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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Reinforcement Learning Control of Quantum Error Correction
Cameron Maxfield
Guifre Vidal
Bob Buckley
Jonathan Waltz
Christopher Wood
Reza Molavi
John Mark Kreikebaum
Rajeev Acharya
David Sobel
Abeer Vaishnav
Ali Hadjikhani
Ryuho Kudo
Wendy Leung
Brett Buchea
Ningfeng Zhu
Shirin Montazeri
Jamie Yao
Bicheng Ying
Eric Mascot
Lenny Fuste
Zhenjie Zou
Rodrigo Cortinas
Matt Lloyd
Clarke Smith
Kris Ottosson
Emma Ropes
Felix Borjans
Rebecca Potter
Sean Harrington
Jeremy Hilton
David Enriquez
Stephen Heslin
Paula Heu
Daniel Lundahl
Elliot Young
Alex Crook
Fedor Kostritsa
Roberto Rodriguez
Chia Ni
Kim Ming Lau
Priyanka Thiruraman
Martin Damyanov
Logan Oas
Dmitry Abanin
Oscar Higgott
Aaron Shorter
Steve Habegger
Aniket Maiti
Ryan Kaufman
Valerie Ehimhen
Sayra Alcaraz
Marcos Flores
Elizabeth Rossi
Aria Shahingohar
Dario Rosenstock
Travis Weidel
Steven Waltman
Kristi Wong
Murat Sarihan
Arun Kumar
Vladimir Shvarts
Matt Reagor
Alfredo Torres
Michael Qian
Anthony Megrant
Charles Neill
Christopher Hudspeth
Michael Hamilton
Bill Huggins
Laura De Lorenzo
Tan Ha
Ran Zhang
Dar Gilboa
Nicholas Bushnell
Sherman Peek
David Rhodes
Leigh Martin
Mike Shearn
Vlad Kurilovich
David Browne
Spencer Small
Brian Ballard
Will Oliver
Lior Ella
Orion Pritchard
Josh Cogan
Rachel Resnick
Dmitri Maslov
Jose Guerrero
Paul Masih Das
Theodore White
Helge Gehring
Nikita Astrakhantsev
Can Knaut
Maddy Woodson
Brooks Foxen
Frank Arute
Alejo Grajales Dau
Yaxing Zhang
Aaron Szasz
Alexander Lill
Justin Ledford
Xiaoxuan Jin
Andreas Kabel
Sid Madhuk
Orion Martin
Catherine Vollgraff Heidweiller
Gabrielle Roberts
Juan Campero
Juhwan Yoo
Robert Salazar
Michael Newman
Arpit Ranadive
James Goeders
William Giang
Gonzalo Garcia
Agnetta Cleland
Maddie Taylor
Dogan Timucin
Ross Alcaraz
Hui Kang
Johannes Bausch
William Courtney
Robert Gasca
Kevin Satzinger
Meghan Voorhees
Silas Chen
Laleh Beni
Andrew Dunsworth
Jamal Busnaina
Pavel Laptev
Kiseo Kang
Shannon Wang
Paul Donohoe
Paul Conner
Vadim Smelyanskiy
James Spencer
Benjamin Chiaro
Grayson Young
Tim Burger
ILYA Drozdov
Peter Brooks
Jordan Suchard
Austin Fowler
Jimmy Chen
Alec Eickbusch
Francisco Heras
Hung-Shen Chang
Michael Broughton
Jeanne Hartshorn
Aviv Elbag
Martin Bigdeli
Tanner Hadick
Juan Atalaya
Mahmoud Elzouka
Melvin Mathews
Alex Sztein
Markus Ansmann
Pavol Juhas
Bryan Cochrane
Murray Ich Nguyen
Ashley Maloney
Will Livingston
Roberto Collins
Ming Li
Élie Genois
Jeremiah Ford
Christopher Garrick
Sayan Das
David Peterson
Eifu Tomita
Suhas Ganjam
Reno Hiltermann
Dylan Bowers
Bryce Kobrin
Yu Chen
Dan Riley
Leon Brill
Barrett Spells
Ben Curtin
Mike Hucka
Seneca Meeks
Sebastian Molina
Tiano Lange-Dei
Georg Aigeldinger
Ashley Huff
Wing Li
ZLATKO MINEV
Monica Hansen
Sebastian Schroeder
Walt Askew
Dietrich Graumann
Elias Portoles
Stijn de Graaf
Matt Cockrell
Harold Cook
Masaya Fukami
Ed Gonzales
Robert Geiger
Amir Karamlou
Loick Le Guevel
Ebrahim Forati
Justin Vargas
Doug Thor
Joel Grebel
Lucia De Rose
LILY LI
Dave Landhuis
Emma Rosenfeld
Hsin-Yuan (Robert) Huang
Kenny Lee
Shaun Jevons
Ping Yeh
Amira Abbas
Kunal Arya
Henry Schurkus
Hector Bates
Ganesh Ramachandran
Sergey Vdovichev
Brayden Ware
Max Schaefer
Cheng Xing
Brandon Langley
Anthony Cabrera
Michel Devoret
Cody Jones
Vlad Sivak
Mert Torunbalci
Ben Kueffler
Chaitali Joshi
Raja Gosula
Joy Lee
Alexander Korotkov
Thomas Edlich
Aditya Locharla
Nathan Lacroix
George Sterling
Hao Tran
Kostyantyn Kechedzhi
Trond Andersen
Alexandre Bourassa
Aaron Lunt
Alan Fung
Alex Pizzuto
Salvatore Mandra
Alex Greene
Vitali Kutsko
Kannan Sankaragomathi
Sofia Springer
Vinicius Ferreira
Raymond Orosco
Nature (2026)
Preview abstract
