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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    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
    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
    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
    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
    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
    Shadow Hamiltonian Simulation
    Rolando Somma
    Robbie King
    Thomas O'Brien
    arXiv:2407.21775 (2024)
    Preview abstract We present shadow Hamiltonian simulation, a framework for simulating quantum dynamics using a compressed quantum state that we call the “shadow state”. The amplitudes of this shadow state are proportional to the expectations of a set of operators of interest. The shadow state evolves according to its own Schrodinger equation, and under broad conditions can be simulated on a quantum computer. We analyze a number of applications of this framework to quantum simulation problems. This includes simulating the dynamics of exponentially large systems of free fermions, or exponentially large systems of free bosons, the latter example recovering a recent algorithm for simulating exponentially many classical harmonic oscillators. Shadow Hamiltonian simulation can 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
    Preview abstract 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. View details
    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. View details