Adaptive variational quantum minimally entangled typical thermal states for finite temperature simulations

Abstract

Scalable quantum algorithms for the simulation of quantum many-body systems in thermal equilibrium are important for predicting properties of quantum matter at finite temperatures. Here we describe and benchmark a quantum computing version of the minimally entangled typical thermal states (METTS) algorithm for which we adopt an adaptive variational approach to perform the required quantum imaginary time evolution. The algorithm, which we name AVQMETTS, dynamically generates compact and problem-specific quantum circuits, which are suitable for noisy intermediate-scale quantum (NISQ) hardware. We benchmark AVQMETTS on statevector simulators and perform thermal energy calculations of integrable and nonintegrable quantum spin models in one and two dimensions and demonstrate an approximately linear system-size scaling of the circuit complexity. We further map out the finite-temperature phase transition line of the two-dimensional transverse field Ising model. Finally, we study the impact of noise on AVQMETTS calculations using a phenomenological noise model.

23 pages, 6 figures

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• Variational Gibbs State Preparation on NISQ devices
• Adaptive variational simulation for open quantum systems
• Hamiltonian learning from time dynamics using variational algorithms
• Stochastic Approximation of Variational Quantum Imaginary Time Evolution
• Adaptive variational ground state preparation for spin-1 models on qubit-based architectures
• Problem-tailored Simulation of Energy Transport on Noisy Quantum Computers
• Adaptive variational quantum computing approaches for Green's functions and nonlinear susceptibilities
• Quantum many-body simulation of finite-temperature systems with sampling a series expansion of a quantum imaginary-time evolution
• Sample complexity of matrix product states at finite temperature
• Gibbs state sampling via cluster expansions
• Co-Designing Spectral Transformation Oracles with Hybrid Oscillator-Qubit Quantum Processors: From Algorithms to Compilation
• Quantum simulation of massive Thirring and Gross--Neveu models for arbitrary number of flavors
• Quantum imaginary time evolution and UD-MIS problem