular environment involving several thousands of atoms at finite temperatures. Although quantum computers are still far from being used as daily tools in the pharmaceutical industry, here we explore the challenges and opportunities of applying quantum computers to drug design. We discuss where these could transform industrial research and identify the substantial further developments needed to reach this goal.
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Stable quantum-correlated many-body states through engineered dissipation

Xiao Mi

Alexios Michailidis

Sara Shabani

Jerome Lloyd

Rajeev Acharya

Igor Aleiner

Trond Andersen

Markus Ansmann

Frank Arute

Kunal Arya

Juan Atalaya

Gina Bortoli

Alexandre Bourassa

Leon Brill

Michael Broughton

Bob Buckley

Tim Burger

Nicholas Bushnell

Jimmy Chen

Benjamin Chiaro

Desmond Chik

Charina Chou

Josh Cogan

Roberto Collins

Paul Conner

William Courtney

Alex Crook

Ben Curtin

Alejo Grajales Dau

Dripto Debroy

Agustin Di Paolo

ILYA Drozdov

Andrew Dunsworth

Lara Faoro

Edward Farhi

Reza Fatemi

Vinicius Ferreira

Ebrahim Forati

Austin Fowler

Brooks Foxen

Élie Genois

William Giang

Dar Gilboa

Raja Gosula

Steve Habegger

Michael Hamilton

Monica Hansen

Sean Harrington

Paula Heu

Trent Huang

Ashley Huff

Bill Huggins

Sergei Isakov

Justin Iveland

Zhang Jiang

Cody Jones

Pavol Juhas

Kostyantyn Kechedzhi

Mostafa Khezri

Marika Kieferova

Alexei Kitaev

Andrey Klots

Alexander Korotkov

Fedor Kostritsa

John Mark Kreikebaum

Dave Landhuis

Pavel Laptev

Kim Ming Lau

Lily Laws

Joonho Lee

Kenny Lee

Yuri Lensky

Alexander Lill

Wayne Liu

Orion Martin

Amanda Mieszala

Shirin Montazeri

Alexis Morvan

Ramis Movassagh

Wojtek Mruczkiewicz

Charles Neill

Ani Nersisyan

Michael Newman

JiunHow Ng

Murray Ich Nguyen

Tom O'Brien

Alex Opremcak

Andre Petukhov

Rebecca Potter

Leonid Pryadko

Charles Rocque

Negar Saei

Kannan Sankaragomathi

Henry Schurkus

Christopher Schuster

Mike Shearn

Aaron Shorter

Noah Shutty

Vladimir Shvarts

Jindra Skruzny

Clarke Smith

Rolando Somma

George Sterling

Doug Strain

Marco Szalay

Alfredo Torres

Guifre Vidal

Benjamin Villalonga

Cheng Xing

Jamie Yao

Ping Yeh

Juhwan Yoo

Grayson Young

Yaxing Zhang

Ningfeng Zhu

Jeremy Hilton

Anthony Megrant

Yu Chen

Vadim Smelyanskiy

Dmitry Abanin

Science, 383(2024), pp. 1332-1337

Preview abstract
Engineered dissipative reservoirs have the potential to steer many-body quantum systems toward correlated steady states useful for quantum simulation of high-temperature superconductivity or quantum magnetism. Using up to 49 superconducting qubits, we prepared low-energy states of the transverse-field Ising model through coupling to dissipative auxiliary qubits. In one dimension, we observed long-range quantum correlations and a ground-state fidelity of 0.86 for 18 qubits at the critical point. In two dimensions, we found mutual information that extends beyond nearest neighbors. Lastly, by coupling the system to auxiliaries emulating reservoirs with different chemical potentials, we explored transport in the quantum Heisenberg model. Our results establish engineered dissipation as a scalable alternative to unitary evolution for preparing entangled many-body states on noisy quantum processors.
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Dynamics of magnetization at infinite temperature in a Heisenberg spin chain

