Multidimensional Quantum Generative Modeling by Quantum Hartley Transform
arXiv:2406.03856 · doi:10.1002/qute.202400337
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.
References in corpus (38)
- Quantum Machine Learning
- A variational eigenvalue solver on a quantum processor
- Elementary gates for quantum computation
- Quantum algorithm for solving linear systems of equations
- Variational Quantum Algorithms
- Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
- Supervised learning with quantum enhanced feature spaces
- Quantum machine learning in feature Hilbert spaces
- Quantum Circuit Learning
- An introduction to quantum machine learning
- Quantum Algorithms Revisited
- Parameterized quantum circuits as machine learning models
- Cost Function Dependent Barren Plateaus in Shallow Parametrized Quantum Circuits
- Evaluating analytic gradients on quantum hardware
- Circuit-centric quantum classifiers
- From the Quantum Approximate Optimization Algorithm to a Quantum Alternating Operator Ansatz
- The effect of data encoding on the expressive power of variational quantum machine learning models
- Quantum algorithm for systems of linear equations with exponentially improved dependence on precision
- Quantum generative adversarial learning
- Quantum generative adversarial networks
- Quantum Generative Adversarial Networks for Learning and Loading Random Distributions
- A generative modeling approach for benchmarking and training shallow quantum circuits
- Quantum Boltzmann Machine
- Variational quantum algorithms for nonlinear problems
- Differentiable Learning of Quantum Circuit Born Machine
- Opportunities and challenges for quantum-assisted machine learning in near-term quantum computers
- High-order quantum algorithm for solving linear differential equations
- Variational Quantum Linear Solver
- Solving nonlinear differential equations with differentiable quantum circuits
- The Born Supremacy: Quantum Advantage and Training of an Ising Born Machine
- Universal Variational Quantum Computation
- Variational Quantum Boltzmann Machines
- Generative quantum machine learning via denoising diffusion probabilistic models
- Sampling, rates, and reaction currents through reverse stochastic quantization on quantum computers
- Quantum Quantile Mechanics: Solving Stochastic Differential Equations for Generating Time-Series
- Protocols for classically training quantum generative models on probability distributions
- Protocols for Trainable and Differentiable Quantum Generative Modelling
- Quantum Computing and a Unified Approach to Fast Unitary Transforms