Minimally Entangled Typical Thermal States for Classical and Quantum Simulation of 1+1-Dimensional $\mathbb Z_2$ Lattice Gauge Theory at Finite Temperature and Density

TL;DR

This paper introduces minimally entangled typical thermal states (METTS) for simulating 1+1D $ ext{Z}_2$ lattice gauge theories at finite temperature and density, enabling efficient classical and quantum studies of these complex systems.

Contribution

It develops and benchmarks METTS methods, including a classical matrix-product-state implementation and a quantum-adaptive variational approach, for studying gauge theories on classical and quantum hardware.

Findings

METTS effectively estimate thermal averages in gauge theories.

The choice of basis significantly affects sampling and circuit complexity.

The approaches are promising for future quantum simulations of strongly coupled systems.

Abstract

Simulating strongly coupled gauge theories at finite temperature and density is a longstanding challenge in nuclear and high-energy physics that also has fundamental implications for condensed matter physics. In this work, we use minimally entangled typical thermal state (METTS) approaches to facilitate both classical and quantum computational studies of such systems. METTS techniques combine classical random sampling with imaginary time evolution, which can be performed on either a classical or a quantum computer, to estimate thermal averages of observables. We study 1+1-dimensional $\mathbb{Z}_2$ gauge theory coupled to spinless fermionic matter, which maps onto a local quantum spin chain. We benchmark both a classical matrix-product-state implementation of METTS and a recently proposed adaptive variational approach that is a promising candidate for implementation on near-term quantum devices, focusing on the equation of state as well as on various measures of fermion confinement. Of particular importance is the choice of basis for obtaining new METTS samples, which impacts both the classical sampling complexity (a key factor in both classical and quantum simulation applications) and complexity of circuits used in the quantum computing approach. Our work sets the stage for future studies of strongly coupled gauge theories with both classical and quantum hardware.