The promise of fault-tolerant quantum computing is challenged by environmental drift that relentlessly degrades the quality of quantum operations. The contemporary solution, halting the entire quantum computation for recalibration, is unsustainable for the long runtimes of the future algorithms \cite{reiher2017elucidating,gidney2025factor}. We address this challenge by unifying calibration with computation, granting the quantum error correction process \cite{ryan2021realization,krinner2022realizing,sivak2023real,acharya2024quantum, bluvstein2024logical,bluvstein2025architectural,lacroix2025scaling} a dual role: its error detection events are not only used to correct the logical quantum state, but are also repurposed as a learning signal, teaching a reinforcement learning (RL) agent \cite{silver2017mastering,mnih2015human,levine2016end, shalev2016safe,ouyang2022training} to continuously steer the physical control parameters and stabilize the quantum system during the computation. We experimentally demonstrate this framework on a Willow superconducting processor, improving the logical stability of the surface code 3.5-fold against injected drift. By synthesizing our full suite of technological advances, including RL fine-tuning of the entire system and near-optimal decoding \cite{senior2025scalable, beni2025tesseract}, we achieve record performance of the surface and color codes, with average logical error per cycle of $\varepsilon_L=7.7\times10^{-4}$ and $\varepsilon_L=8.2\times10^{-3}$ respectively. Simulations of surface codes up to distance-15 with tens of thousands control parameters confirm the scalability of our RL framework, revealing an optimization speed that is independent of the system size. This work thus enables a new paradigm: a quantum computer that learns to self-improve directly from its errors and never stops computing.
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Securing Elliptic Curve Cryptocurrencies against Quantum Vulnerabilities: Resource Estimates and Mitigations
Michael Broughton
Thiago Bergamaschi
Justin Drake
Dan Boneh
PRX Quantum, 7 (2026), pp. 031001
Preview abstract
The expected emergence of cryptographically relevant quantum computers (CRQCs) will represent a singular discontinuity in the history of digital security, with wide ranging impacts. This whitepaper seeks to elucidate specific implications that the capabilities of developing quantum architectures have on blockchain vulnerabilities and potential mitigation strategies. First, we provide new resource estimates for breaking the 256-bit Elliptic Curve Discrete Logarithm Problem over the secp256k1 curve, the core of modern blockchain cryptography. We demonstrate that Shor's algorithm for this problem can execute with either $\leq 1200$ logical qubits and $\leq 90$ million Toffoli gates or $\leq 1450$ logical qubits and $\leq 70$ million Toffoli gates. In the interest of responsible disclosure, we use a zero-knowledge proof to validate these results without disclosing attack vectors. On superconducting architectures with $10^{-3}$ physical error rates and planar connectivity, those circuits can execute in minutes using fewer than half a million physical qubits. We introduce a critical distinction between ``fast-clock'' (such as superconducting and photonic) and ``slow-clock'' (such as neutral atom and ion trap) architectures. Our analysis reveals that the first fast-clock CRQCs would enable ``on-spend'' attacks on public mempool transactions of some cryptocurrencies. We survey major cryptocurrency vulnerabilities through this lens, identifying systemic risks associated with advanced features in some blockchains such as smart contracts, Proof-of-Stake consensus, and Data Availability Sampling mechanism, as well as the enduring concern of ``abandoned'' assets. We argue that technical solutions would benefit from accompanying public policy and discuss various frameworks of ``digital salvage'' to regulate the recovery or destruction of dormant assets while preventing adversarial seizure. We also discuss implications for other digital assets and tokenization as well as challenges and successful examples of the ongoing transition to Post-Quantum Cryptography (PQC). Finally, we urge all vulnerable cryptocurrency communities to join the migration to PQC without delay.
