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.
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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)
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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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Quantum Advantage in Topological Data Analysis via Mayer Homology
Anh Nghiem
Dominic Berry
Trung Phan
Guo-Wei Wei
Ryu Hayakawa
arXiv:2609.28058 (2026)
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Prior work has explored quantum algorithms for topological data analysis (TDA), revealing the possibility of exponential quantum speedups in estimating the ratios of Betti numbers to the dimension of the combinatorial Laplacian. However, this quantity is only non-vanishing and efficient-to-quantumly-estimate when Betti numbers are exponentially large, a case for which concrete examples are rarely known. Furthermore, certain randomized classical algorithms are sometimes efficient in this regime. Thus, the prospect of achieving quantum advantage in conventional TDA appears fairly narrow. Here, we address these challenges to the quantum advantage in TDA by developing quantum algorithms for Mayer homology, which generalize simplicial homology to N-nilpotent boundary operators (∂N=0) and have recently been successfully applied to real-world TDA contexts. We introduce an efficient quantum algorithm for estimating Mayer Betti numbers and their persistent counterparts. We then prove that for high-order simplices, Mayer Betti numbers are often exponentially large in the dense regime, which ameliorates the normalization bottleneck of conventional quantum TDA. In the same regime, we argue that existing dequantization algorithms developed for conventional TDA, when applied to Mayer homology, generally lose theoretical guaranties, facing certain structural barriers that prevent their practical utilities. We also provide logical resource estimates revealing that a quantum computer with roughly a few hundred qubits and sixty million Toffoli gates could solve Mayer homology problems beyond the capabilities of known classical approaches. Finally, we discuss real-world applications of Mayer homology in genomics, supersymmetry, drug discovery, and neuroscience, revealing the potential of our quantum algorithm to deliver real-world impacts via Mayer homology.
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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)
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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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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
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
Noah Shutty
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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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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Machine learning quantum data to accelerate quantum Monte Carlo
Tong Jiang
Andrew Zhao
Shashwat Kumar
Jigyasa Nigam
Andrew Baczewski
Bill Huggins
Joonho Lee
arXiv:2611.08151 (2026)
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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The Grand Challenge of Quantum Applications
Robbie King
Bill Huggins
Guang Hao Low
Tom O'Brien
arXiv:2511.09124 (2025)
Preview abstract
This perspective outlines promising pathways and critical obstacles on the road to developing useful quantum computing applications, drawing on insights from the Google Quantum AI team. We propose a five-stage framework for this process, spanning from theoretical explorations of quantum advantage to the practicalities of compilation and resource estimation. For each stage, we discuss key trends, milestones, and inherent scientific and sociological impediments. We argue that two central stages -- identifying concrete problem instances expected to exhibit quantum advantage, and connecting such problems to real-world use cases -- represent essential and currently under-resourced challenges. Throughout, we touch upon related topics, including the promise of generative artificial intelligence for aspects of this research, criteria for compelling demonstrations of quantum advantage, and the future of compilation as we enter the era of early fault-tolerant quantum computing.
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The FLuid Allocation of Surface Code Qubits (FLASQ) Cost Model for Early Fault-Tolerant Quantum Algorithms
Bill Huggins
Amanda Xu
Matthew Harrigan
Christopher Kang
Guang Hao Low
Austin Fowler
arXiv:2511.08508 (2025)
Preview abstract
Holistic resource estimates are essential for guiding the development of fault-tolerant quantum algorithms and the computers they will run on. This is particularly true when we focus on highly-constrained early fault-tolerant devices. Many attempts to optimize algorithms for early fault-tolerance focus on simple metrics, such as the circuit depth or T-count. These metrics fail to capture critical overheads, such as the spacetime cost of Clifford operations and routing, or miss they key optimizations. We propose the FLuid Allocation of Surface code Qubits (FLASQ) cost model, tailored for architectures that use a two-dimensional lattice of qubits to implement the two-dimensional surface code. FLASQ abstracts away the complexity of routing by assuming that ancilla space and time can be fluidly rearranged, allowing for the tractable estimation of spacetime volume while still capturing important details neglected by simpler approaches. At the same time, it enforces constraints imposed by the circuit's measurement depth and the processor's reaction time. We apply FLASQ to analyze the cost of a standard two-dimensional lattice model simulation, finding that modern advances (such as magic state cultivation and the combination of quantum error correction and mitigation) reduce both the time and space required for this task by an order of magnitude compared with previous estimates. We also analyze the Hamming weight phasing approach to synthesizing parallel rotations, revealing that despite its low T-count, the overhead from imposing a 2D layout and from its use of additional ancilla qubits will make it challenging to benefit from in early fault-tolerance. We hope that the FLASQ cost model will help to better align early fault-tolerant algorithmic design with actual hardware realization costs without demanding excessive knowledge of quantum error correction from quantum algorithmists.
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Generative Quantum Advantage for Classical and Quantum Problems
Robert Huang
Michael Broughton
Norhan Eassa
arXiv:2509.09033 (2025)
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Recent breakthroughs in generative machine learning, powered by massive computational resources, have demonstrated unprecedented human-like capabilities. While beyond-classical quantum experiments can generate samples from classically intractable distributions, their complexity has thwarted all efforts toward efficient learning. This challenge has hindered demonstrations of generative quantum advantage: the ability of quantum computers to learn and generate desired outputs substantially better than classical computers. We resolve this challenge by introducing families of generative quantum models that are hard to simulate classically, are efficiently trainable, exhibit no barren plateaus or proliferating local minima, and can learn to generate distributions beyond the reach of classical computers. Using a 68-qubit superconducting quantum processor, we demonstrate these capabilities in two scenarios: learning classically intractable probability distributions and learning quantum circuits for accelerated physical simulation. Our results establish that both learning and sampling can be performed efficiently in the beyond-classical regime, opening new possibilities for quantum-enhanced generative models with provable advantage.
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