Power of data in quantum machine learning

By Hsin-Yuan Huang, M. Broughton, Masoud Mohseni, Ryan Babbush, Sergio Boixo, Hartmut Neven, Jarrod R. McClean. Nature Communications, 2020

1,021 citations recorded by the source corpus.

The use of quantum computing for machine learning is among the most exciting prospective applications of quantum technologies. However, machine learning tasks where data is provided can be considerably different than commonly studied computational tasks. In this work, we show that some problems that are classically hard to compute can be easily predicted by classical machines learning from data. Using rigorous prediction error bounds as a foundation, we develop a methodology for assessing potential quantum advantage in learning tasks. The bounds are tight asymptotically and empirically predictive for a wide range of learning models. These constructions explain numerical results showing that with the help of data, classical machine learning models can be competitive with quantum models even if they are tailored to quantum problems. We then propose a projected quantum model that provides a simple and rigorous quantum speed-up for a learning problem in the fault-tolerant regime. For near-term implementations, we demonstrate a significant prediction advantage over some classical models on engineered data sets designed to demonstrate a maximal quantum advantage in one of the largest numerical tests for gate-based quantum machine learning to date, up to 30 qubits. Expectations for quantum machine learning are high, but there is currently a lack of rigorous results on which scenarios would actually exhibit a quantum advantage. Here, the authors show how to tell, for a given dataset, whether a quantum model would give any prediction advantage over a classical one.

Subfields: Artificial Intelligence

View Paper: https://www.semanticscholar.org/paper/57e6cca1479a4642f867e69b4dee93d14259dc3d

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Citations in the corpus

Barren plateaus in variational quantum computing (2024, neutral): “Exponential concentration also arises in kernel-based schemes 97,237–244 , in which a quantum computer is used as an enhanced feature space from which inner products or similarity measures between the data states can be estimated (similar to the kernel trick) 245–248 .”
Challenges and opportunities in quantum machine learning (2022, methodology): “However, one should be cautious about the availability of data in ML tasks, which makes classical ML algorithms computationally more powerful [13, 119].”
Quantum machine learning models are kernel methods (2021, background): “Section III C will discuss that this deﬁnition of the feature space is equivalent to the tensor product space of complex vectors ∣ ψ ⟩ ⊗ ∣ ψ ∗ ⟩ used in [12].”
Practical quantum advantage in quantum simulation (2022, methodology): “…simulating these models by using the large-scale entangling operations implied by many-body dynamics as a variational circuit that can form the basis for methods such as variational quantum eigensolver 105 , quantum approximate optimization 106 and quantum machine learning 53,69,71–73, 107 , 108 on”
Provably efficient machine learning for quantum many-body problems (2021, methodology): “Together, we rigorously establish the advantage ofMLalgorithms withdata over thosewithout data ( 36 ) in a physically relevant task.”
AI for Next Generation Computing: Emerging Trends and Future Directions (2022, neutral): “With quantum computers accelerating machine learning, the potential for impact s certain to be enormous [173].”
Quantum technology for military applications (2021, background): “A recent study [181] shows that quantum ML provides an advantage just for some kernels fitting particular problems.”