Trond Andersen

Rhine Samajdar

Andre Petukhov

Jesse Hoke

Dmitry Abanin

ILYA Drozdov

Xiao Mi

Alexis Morvan

Charles Neill

Rajeev Acharya

Richard Ross Allen

Kyle Anderson

Markus Ansmann

Frank Arute

Kunal Arya

Juan Atalaya

Gina Bortoli

Alexandre Bourassa

Leon Brill

Michael Broughton

Bob Buckley

Tim Burger

Nicholas Bushnell

Juan Campero

Hung-Shen Chang

Jimmy Chen

Benjamin Chiaro

Desmond Chik

Josh Cogan

Roberto Collins

Paul Conner

William Courtney

Alex Crook

Ben Curtin

Agustin Di Paolo

Andrew Dunsworth

Clint Earle

Lara Faoro

Edward Farhi

Reza Fatemi

Vinicius Ferreira

Ebrahim Forati

Austin Fowler

Brooks Foxen

Gonzalo Garcia

Élie Genois

William Giang

Dar Gilboa

Raja Gosula

Alejo Grajales Dau

Steve Habegger

Michael Hamilton

Monica Hansen

Sean Harrington

Paula Heu

Gordon Hill

Trent Huang

Ashley Huff

Bill Huggins

Sergei Isakov

Justin Iveland

Zhang Jiang

Cody Jones

Pavol Juhas

Mostafa Khezri

Marika Kieferova

Alexei Kitaev

Andrey Klots

Alexander Korotkov

Fedor Kostritsa

John Mark Kreikebaum

Dave Landhuis

Pavel Laptev

Kim Ming Lau

Lily Laws

Joonho Lee

Kenny Lee

Yuri Lensky

Alexander Lill

Wayne Liu

Salvatore Mandra

Orion Martin

Steven Martin

Seneca Meeks

Amanda Mieszala

Shirin Montazeri

Ramis Movassagh

Wojtek Mruczkiewicz

Ani Nersisyan

Michael Newman

JiunHow Ng

Murray Ich Nguyen

Tom O'Brien

Seun Omonije

Alex Opremcak

Rebecca Potter

Leonid Pryadko

David Rhodes

Charles Rocque

Negar Saei

Kannan Sankaragomathi

Henry Schurkus

Christopher Schuster

Mike Shearn

Aaron Shorter

Noah Shutty

Vladimir Shvarts

Vlad Sivak

Jindra Skruzny

Clarke Smith

Rolando Somma

George Sterling

Doug Strain

Marco Szalay

Doug Thor

Alfredo Torres

Guifre Vidal

Benjamin Villalonga

Cheng Xing

Jamie Yao

Ping Yeh

Juhwan Yoo

Grayson Young

Yaxing Zhang

Ningfeng Zhu

Jeremy Hilton

Anthony Megrant

Yu Chen

Vadim Smelyanskiy

Vedika Khemani

Sarang Gopalakrishnan

Tomaž Prosen

Science, 384(2024), pp. 48-53

Preview abstract
Understanding universal aspects of quantum dynamics is an unresolved problem in statistical mechanics. In particular, the spin dynamics of the one-dimensional Heisenberg model were conjectured as to belong to the Kardar-Parisi-Zhang (KPZ) universality class based on the scaling of the infinite-temperature spin-spin correlation function. In a chain of 46 superconducting qubits, we studied the probability distribution of the magnetization transferred across the chain’s center, P(M). The first two moments of P(M) show superdiffusive behavior, a hallmark of KPZ universality. However, the third and fourth moments ruled out the KPZ conjecture and allow for evaluating other theories. Our results highlight the importance of studying higher moments in determining dynamic universality classes and provide insights into universal behavior in quantum systems.
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Quantum Computation of Stopping power for Inertial Fusion Target Design

Dominic Berry

Alina Kononov

Alec White

Joonho Lee

Andrew Baczewski

Proceedings of the National Academy of Sciences, 121(2024), e2317772121

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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Quantum Simulation of Exact Electron Dynamics can be more Efficient than Classical Mean-Field Methods

William J. Huggins

Dominic W. Berry

Shu Fay Ung

Andrew Zhao

David Reichman

Andrew Baczewski

Joonho Lee

Nature Communications, 14(2023), pp. 4058

Preview abstract
Quantum algorithms for simulating electronic ground states are slower than popular classical mean-field algorithms such as Hartree-Fock and density functional theory, but offer higher accuracy. Accordingly, quantum computers have been predominantly regarded as competitors to only the most accurate and costly classical methods for treating electron correlation. However, here we tighten bounds showing that certain first quantized quantum algorithms enable exact time evolution of electronic systems with exponentially less space and polynomially fewer operations in basis set size than conventional real-time time-dependent Hartree-Fock and density functional theory. Although the need to sample observables in the quantum algorithm reduces the speedup, we show that one can estimate all elements of the k-particle reduced density matrix with a number of samples scaling only polylogarithmically in basis set size. We also introduce a more efficient quantum algorithm for first quantized mean-field state preparation that is likely cheaper than the cost of time evolution. We conclude that quantum speedup is most pronounced for finite temperature simulations and suggest several practically important electron dynamics problems with potential quantum advantage.
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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, 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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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

Austin Fowler

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

Mostafa Khezri

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

Benjamin Villalonga

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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