Quantum computers hold promise for simulating gauge theories, which model the fundamental forces of nature and more. Gauge theories obey local constraints called Gauss’s laws. For instance, Gauss’s law in electromagnetism constrains a site’s charge density in terms of the electric-field flux passing through the site. Gauss’s laws restrict a gauge theory to a physical subspace, an entangled subspace of the global Hilbert space. The physical subspace appears unable to factorize into a system-of-interest subspace and an environmental subspace. How, then, can one describe an open-system gauge theory’s thermodynamics? We apply strong-coupling thermodynamics, a toolkit of recent interest in the field of quantum thermodynamics. Using this toolkit, we define the work and heat exchanged within a lattice gauge theory (LGT) during a quench protocol performable on quantum hardware. The heat and work, we show, obey the first and second laws of thermodynamics. We illustrate our framework with numerical simulations of a Z2 LGT coupled to matter in 1+1 dimensions. Thermodynamic quantities, we find, evidence a phase transition. We also show how to measure them experimentally. I will explain our results through the lens of ten lessons I learned from Bell Prize honoree John Preskill.

Reference: Davoudi, Jarzynski, Mueller, