Multidimensional Quantum Generative Modeling by Quantum Hartley Transform

• URL: http://arxiv.org/abs/2406.03856v1
• Date: Thu, 6 Jun 2024 08:42:09 GMT
• Title: Multidimensional Quantum Generative Modeling by Quantum Hartley Transform
• Authors: Hsin-Yu Wu, Vincent E. Elfving, Oleksandr Kyriienko,
• Abstract summary: We develop an approach for building quantum models based on the exponentially growing orthonormal basis of Hartley kernel functions. As a result, the developed quantum Hartley models offer a distinct quantum approach to generative AI at increasing scale.
• Score: 16.34646723046073
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We develop an approach for building quantum models based on the exponentially growing orthonormal basis of Hartley kernel functions. First, we design a differentiable Hartley feature map parametrized by real-valued argument that enables quantum models suitable for solving stochastic differential equations and regression problems. Unlike the naturally complex Fourier encoding, the proposed Hartley feature map circuit leads to quantum states with real-valued amplitudes, introducing an inductive bias and natural regularization. Next, we propose a quantum Hartley transform circuit as a map between computational and Hartley basis. We apply the developed paradigm to generative modeling from solutions of stochastic differential equations, and utilize the quantum Hartley transform for fine sampling from parameterized distributions through an extended register. Finally, we present tools for implementing multivariate quantum generative modeling for both correlated and uncorrelated distributions. As a result, the developed quantum Hartley models offer a distinct quantum approach to generative AI at increasing scale.

Related papers

• Wasserstein Quantum Monte Carlo: A Novel Approach for Solving the Quantum Many-Body Schr\"odinger Equation [56.9919517199927]
  "Wasserstein Quantum Monte Carlo" (WQMC) uses the gradient flow induced by the Wasserstein metric, rather than Fisher-Rao metric, and corresponds to transporting the probability mass, rather than teleporting it. We demonstrate empirically that the dynamics of WQMC results in faster convergence to the ground state of molecular systems.
  arXiv  Detail & Related papers  (2023-07-06T17:54:08Z)
• Quantum Chebyshev Transform: Mapping, Embedding, Learning and Sampling Distributions [18.124351208075062]
  We show how to encode data into quantum states with amplitudes growing exponentially in the system size. We propose an embedding circuit for generating the orthonormal Chebyshev basis of exponential capacity. This enables automatic model differentiation, and opens a route to solving differential equations.
  arXiv  Detail & Related papers  (2023-06-29T15:19:32Z)
• Quantum Gate Generation in Two-Level Open Quantum Systems by Coherent and Incoherent Photons Found with Gradient Search [77.34726150561087]
  We consider an environment formed by incoherent photons as a resource for controlling open quantum systems via an incoherent control. We exploit a coherent control in the Hamiltonian and an incoherent control in the dissipator which induces the time-dependent decoherence rates.
  arXiv  Detail & Related papers  (2023-02-28T07:36:02Z)
• On Quantum Circuits for Discrete Graphical Models [1.0965065178451106]
  We provide the first method that allows one to provably generate unbiased and independent samples from general discrete factor models. Our method is compatible with multi-body interactions and its success probability does not depend on the number of variables. Experiments with quantum simulation as well as actual quantum hardware show that our method can carry out sampling and parameter learning on quantum computers.
  arXiv  Detail & Related papers  (2022-06-01T11:03:51Z)
• Quantum Kernel Methods for Solving Differential Equations [21.24186888129542]
  We propose several approaches for solving differential equations (DEs) with quantum kernel methods. We compose quantum models as weighted sums of kernel functions, where variables are encoded using feature maps and model derivatives are represented.
  arXiv  Detail & Related papers  (2022-03-16T18:56:35Z)
• Protocols for Trainable and Differentiable Quantum Generative Modelling [21.24186888129542]
  We propose an approach for learning probability distributions as differentiable quantum circuits (DQC) We perform training of a DQC-based model, where data is encoded in a latent space with a phase feature map, followed by a variational quantum circuit. This allows fast sampling from parametrized distributions using a single-shot readout.
  arXiv  Detail & Related papers  (2022-02-16T18:55:48Z)
• 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)
• Algebraic Compression of Quantum Circuits for Hamiltonian Evolution [52.77024349608834]
  Unitary evolution under a time dependent Hamiltonian is a key component of simulation on quantum hardware. We present an algorithm that compresses the Trotter steps into a single block of quantum gates. This results in a fixed depth time evolution for certain classes of Hamiltonians.
  arXiv  Detail & Related papers  (2021-08-06T19:38:01Z)
• Bernstein-Greene-Kruskal approach for the quantum Vlasov equation [91.3755431537592]
  The one-dimensional stationary quantum Vlasov equation is analyzed using the energy as one of the dynamical variables. In the semiclassical case where quantum tunneling effects are small, an infinite series solution is developed.
  arXiv  Detail & Related papers  (2021-02-18T20:55:04Z)
• Alternative quantisation condition for wavepacket dynamics in a hyperbolic double well [0.0]
  We propose an analytical approach for computing the eigenspectrum and corresponding eigenstates of a hyperbolic double well potential of arbitrary height or width. Considering initial wave packets of different widths and peak locations, we compute autocorrelation functions and quasiprobability distributions.
  arXiv  Detail & Related papers  (2020-09-18T10:29:04Z)
• Quantum Statistical Complexity Measure as a Signalling of Correlation Transitions [55.41644538483948]
  We introduce a quantum version for the statistical complexity measure, in the context of quantum information theory, and use it as a signalling function of quantum order-disorder transitions. We apply our measure to two exactly solvable Hamiltonian models, namely: the $1D$-Quantum Ising Model and the Heisenberg XXZ spin-$1/2$ chain. We also compute this measure for one-qubit and two-qubit reduced states for the considered models, and analyse its behaviour across its quantum phase transitions for finite system sizes as well as in the thermodynamic limit by using Bethe ansatz.
  arXiv  Detail & Related papers  (2020-02-05T00:45:21Z)

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.