Jarrod R. McClean
Jarrod is a research scientist in the Google Quantum Artificial Intelligence laboratory. He received his PhD in Chemical Physics from Harvard University specializing in quantum chemistry and quantum computation supported by the US Department of Energy as a Computational Science Graduate Fellow. His research interests broadly include quantum computation, quantum chemistry, numerical methods, and information sparsity.
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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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The quest to identify quantum advantages, where quantum physics truly outperforms classical physics, lies at the heart of quantum technology. While quantum devices promise extraordinary capabilities, from exponential computational speedups to unprecedented measurement precision, distinguishing genuine advantages from mere illusions remains a formidable challenge. In this endeavor, quantum theorists are like prophets trying to foretell a future where quantum technologies reign supreme. Yet, the boundary between visionary insight and unfounded fantasy is perilously thin. In this perspective, we explore the properties defining an ideal quantum advantage and examine our mathematical tools for navigating the vast world of quantum advantages across computation, learning, sensing, communication, and beyond. We show that some quantum advantages are inherently unpredictable using classical resources alone, suggesting a landscape far richer than what we can currently foresee. While mathematical rigor remains our indispensable guide in this exploration, the ultimate power of quantum technologies may emerge from the quantum advantages we cannot yet conceive.
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Preview abstract
The quest to identify quantum advantages, where quantum physics truly outperforms classical physics, lies at the heart of quantum technology. While quantum devices promise extraordinary capabilities, from exponential computational speedups to unprecedented measurement precision, distinguishing genuine advantages from mere illusions remains a formidable challenge. In this endeavor, quantum theorists are like prophets trying to foretell a future where quantum technologies reign supreme. Yet, the boundary between visionary insight and unfounded fantasy is perilously thin. In this perspective, we explore the properties defining an ideal quantum advantage and examine our mathematical tools for navigating the vast world of quantum advantages across computation, learning, sensing, communication, and beyond. We show that some quantum advantages are inherently unpredictable using classical resources alone, suggesting a landscape far richer than what we can currently foresee. While mathematical rigor remains our indispensable guide in this exploration, the ultimate power of quantum technologies may emerge from the quantum advantages we cannot yet conceive.
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The application of quantum computers to machine learning tasks is an exciting potential direction to explore in search of quantum advantage. In the absence of large quantum computers to empirically evaluate performance, theoretical frameworks such as the quantum probably approximately correct (PAC) and quantum statistical query (QSQ) models have been proposed to study quantum algorithms for learning classical functions.
Despite numerous works investigating quantum advntage in these models, we nevertheless only understand it at two extremes: either exponential quantum advantages for uniform input distributions or no advantage for potentially adversarial distributions.
In this work, we study the gap between these two regimes by designing an efficient quantum algorithm for learning periodic neurons in the QSQ model over a broad range of non-uniform distributions, which includes Gaussian, generalized Gaussian, and logistic distributions.
To our knowledge, our work is also the first result in quantum learning theory for classical functions that explicitly considers real-valued functions.
Recent advances in classical learning theory prove that learning periodic neurons is hard for any classical gradient-based algorithm, giving us an exponential quantum advantage over such algorithms, which are the standard workhorses of machine learning.
Moreover, in some parameter regimes, the problem remains hard for classical statistical query algorithms and even general classical algorithms learning under small amounts of noise.
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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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Preview abstract
The application of quantum computers to machine learning tasks is an exciting potential direction to explore in search of quantum advantage. In the absence of large quantum computers to empirically evaluate performance, theoretical frameworks such as the quantum probably approximately correct (PAC) and quantum statistical query (QSQ) models have been proposed to study quantum algorithms for learning classical functions.
Despite numerous works investigating quantum advntage in these models, we nevertheless only understand it at two extremes: either exponential quantum advantages for uniform input distributions or no advantage for potentially adversarial distributions.
In this work, we study the gap between these two regimes by designing an efficient quantum algorithm for learning periodic neurons in the QSQ model over a broad range of non-uniform distributions, which includes Gaussian, generalized Gaussian, and logistic distributions.
To our knowledge, our work is also the first result in quantum learning theory for classical functions that explicitly considers real-valued functions.
Recent advances in classical learning theory prove that learning periodic neurons is hard for any classical gradient-based algorithm, giving us an exponential quantum advantage over such algorithms, which are the standard workhorses of machine learning.
Moreover, in some parameter regimes, the problem remains hard for classical statistical query algorithms and even general classical algorithms learning under small amounts of noise.
View details
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Protecting user privacy in financial transactions is desirable, yet in the classical world it is effectively impossible without hardware assumptions. Most existing quantum money schemes also fail to guarantee anonymity. We introduce a construction of single-use quantum tokens that give users the ability to detect whether the issuing authority is tracking them, for which we prove unconditional security. Our tokens do not require quantum communication from the users themselves, making them relatively practical to deploy.
We discuss potential applications including one-time payment tokens, anonymous one-time pads and voting.
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The Grand Challenge of Quantum Applications
Robbie King
Bill Huggins
Guang Hao Low
Tom O'Brien
arXiv:2511.09124 (2025)
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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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Preview abstract
The quest to identify quantum advantages, where quantum physics truly outperforms classical physics, lies at the heart of quantum technology. While quantum devices promise extraordinary capabilities, from exponential computational speedups to unprecedented measurement precision, distinguishing genuine advantages from mere illusions remains a formidable challenge. In this endeavor, quantum theorists are like prophets trying to foretell a future where quantum technologies reign supreme. Yet, the boundary between visionary insight and unfounded fantasy is perilously thin. In this perspective, we explore the properties defining an ideal quantum advantage and examine our mathematical tools for navigating the vast world of quantum advantages across computation, learning, sensing, communication, and beyond. We show that some quantum advantages are inherently unpredictable using classical resources alone, suggesting a landscape far richer than what we can currently foresee. While mathematical rigor remains our indispensable guide in this exploration, the ultimate power of quantum technologies may emerge from the quantum advantages we cannot yet conceive.
View details
Preview abstract
The quest to identify quantum advantages, where quantum physics truly outperforms classical physics, lies at the heart of quantum technology. While quantum devices promise extraordinary capabilities, from exponential computational speedups to unprecedented measurement precision, distinguishing genuine advantages from mere illusions remains a formidable challenge. In this endeavor, quantum theorists are like prophets trying to foretell a future where quantum technologies reign supreme. Yet, the boundary between visionary insight and unfounded fantasy is perilously thin. In this perspective, we explore the properties defining an ideal quantum advantage and examine our mathematical tools for navigating the vast world of quantum advantages across computation, learning, sensing, communication, and beyond. We show that some quantum advantages are inherently unpredictable using classical resources alone, suggesting a landscape far richer than what we can currently foresee. While mathematical rigor remains our indispensable guide in this exploration, the ultimate power of quantum technologies may emerge from the quantum advantages we cannot yet conceive.
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