Experimental Quantum Learning of a Spectral Decomposition

• URL: http://arxiv.org/abs/2104.03295v1
• Date: Wed, 7 Apr 2021 17:53:50 GMT
• Title: Experimental Quantum Learning of a Spectral Decomposition
• Authors: Michael R. Geller, Zo\"e Holmes, Patrick J. Coles, and Andrew Sornborger
• Abstract summary: Currently available quantum hardware allows for small scale implementations of quantum machine learning algorithms. Here we demonstrate the quantum learning of a two-qubit unitary by a sequence of three parameterized quantum circuits. We variationally diagonalize the unitary to learn its spectral decomposition.
• Score: 1.0499611180329804
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Currently available quantum hardware allows for small scale implementations of quantum machine learning algorithms. Such experiments aid the search for applications of quantum computers by benchmarking the near-term feasibility of candidate algorithms. Here we demonstrate the quantum learning of a two-qubit unitary by a sequence of three parameterized quantum circuits containing a total of 21 variational parameters. Moreover, we variationally diagonalize the unitary to learn its spectral decomposition, i.e., its eigenvalues and eigenvectors. We illustrate how this can be used as a subroutine to compress the depth of dynamical quantum simulations. One can view our implementation as a demonstration of entanglement-enhanced machine learning, as only a single (entangled) training data pair is required to learn a 4x4 unitary matrix.

Related papers

• Quantum algorithms for solving a drift-diffusion equation: A complexity analysis [0.04297070083645049]
  We present four quantum algorithms for solving a multidimensional drift-diffusion equation.<n>They rely on a quantum linear system solver, a quantum Hamiltonian simulation, a quantum random walk, and the quantum Fourier transform.
  arXiv  Detail & Related papers  (2025-05-27T14:09:14Z)
• Addressing the Readout Problem in Quantum Differential Equation Algorithms with Quantum Scientific Machine Learning [14.379311972506791]
  We show that the readout of exact quantum states poses a bottleneck due to the complexity of tomography. Treating outputs of quantum differential equation solvers as quantum data, we demonstrate that low-dimensional output can be extracted. We apply this quantum scientific machine learning approach to classify solutions for shock wave detection and turbulence modeling.
  arXiv  Detail & Related papers  (2024-11-21T16:09:08Z)
• 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)
• The curse of random quantum data [62.24825255497622]
  We quantify the performances of quantum machine learning in the landscape of quantum data. We find that the training efficiency and generalization capabilities in quantum machine learning will be exponentially suppressed with the increase in qubits. Our findings apply to both the quantum kernel method and the large-width limit of quantum neural networks.
  arXiv  Detail & Related papers  (2024-08-19T12:18:07Z)
• Supervised binary classification of small-scale digits images with a trapped-ion quantum processor [56.089799129458875]
  We show that a quantum processor can correctly solve the basic classification task considered. With the increase of the capabilities quantum processors, they can become a useful tool for machine learning.
  arXiv  Detail & Related papers  (2024-06-17T18:20:51Z)
• An Amplitude-Based Implementation of the Unit Step Function on a Quantum Computer [0.0]
  We introduce an amplitude-based implementation for approximating non-linearity in the form of the unit step function on a quantum computer. We describe two distinct circuit types which receive their input either directly from a classical computer, or as a quantum state when embedded in a more advanced quantum algorithm.
  arXiv  Detail & Related papers  (2022-06-07T07:14:12Z)
• Quantum Algorithms for Unsupervised Machine Learning and Neural Networks [2.28438857884398]
  We introduce quantum algorithms to solve tasks such as matrix product or distance estimation. These results are then used to develop new quantum algorithms for unsupervised machine learning. We will also present new quantum algorithms for neural networks, or deep learning.
  arXiv  Detail & Related papers  (2021-11-05T16:36:09Z)
• Adiabatic Quantum Graph Matching with Permutation Matrix Constraints [75.88678895180189]
  Matching problems on 3D shapes and images are frequently formulated as quadratic assignment problems (QAPs) with permutation matrix constraints, which are NP-hard. We propose several reformulations of QAPs as unconstrained problems suitable for efficient execution on quantum hardware. The proposed algorithm has the potential to scale to higher dimensions on future quantum computing architectures.
  arXiv  Detail & Related papers  (2021-07-08T17:59:55Z)
• Facial Expression Recognition on a Quantum Computer [68.8204255655161]
  We show a possible solution to facial expression recognition using a quantum machine learning approach. We define a quantum circuit that manipulates the graphs adjacency matrices encoded into the amplitudes of some appropriately defined quantum states.
  arXiv  Detail & Related papers  (2021-02-09T13:48:00Z)
• Information Scrambling in Computationally Complex Quantum Circuits [56.22772134614514]
  We experimentally investigate the dynamics of quantum scrambling on a 53-qubit quantum processor. We show that while operator spreading is captured by an efficient classical model, operator entanglement requires exponentially scaled computational resources to simulate.
  arXiv  Detail & Related papers  (2021-01-21T22:18:49Z)
• Quantum ensemble of trained classifiers [2.048335092363436]
  A quantum computer is capable of representing an exponentially large set of states, according to the number of qubits available. Quantum machine learning explores the potential of quantum computing to enhance machine learning algorithms.
  arXiv  Detail & Related papers  (2020-07-18T01:01:33Z)
• Variational Quantum Singular Value Decomposition [8.145223158030259]
  We propose a variational quantum algorithm for singular value decomposition (VQSVD) By exploiting the variational principles for singular values and the Ky Fan Theorem, we design a novel loss function such that two quantum neural networks could be trained to learn the singular vectors and output the corresponding singular values. Our work explores new avenues for quantum information processing beyond the conventional protocols that only works for Hermitian data.
  arXiv  Detail & Related papers  (2020-06-03T15:32:08Z)

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.