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Securing Elliptic Curve Cryptocurrencies against Quantum Vulnerabilities: Resource Estimates and Mitigations
Michael Broughton
Thiago Bergamaschi
Justin Drake
Dan Boneh
arXiv:2603.28846 (2026)
Preview abstract
This whitepaper seeks to elucidate implications that the capabilities of developing quantum architectures have on blockchain vulnerabilities and mitigation strategies. First, we provide new resource estimates for breaking the 256-bit Elliptic Curve Discrete Logarithm Problem, the core of modern blockchain cryptography. We demonstrate that Shor's algorithm for this problem can execute with either <1200 logical qubits and <90 million Toffoli gates or <1450 logical qubits and <70 million Toffoli gates. In the interest of responsible disclosure, we use a zero-knowledge proof to validate these results without disclosing attack vectors. On superconducting architectures with 1e-3 physical error rates and planar connectivity, those circuits can execute in minutes using fewer than half a million physical qubits. We introduce a critical distinction between fast-clock (such as superconducting and photonic) and slow-clock (such as neutral atom and ion trap) architectures. Our analysis reveals that the first fast-clock CRQCs would enable on-spend attacks on public mempool transactions of some cryptocurrencies. We survey major cryptocurrency vulnerabilities through this lens, identifying systemic risks associated with advanced features in some blockchains such as smart contracts, Proof-of-Stake consensus, and Data Availability Sampling, as well as the enduring concern of abandoned assets. We argue that technical solutions would benefit from accompanying public policy and discuss various frameworks of digital salvage to regulate the recovery or destruction of dormant assets while preventing adversarial seizure. We also discuss implications for other digital assets and tokenization as well as challenges and successful examples of the ongoing transition to Post-Quantum Cryptography (PQC). Finally, we urge all vulnerable cryptocurrency communities to join the ongoing migration to PQC without delay.
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Spectral amplification for ground-state energy estimation of electronic structure in first quantization
Alicja Dutkiewicz
Alec White
Guang Hao Low
Albert Eugene DePrince III
Marika Kieferova
Dominic Berry
arXiv:2607.15358 (2026)
Preview abstract
We demonstrate an asymptotic gate complexity improvement in first-quantized ground-state energy estimation of electronic structure Hamiltonians in a plane wave basis by employing the sum-of-squares spectral gap amplification protocol. The improvement relies on identifying a sum-of-squares representation of the Hamiltonian which provides a lower bound certificate and low cost block encoding that leads to a provably lower quantum phase estimation gate cost. This is achieved by using a sum-of-squares operator generated by the total charge density operator resulting in a block encoding normalization improvement of $\lambda = \mathcal{O}\left(\eta\Delta^{-1.5}+\eta^{1.5}\Delta^{-1} \right)$ compared to prior work $\lambda = \mathcal{O}(\eta\Delta^{-2}+\eta^2\Delta^{-1})$ where $\eta$ is the number of electrons and $\Delta$ is the simulation grid spacing. The asymptotic reduction in block encoding normalization and similar block encoding costs to prior work is demonstrated to reduce resource estimates for materials and chemical systems by a factor of $2 - 44\times$ corresponding to the lowest cost estimates for \textit{ab initio} materials simulation.
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Exponential quantum advantage in processing massive classical data
Haimeng Zhao
Alexander Zlokapa
John Preskill
Hsin-Yuan (Robert) Huang
arXiv:2604.07639 (2026)
Preview abstract
Broadly applicable quantum advantage, particularly in classical data processing and machine learning, has been a fundamental open problem. In this work, we prove that a small quantum computer of polylogarithmic size can perform large-scale classification and dimension reduction on massive classical data by processing samples on the fly, whereas any classical machine achieving the same prediction performance requires exponentially larger size. Furthermore, classical machines that are exponentially larger yet below the required size need superpolynomially more samples and time. We validate these quantum advantages in real-world applications, including single-cell RNA sequencing and movie review sentiment analysis, demonstrating four to six orders of magnitude reduction in size with fewer than 60 logical qubits. These quantum advantages are enabled by quantum oracle sketching, an algorithm for accessing the classical world in quantum superposition using only random classical data samples. Combined with classical shadows, our algorithm circumvents the data loading and readout bottleneck to construct succinct classical models from massive classical data, a task provably impossible for any classical machine that is not exponentially larger than the quantum machine. These quantum advantages persist even when classical machines are granted unlimited time or if BPP=BQP, and rely only on the correctness of quantum mechanics. Together, our results establish machine learning on classical data as a broad and natural domain of quantum advantage and a fundamental test of quantum mechanics at the complexity frontier.
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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.
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Preview abstract
We describe an efficient quantum algorithm for solving the linear matrix equation AX+XB=C, where A, B and C are given complex matrices and X is unknown. This is known as the Sylvester equation, a fundamental equation with applications in control theory and physics. Rather than encoding the solution in a quantum state in a fashion analogous to prior quantum linear algebra solvers, our approach constructs the solution matrix X in a block-encoding, rescaled by some factor. This allows us to obtain certain properties of the entries of X exponentially faster than would be possible from preparing X as a quantum state. The query and gate complexities of the quantum circuit that implements this block-encoding are almost linear in a condition number that depends on A and B, and depend logarithmically in the dimension and inverse error. We show how our quantum circuits can solve BQP-complete problems efficiently, discuss potential applications and extensions of our approach, its connection to Riccati equation, and comment on open problems.
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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.
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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.
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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 FeMo cofactor by estimating the overlap of different MPS initial states with potential ground states of the FeMo 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 FeMo 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.
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