Variational Quantum Boltzmann Machines

Abstract

This work presents a novel realization approach to Quantum Boltzmann Machines (QBMs). The preparation of the required Gibbs states, as well as the evaluation of the loss function's analytic gradient is based on Variational Quantum Imaginary Time Evolution, a technique that is typically used for ground state computation. In contrast to existing methods, this implementation facilitates near-term compatible QBM training with gradients of the actual loss function for arbitrary parameterized Hamiltonians which do not necessarily have to be fully-visible but may also include hidden units. The variational Gibbs state approximation is demonstrated with numerical simulations and experiments run on real quantum hardware provided by IBM Quantum. Furthermore, we illustrate the application of this variational QBM approach to generative and discriminative learning tasks using numerical simulation.

References in corpus (40)

• Adam: A Method for Stochastic Optimization
• Scikit-learn: Machine Learning in Python
• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• Quantum Circuit Learning
• On the Convergence of Adam and Beyond
• Quantum Amplitude Amplification and Estimation
• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Evaluating analytic gradients on quantum hardware
• Many-body quantum state tomography with neural networks
• A quantum algorithm providing exponential speed increase for finding eigenvalues and eigenvectors
• Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution
• Variational ansatz-based quantum simulation of imaginary time evolution
• Quantum generative adversarial networks
• Quantum Generative Adversarial Networks for Learning and Loading Random Distributions
• Theory of variational quantum simulation
• Simulating Physical Phenomena by Quantum Networks
• Quantum Algorithms for Fermionic Simulations
• Restricted-Boltzmann-Machine Learning for Solving Strongly Correlated Quantum Systems
• Quantum Metropolis Sampling
• Improving Variational Quantum Optimization using CVaR
• Option Pricing using Quantum Computers
• Sampling from the thermal quantum Gibbs state and evaluating partition functions with a quantum computer
• Solving fermion sign problem in quantum Monte Carlo by Majorana representation
• Tomography and Generative Data Modeling via Quantum Boltzmann Training
• Constructing exact representations of quantum many-body systems with deep neural networks
• A Quantum-Quantum Metropolis Algorithm
• Variational Thermal Quantum Simulation via Thermofield Double States
• A Quantum Approximate Optimization Algorithm Applied to a Bounded Occurrence Constraint Problem
• Sample-efficient learning of quantum many-body systems
• Majorana-time-reversal symmetries: a fundamental principle for sign-problem-free quantum Monte Carlo simulations
• Characterization of a two-transmon processor with individual single-shot qubit readout
• Easing the Monte Carlo sign problem
• Learning models of quantum systems from experiments
• Sign-problem-free Monte Carlo simulation of certain frustrated quantum magnets
• A Variational Quantum Algorithm for Preparing Quantum Gibbs States
• Generative training of quantum Boltzmann machines with hidden units
• Symmetry-protected topological order and negative-sign problem for SO(N) bilinear-biquadratic chains
• The Complexity of Stoquastic Local Hamiltonian Problems
• Synthesizing Credit Card Transactions
• Realizing Quantum Boltzmann Machines Through Eigenstate Thermalization

Cited by in corpus (40)

• Quantum computing for finance
• Beyond Barren Plateaus: Quantum Variational Algorithms Are Swamped With Traps
• Quantum agents in the Gym: a variational quantum algorithm for deep Q-learning
• Quantum computing models for artificial neural networks
• Simultaneous Perturbation Stochastic Approximation of the Quantum Fisher Information
• Quantum Machine Learning for Finance
• ResQNets: A Residual Approach for Mitigating Barren Plateaus in Quantum Neural Networks
• Variational Quantum Time Evolution without the Quantum Geometric Tensor
• Quantum-assisted associative adversarial network: Applying quantum annealing in deep learning
• Error Bounds for Variational Quantum Time Evolution
• Variational Gibbs State Preparation on NISQ devices
• Fragmented imaginary-time evolution for early-stage quantum signal processors
• Tight and Efficient Gradient Bounds for Parameterized Quantum Circuits
• Boltzmann machine learning with a variational quantum algorithm
• A review of Quantum Neural Networks: Methods, Models, Dilemma
• Provable bounds for noise-free expectation values computed from noisy samples
• Extending the Variational Quantum Eigensolver to Finite Temperatures
• Simulating noisy variational quantum eigensolver with local noise models
• Conditional Born machine for Monte Carlo event generation
• VQC-Based Reinforcement Learning with Data Re-uploading: Performance and Trainability
• Critical behavior of Ising model by preparing thermal state on quantum computer
• Dissipative variational quantum algorithms for Gibbs state preparation
• A hybrid quantum-classical approach for inference on restricted Boltzmann machines
• Variational secure cloud quantum computing
• Training Quantum Boltzmann Machines with the $\beta$-Variational Quantum Eigensolver
• Nonunitary Gate Operations by Dissipation Engineering
• Gradients and frequency profiles of quantum re-uploading models
• Stochastic Approximation of Variational Quantum Imaginary Time Evolution
• Gate-based quantum simulation of Gaussian bosonic circuits on exponentially many modes
• On Quantum Circuits for Discrete Graphical Models
• Quantum Inception Score
• Efficient Quantum Cooling Algorithm for Fermionic Systems
• Sampling Problems on a Quantum Computer
• Multidimensional Quantum Generative Modeling by Quantum Hartley Transform
• Unitary Evolutions Sourced By Interacting Quantum Memories: Closed Quantum Systems Directing Themselves Using Their State Histories
• Error Mitigation in Quantum Computers through Instruction Scheduling
• Variational Quantum Algorithms for Gibbs State Preparation
• Expressive equivalence of classical and quantum restricted Boltzmann machines
• Quantum Chebyshev Probabilistic Models for Fragmentation Functions
• Quantum generative classification with mixed states