Ryan Babbush

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, discover and analyze new applications of quantum computers, build and open source tools for accelerating quantum algorithms research and compilation, and to design algorithmic experiments to execute on existing and future fault-tolerant quantum devices.
Authored Publications
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    Quantum simulation with sum-of-squares spectral amplification
    Robbie King
    Guang Hao Low
    Rolando Somma
    arXiv:2505.01528 (2025)
    Preview abstract We introduce sum-of-squares spectral amplification (SOSSA), a framework for improving quantum simulation algorithms relevant to low-energy problems. SOSSA first represents the Hamiltonian as a sum-of-squares and then applies spectral amplification to amplify the low-energy spectrum. The sum-of-squares representation can be obtained using semidefinite programming. We show that SOSSA can improve the efficiency of traditional methods in several simulation tasks involving low-energy states. Specifically, we provide fast quantum algorithms for energy and phase estimation that improve over the state-of-the-art in both query and gate complexities, complementing recent results on fast time evolution of low-energy states. To further illustrate the power of SOSSA, we apply it to the Sachdev-Ye-Kitaev model, a representative strongly correlated system, where we demonstrate asymptotic speedups by a factor of the square root of the system size. Notably, SOSSA was recently used in [G.H. Low \textit{et al.}, arXiv:2502.15882 (2025)] to achieve state-of-art costs for phase estimation of real-world quantum chemistry systems. View details
    Fast electronic structure quantum simulation by spectrum amplification
    Guang Hao Low
    Robbie King
    Dominic Berry
    Qiushi Han
    Albert Eugene DePrince III
    Alec White
    Rolando Somma
    arXiv:2502.15882 (2025)
    Preview abstract The most advanced techniques using fault-tolerant quantum computers to estimate the ground-state energy of a chemical Hamiltonian involve compression of the Coulomb operator through tensor factorizations, enabling efficient block-encodings of the Hamiltonian. A natural challenge of these methods is the degree to which block-encoding costs can be reduced. We address this challenge through the technique of spectrum amplification, which magnifies the spectrum of the low-energy states of Hamiltonians that can be expressed as sums of squares. Spectrum amplification enables estimating ground-state energies with significantly improved cost scaling in the block encoding normalization factor $\Lambda$ to just $\sqrt{2\Lambda E_{\text{gap}}}$, where $E_{\text{gap}} \ll \Lambda$ is the lowest energy of the sum-of-squares Hamiltonian. To achieve this, we show that sum-of-squares representations of the electronic structure Hamiltonian are efficiently computable by a family of classical simulation techniques that approximate the ground-state energy from below. In order to further optimize, we also develop a novel factorization that provides a trade-off between the two leading Coulomb integral factorization schemes-- namely, double factorization and tensor hypercontraction-- that when combined with spectrum amplification yields a factor of 4 to 195 speedup over the state of the art in ground-state energy estimation for models of Iron-Sulfur complexes and a CO$_{2}$-fixation catalyst. View details
    Shadow Hamiltonian Simulation
    Rolando Somma
    Robbie King
    Tom O'Brien
    Nature Communications, 16 (2025), pp. 2690
    Preview abstract Simulating quantum dynamics is one of the most important applications of quantum computers. Traditional approaches for quantum simulation involve preparing the full evolved state of the system and then measuring some physical quantity. Here, we present a different and novel approach to quantum simulation that uses a compressed quantum state that we call the "shadow state". The amplitudes of this shadow state are proportional to the time-dependent expectations of a specific set of operators of interest, and it evolves according to its own Schrödinger equation. This evolution can be simulated on a quantum computer efficiently under broad conditions. Applications of this approach to quantum simulation problems include simulating the dynamics of exponentially large systems of free fermions or free bosons, the latter example recovering a recent algorithm for simulating exponentially many classical harmonic oscillators. These simulations are hard for classical methods and also for traditional quantum approaches, as preparing the full states would require exponential resources. Shadow Hamiltonian simulation can also be extended to simulate expectations of more complex operators such as two-time correlators or Green's functions, and to study the evolution of operators themselves in the Heisenberg picture. View details
