Solving Quantum Statistical Mechanics with Variational Autoregressive Networks and Quantum Circuits
arXiv:1912.11381
Abstract
We extend the ability of unitary quantum circuits by interfacing it with classical autoregressive neural networks. The combined model parametrizes a variational density matrix as a classical mixture of quantum pure states, where the autoregressive network generates bitstring samples as input states to the quantum circuit. We devise an efficient variational algorithm to jointly optimize the classical neural network and the quantum circuit for quantum statistical mechanics problems. One can obtain thermal observables such as the variational free energy, entropy, and specific heat. As a by product, the algorithm also gives access to low energy excitation states. We demonstrate applications to thermal properties and excitation spectra of the quantum Ising model with resources that are feasible on near-term quantum computers.
7 pages, 5 figures, code: https://github.com/wangleiphy/BetaVQE.jl
References in corpus (35)
- Auto-Encoding Variational Bayes
- A variational eigenvalue solver on a quantum processor
- Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
- Quantum Circuit Learning
- Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
- Evaluating analytic gradients on quantum hardware
- Towards Practical Quantum Variational Algorithms
- Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution
- Robust determination of molecular spectra on a quantum processor
- MADE: Masked Autoencoder for Distribution Estimation
- Observation of topological phenomena in a programmable lattice of 1,800 qubits
- Quantum Metropolis Sampling
- Quantum Implementation of Unitary Coupled Cluster for Simulating Molecular Electronic Structure
- Minimal Universal Two-qubit Quantum Circuits
- Hybrid Quantum-Classical Approach to Quantum Optimal Control
- Unsupervised Generative Modeling Using Matrix Product States
- Deep autoregressive models for the efficient variational simulation of many-body quantum systems
- Variational Fast Forwarding for Quantum Simulation Beyond the Coherence Time
- Solving Statistical Mechanics Using Variational Autoregressive Networks
- Feynman diagrams versus Fermi-gas Feynman emulator
- Sampling from the thermal quantum Gibbs state and evaluating partition functions with a quantum computer
- Thermalization in Nature and on a Quantum Computer
- The problem of equilibration and the computation of correlation functions on a quantum computer
- Quantum circuits for strongly correlated quantum systems
- REBAR: Low-variance, unbiased gradient estimates for discrete latent variable models
- Variational Thermal Quantum Simulation via Thermofield Double States
- Simulation of Nonequilibrium Dynamics on a Quantum Computer
- Tree Tensor Networks for Generative Modeling
- Backpropagation through the Void: Optimizing control variates for black-box gradient estimation
- Thermal Ising transitions in the vicinity of two-dimensional quantum critical points
- Product Spectrum Ansatz and the Simplicity of Thermal States
- Quantum Hamiltonian-Based Models and the Variational Quantum Thermalizer Algorithm
- Non-unitary operations for ground-state calculations in near term quantum computers
- Neural Canonical Transformation with Symplectic Flows
- Inferring the quantum density matrix with machine learning