# 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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Rapid initial state preparation for the quantum simulation of strongly correlated molecules and materials

Dominic Berry

Yu Tong

Alec White

Tae In Kim

Lin Lin

Seunghoon Lee

Garnet Chan

arXiv:2409.11748 (2024)

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Studies on quantum algorithms for ground state energy estimation often assume perfect ground state preparation; however, in reality the initial state will have imperfect overlap with the true ground state. Here we address that problem in two ways: by faster preparation of matrix product state (MPS) approximations, and more efficient filtering of the prepared state to find the ground state energy. We show how to achieve unitary synthesis with a Toffoli complexity about $7 \times$ lower than that in prior work, and use that to derive a more efficient MPS preparation method. For filtering we present two different approaches: sampling and binary search. For both we use the theory of window functions to avoid large phase errors and minimise the complexity. We find that the binary search approach provides better scaling with the overlap at the cost of a larger constant factor, such that it will be preferred for overlaps less than about 0.003. Finally, we estimate the total resources to perform ground state energy estimation of FeMoco and Iron cluster systems by estimating ground state overlap on an MPS initial state through extrapolation. With a modest bond dimension of 4000 we estimate a 0.96 overlap squared value producing total resources of $7.5 \times 10^{10}$ Toffoli gates; validating naive estimates where we assume perfect ground state overlap. These extrapolations allay practical concerns of exponential overlap decay in challenging-to-compute chemical systems.
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Expressing and Analyzing Quantum Algorithms with Qualtran

Charles Yuan

Anurudh Peduri

arXiv::2409.04643 (2024)

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Quantum computing's transition from theory to reality has spurred the need for novel software tools to manage the increasing complexity, sophistication, toil, and chance for error of quantum algorithm development. We present Qualtran, an open-source library for representing and analyzing quantum algorithms. Using carefully chosen abstractions and data structures, we can simulate and test algorithms, automatically generate information-rich diagrams, and tabulate resource requirements. Qualtran offers a \emph{standard library} of algorithmic building blocks that are essential for modern cost-minimizing compilations. Its capabilities are showcased through the re-analysis of key algorithms in Hamiltonian simulation, chemistry, and cryptography. The resulting architecture-independent resource counts can be forwarded to our implementation of cost models to estimate physical costs like wall-clock time and number of physical qubits assuming a surface-code architecture. Qualtran provides a foundation for explicit constructions and reproducible analysis, fostering greater collaboration within the quantum algorithm development community. We believe tools like Qualtran will accelerate progress in the field.
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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

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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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Optimization by Decoded Quantum Interferometry

Stephen Jordan

Noah Shutty

Mary Wootters

Alexander Schmidhuber

Robbie King

Sergei Isakov

arXiv:2408.08292 (2024)

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We introduce Decoded Quantum Interferometry (DQI), a quantum algorithm for reducing classical optimization problems to classical decoding problems by exploiting structure in the Fourier spectrum of the objective function. DQI reduces sparse max-XORSAT to decoding LDPC codes, which can be decoded using powerful classical algorithms such as belief propagation. As an initial benchmark, we compare DQI using belief propagation decoding against classical optimization via simulated annealing. In this setting we identify a family of max-XORSAT instances where DQI achieves a better approximation ratio on average than simulated annealing, although not better than specialized classical algorithms tailored to those instances. We also analyze a combinatorial optimization problem corresponding to finding polynomials that intersect the maximum number of points. There, DQI efficiently achieves a better approximation ratio than any polynomial-time classical algorithm known to us, thus realizing an apparent exponential quantum speedup. Finally, we show that the problem defined by Yamakawa and Zhandry in order to prove an exponential separation between quantum and classical query complexity is a special case of the optimization problem efficiently solved by DQI.
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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

Brooks Foxen

Élie Genois

William Giang

Dar Gilboa

Raja Gosula

Steve Habegger

Michael Hamilton

Monica Hansen

Sean Harrington

Paula Heu

Markus Hoffmann

Trent Huang

Ashley Huff

Bill Huggins

Sergei Isakov

Justin Iveland

Cody Jones

Pavol Juhas

Kostyantyn Kechedzhi

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

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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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)

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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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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

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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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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

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

Markus Hoffmann

Trent Huang

Ashley Huff

Bill Huggins

Sergei Isakov

Justin Iveland

Cody Jones

Pavol Juhas

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

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

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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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