Quantum Advantage in Learning Quantum Dynamics via Fourier coefficient extraction

• URL: http://arxiv.org/abs/2506.17089v1
• Date: Fri, 20 Jun 2025 15:51:27 GMT
• Title: Quantum Advantage in Learning Quantum Dynamics via Fourier coefficient extraction
• Authors: Alice Barthe, Mahtab Yaghubi Rad, Michele Grossi, Vedran Dunjko,
• Abstract summary: We tackle the supervised learning version of the problem of learning unknown Hamiltonian dynamics.<n>We prove that this task can yield provable exponential classical-quantum learning advantages under common complexity assumptions in natural settings.<n>We discuss the limitations of generalizing our method to arbitrary quantum dynamics while maintaining provable guarantees.
• Score: 1.1999555634662633
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: One of the key challenges in quantum machine learning is finding relevant machine learning tasks with a provable quantum advantage. A natural candidate for this is learning unknown Hamiltonian dynamics. Here, we tackle the supervised learning version of this problem, where we are given random examples of the inputs to the dynamics as classical data, paired with the expectation values of some observable after the time evolution, as corresponding output labels. The task is to replicate the corresponding input-output function. We prove that this task can yield provable exponential classical-quantum learning advantages under common complexity assumptions in natural settings. To design our quantum learning algorithms, we introduce a new method, which we term \textit{\subroutine}~algorithm for parametrized circuit functions, and which may be of independent interest. Furthermore, we discuss the limitations of generalizing our method to arbitrary quantum dynamics while maintaining provable guarantees. We explain that significant generalizations are impossible under certain complexity-theoretic assumptions, but nonetheless, we provide a heuristic kernel method, where we trade-off provable correctness for broader applicability.

Related papers

• Quantum advantage for learning shallow neural networks with natural data distributions [4.363673971859799]
  We study an efficient quantum algorithm for learning periodic neurons in the QSQ model over a broad range of non-uniform distributions.<n>To our knowledge, our work is the first result in quantum learning theory for classical functions that explicitly considers real-valued functions.
  arXiv  Detail & Related papers  (2025-03-26T18:00:17Z)
• Fourier Neural Operators for Learning Dynamics in Quantum Spin Systems [77.88054335119074]
  We use FNOs to model the evolution of random quantum spin systems. We apply FNOs to a compact set of Hamiltonian observables instead of the entire $2n$ quantum wavefunction.
  arXiv  Detail & Related papers  (2024-09-05T07:18:09Z)
• Efficient Learning for Linear Properties of Bounded-Gate Quantum Circuits [63.733312560668274]
  Given a quantum circuit containing d tunable RZ gates and G-d Clifford gates, can a learner perform purely classical inference to efficiently predict its linear properties? We prove that the sample complexity scaling linearly in d is necessary and sufficient to achieve a small prediction error, while the corresponding computational complexity may scale exponentially in d. We devise a kernel-based learning model capable of trading off prediction error and computational complexity, transitioning from exponential to scaling in many practical settings.
  arXiv  Detail & Related papers  (2024-08-22T08:21:28Z)
• Noise-tolerant learnability of shallow quantum circuits from statistics and the cost of quantum pseudorandomness [0.0]
  We study the learnability of quantum circuits in the near term.<n>We adapt a learning algorithm for constant-depth quantum circuits to the quantum statistical query setting.<n>We prove that pseudorandom unitaries (PRUs) cannot be constructed using circuits of constant depth.
  arXiv  Detail & Related papers  (2024-05-20T14:55:20Z)
• Learning unitaries with quantum statistical queries [0.0]
  We propose several algorithms for learning unitary operators from quantum statistical queries (QSQs) Our methods hinge on a novel technique for estimating the Fourier mass of a unitary on a subset of Pauli strings with a single quantum statistical query. We show that quantum statistical queries lead to an exponentially larger sample complexity for certain tasks, compared to separable measurements to the Choi-Jamiolkowski state.
  arXiv  Detail & Related papers  (2023-10-03T17:56:07Z)
• Exponential separations between classical and quantum learners [2.209921757303168]
  We discuss how subtle differences in definitions can result in significantly different requirements and tasks for the learner to meet and solve. We present two new learning separations where the classical difficulty primarily lies in identifying the function generating the data.
  arXiv  Detail & Related papers  (2023-06-28T08:55:56Z)
• Classical Verification of Quantum Learning [42.362388367152256]
  We develop a framework for classical verification of quantum learning. We propose a new quantum data access model that we call "mixture-of-superpositions" quantum examples. Our results demonstrate that the potential power of quantum data for learning tasks, while not unlimited, can be utilized by classical agents.
  arXiv  Detail & Related papers  (2023-06-08T00:31:27Z)
• The Quantum Path Kernel: a Generalized Quantum Neural Tangent Kernel for Deep Quantum Machine Learning [52.77024349608834]
  Building a quantum analog of classical deep neural networks represents a fundamental challenge in quantum computing. Key issue is how to address the inherent non-linearity of classical deep learning. We introduce the Quantum Path Kernel, a formulation of quantum machine learning capable of replicating those aspects of deep machine learning.
  arXiv  Detail & Related papers  (2022-12-22T16:06:24Z)
• A didactic approach to quantum machine learning with a single qubit [68.8204255655161]
  We focus on the case of learning with a single qubit, using data re-uploading techniques. We implement the different proposed formulations in toy and real-world datasets using the qiskit quantum computing SDK.
  arXiv  Detail & Related papers  (2022-11-23T18:25:32Z)
• Noisy Quantum Kernel Machines [58.09028887465797]
  An emerging class of quantum learning machines is that based on the paradigm of quantum kernels. We study how dissipation and decoherence affect their performance. We show that decoherence and dissipation can be seen as an implicit regularization for the quantum kernel machines.
  arXiv  Detail & Related papers  (2022-04-26T09:52:02Z)
• Quantum algorithms for quantum dynamics: A performance study on the spin-boson model [68.8204255655161]
  Quantum algorithms for quantum dynamics simulations are traditionally based on implementing a Trotter-approximation of the time-evolution operator. variational quantum algorithms have become an indispensable alternative, enabling small-scale simulations on present-day hardware. We show that, despite providing a clear reduction of quantum gate cost, the variational method in its current implementation is unlikely to lead to a quantum advantage.
  arXiv  Detail & Related papers  (2021-08-09T18:00:05Z)
• Quantum advantage for differential equation analysis [13.39145467249857]
  We show how the output of quantum differential equation solving can serve as the input for quantum machine learning. These quantum algorithms provide an exponential advantage over existing classical Monte Carlo methods.
  arXiv  Detail & Related papers  (2020-10-29T17:19:04Z)
• Machine learning transfer efficiencies for noisy quantum walks [62.997667081978825]
  We show that the process of finding requirements on both a graph type and a quantum system coherence can be automated. The automation is done by using a convolutional neural network of a particular type that learns to understand with which network and under which coherence requirements quantum advantage is possible. Our results are of importance for demonstration of advantage in quantum experiments and pave the way towards automating scientific research and discoveries.
  arXiv  Detail & Related papers  (2020-01-15T18:36:53Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.