    Visualizing Dynamics of Charges and Strings in (2+1)D Lattice Gauge Theories
    Tyler Cochran
    Bernhard Jobst
    Yuri Lensky
    Gaurav Gyawali
    Norhan Eassa
    Melissa Will
    Aaron Szasz
    Dmitry Abanin
    Rajeev Acharya
    Laleh Beni
    Trond Andersen
    Markus Ansmann
    Frank Arute
    Kunal Arya
    Abe Asfaw
    Juan Atalaya
    Brian Ballard
    Alexandre Bourassa
    Michael Broughton
    David Browne
    Brett Buchea
    Bob Buckley
    Tim Burger
    Nicholas Bushnell
    Anthony Cabrera
    Juan Campero
    Hung-Shen Chang
    Jimmy Chen
    Benjamin Chiaro
    Jahan Claes
    Agnetta Cleland
    Josh Cogan
    Roberto Collins
    Paul Conner
    William Courtney
    Alex Crook
    Ben Curtin
    Sayan Das
    Laura De Lorenzo
    Agustin Di Paolo
    Paul Donohoe
    ILYA Drozdov
    Andrew Dunsworth
    Alec Eickbusch
    Aviv Elbag
    Mahmoud Elzouka
    Vinicius Ferreira
    Ebrahim Forati
    Austin Fowler
    Brooks Foxen
    Suhas Ganjam
    Robert Gasca
    Élie Genois
    William Giang
    Dar Gilboa
    Raja Gosula
    Alejo Grajales Dau
    Dietrich Graumann
    Alex Greene
    Steve Habegger
    Monica Hansen
    Sean Harrington
    Paula Heu
    Oscar Higgott
    Jeremy Hilton
    Robert Huang
    Ashley Huff
    Bill Huggins
    Cody Jones
    Chaitali Joshi
    Pavol Juhas
    Hui Kang
    Amir Karamlou
    Kostyantyn Kechedzhi
    Trupti Khaire
    Bryce Kobrin
    Alexander Korotkov
    Fedor Kostritsa
    John Mark Kreikebaum
    Vlad Kurilovich
    Dave Landhuis
    Tiano Lange-Dei
    Brandon Langley
    Kim Ming Lau
    Justin Ledford
    Kenny Lee
    Loick Le Guevel
    Wing Li
    Alexander Lill
    Will Livingston
    Daniel Lundahl
    Aaron Lunt
    Sid Madhuk
    Ashley Maloney
    Salvatore Mandra
    Leigh Martin
    Orion Martin
    Cameron Maxfield
    Seneca Meeks
    Anthony Megrant
    Reza Molavi
    Sebastian Molina
    Shirin Montazeri
    Ramis Movassagh
    Charles Neill
    Michael Newman
    Murray Ich Nguyen
    Chia Ni
    Kris Ottosson
    Alex Pizzuto
    Rebecca Potter
    Orion Pritchard
    Ganesh Ramachandran
    Matt Reagor
    David Rhodes
    Gabrielle Roberts
    Kannan Sankaragomathi
    Henry Schurkus
    Mike Shearn
    Aaron Shorter
    Noah Shutty
    Vladimir Shvarts
    Vlad Sivak
    Spencer Small
    Clarke Smith
    Sofia Springer
    George Sterling
    Jordan Suchard
    Alex Sztein
    Doug Thor
    Mert Torunbalci
    Abeer Vaishnav
    Justin Vargas
    Sergey Vdovichev
    Guifre Vidal
    Steven Waltman
    Shannon Wang
    Brayden Ware
    Kristi Wong
    Cheng Xing
    Jamie Yao
    Ping Yeh
    Bicheng Ying
    Juhwan Yoo
    Grayson Young
    Yaxing Zhang
    Ningfeng Zhu
    Yu Chen
    Vadim Smelyanskiy
    Adam Gammon-Smith
    Frank Pollmann
    Michael Knap
    Nature, 642 (2025), 315–320
    Preview abstract Lattice gauge theories (LGTs) can be used to understand a wide range of phenomena, from elementary particle scattering in high-energy physics to effective descriptions of many-body interactions in materials. Studying dynamical properties of emergent phases can be challenging, as it requires solving many-body problems that are generally beyond perturbative limits. Here we investigate the dynamics of local excitations in a LGT using a two-dimensional lattice of superconducting qubits. We first construct a simple variational circuit that prepares low-energy states that have a large overlap with the ground state; then we create charge excitations with local gates and simulate their quantum dynamics by means of a discretized time evolution. As the electric field coupling constant is increased, our measurements show signatures of transitioning from deconfined to confined dynamics. For confined excitations, the electric field induces a tension in the string connecting them. Our method allows us to experimentally image string dynamics in a (2+1)D LGT, from which we uncover two distinct regimes inside the confining phase: for weak confinement, the string fluctuates strongly in the transverse direction, whereas for strong confinement, transverse fluctuations are effectively frozen. We also demonstrate a resonance condition at which dynamical string breaking is facilitated. Our LGT implementation on a quantum processor presents a new set of techniques for investigating emergent excitations and string dynamics. View details
