Variational Quantum Algorithms for Gibbs State Preparation
arXiv:2305.17713 · doi:10.1007/978-3-031-81247-7_5
Abstract
Preparing the Gibbs state of an interacting quantum many-body system on noisy intermediate-scale quantum (NISQ) devices is a crucial task for exploring the thermodynamic properties in the quantum regime. It encompasses understanding protocols such as thermalization and out-of-equilibrium thermodynamics, as well as sampling from faithfully prepared Gibbs states could pave the way to providing useful resources for quantum algorithms. Variational quantum algorithms (VQAs) show the most promise in effciently preparing Gibbs states, however, there are many different approaches that could be applied to effectively determine and prepare Gibbs states on a NISQ computer. In this paper, we provide a concise overview of the algorithms capable of preparing Gibbs states, including joint Hamiltonian evolution of a system-environment coupling, quantum imaginary time evolution, and modern VQAs utilizing the Helmholtz free energy as a cost function, among others. Furthermore, we perform a benchmark of one of the latest variational Gibbs state preparation algorithms, developed by Consiglio et al. (arXiv:2303.11276), by applying it to the spin 1/2 one-dimensional model.
arXiv comment22 pages, 6 figures. Original VQA proposed in arXiv:2303.11276. An abridged version has been accepted in LNCS NUMTA2023 Conference Proceedings
References in corpus (40)
- Quantum Machine Learning
- Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution
- Toward the first quantum simulation with quantum speedup
- Variational ansatz-based quantum simulation of imaginary time evolution
- Theory of variational quantum simulation
- Quantum Boltzmann Machine
- Quantum Metropolis Sampling
- Sampling from the thermal quantum Gibbs state and evaluating partition functions with a quantum computer
- The problem of equilibration and the computation of correlation functions on a quantum computer
- Thermalization in Nature and on a Quantum Computer
- Quantum Simulations of Classical Annealing Processes
- Tomography and Generative Data Modeling via Quantum Boltzmann Training
- A Quantum-Quantum Metropolis Algorithm
- Variational Thermal Quantum Simulation via Thermofield Double States
- Sample-efficient learning of quantum many-body systems
- Quantum Computation of Finite-Temperature Static and Dynamical Properties of Spin Systems Using Quantum Imaginary Time Evolution
- Algorithms for quantum simulation at finite energies
- Variational Quantum Boltzmann Machines
- Preparing thermal states of quantum systems by dimension reduction
- Product Spectrum Ansatz and the Simplicity of Thermal States
- Variational preparation of finite-temperature states on a quantum computer
- Quantum Hamiltonian-Based Models and the Variational Quantum Thermalizer Algorithm
- A Variational Quantum Algorithm for Preparing Quantum Gibbs States
- Transition Probability (Fidelity) and Its Relatives
- Rapid thermalization of spin chain commuting Hamiltonians
- Predicting Gibbs-State Expectation Values with Pure Thermal Shadows
- Engineered thermalization and cooling of quantum many-body systems
- Artificial quantum thermal bath: Engineering temperature for a many-body quantum system
- Generalized Quantum Assisted Simulator
- Quantum rejection sampling
- Minimal Effective Gibbs Ansatz (MEGA): A simple protocol for extracting an accurate thermal representation for quantum simulation
- Quantum Thermal State Preparation
- Adaptive variational algorithms for quantum Gibbs state preparation
- Preparing thermal states on noiseless and noisy programmable quantum processors
- Thermal variational quantum simulation on a superconducting quantum processor
- Dissipative Quantum Gibbs Sampling
- Thermal Multi-scale Entanglement Renormalization Ansatz for Variational Gibbs State Preparation
- Engineering the Cost Function of a Variational Quantum Algorithm for Implementation on Near-Term Devices
- Quantum Computational Complexity
- Variational Quantum Simulations of Finite-Temperature Dynamical Properties via Thermofield Dynamics