    Quartic Quantum Speedups for Planted Inference Problems
    Alexander Schmidhuber
    Ryan O'Donnell
    Physical Review X, 15 (2025), pp. 021077
    Preview abstract We describe a quantum algorithm for the Planted Noisy kXOR problem (also known as sparse Learning Parity with Noise) that achieves a nearly quartic (4th power) speedup over the best known classical algorithm while also only using logarithmically many qubits. Our work generalizes and simplifies prior work of Hastings, by building on his quantum algorithm for the Tensor Principal Component Analysis (PCA) problem. We achieve our quantum speedup using a general framework based on the Kikuchi Method (recovering the quartic speedup for Tensor PCA), and we anticipate it will yield similar speedups for further planted inference problems. These speedups rely on the fact that planted inference problems naturally instantiate the Guided Sparse Hamiltonian problem. Since the Planted Noisy kXOR problem has been used as a component of certain cryptographic constructions, our work suggests that some of these are susceptible to super-quadratic quantum attacks. View details
    Rapid Initial-State Preparation for the Quantum Simulation of Strongly Correlated Molecules
    Dominic Berry
    Yu Tong
    Alec White
    Tae In Kim
    Lin Lin
    Seunghoon Lee
    Garnet Chan
    PRX Quantum, 6 (2025), pp. 020327
    Preview abstract 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 by 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 × 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 minimize 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 Fe-S cluster systems, including the Fe⁢Mo cofactor by estimating the overlap of different MPS initial states with potential ground states of the Fe⁢Mo cofactor using an extrapolation procedure. With a modest MPS bond dimension of 4000, our procedure produces an estimate of approximately 0.9 overlap squared with a candidate ground state of the Fe⁢Mo cofactor, producing a total resource estimate of 7.3e10 Toffoli gates; neglecting the search over candidates and assuming the accuracy of the extrapolation, this validates prior estimates that have used perfect ground-state overlap. This presents an example of a practical path to prepare states of high overlap in a challenging-to-compute chemical system. View details
    Triply efficient shadow tomography
    Robbie King
    David Gosset
    PRX Quantum, 6 (2025), pp. 010336
    Preview abstract Given copies of a quantum state $\rho$, a shadow tomography protocol aims to learn all expectation values from a fixed set of observables, to within a given precision $\epsilon$. We say that a shadow tomography protocol is \textit{triply efficient} if it is sample- and time-efficient, and only employs measurements that entangle a constant number of copies of $\rho$ at a time. The classical shadows protocol based on random single-copy measurements is triply efficient for the set of local Pauli observables. This and other protocols based on random single-copy Clifford measurements can be understood as arising from fractional colorings of a graph $G$ that encodes the commutation structure of the set of observables. Here we describe a framework for two-copy shadow tomography that uses an initial round of Bell measurements to reduce to a fractional coloring problem in an induced subgraph of $G$ with bounded clique number. This coloring problem can be addressed using techniques from graph theory known as \textit{chi-boundedness}. Using this framework we give the first triply efficient shadow tomography scheme for the set of local fermionic observables, which arise in a broad class of interacting fermionic systems in physics and chemistry. We also give a triply efficient scheme for the set of all $n$-qubit Pauli observables. Our protocols for these tasks use two-copy measurements, which is necessary: sample-efficient schemes are provably impossible using only single-copy measurements. Finally, we give a shadow tomography protocol that compresses an $n$-qubit quantum state into a $\poly(n)$-sized classical representation, from which one can extract the expected value of any of the $4^n$ Pauli observables in $\poly(n)$ time, up to a small constant error. View details
    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. View details
    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
    Abe Asfaw
    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
    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. View details
    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. View details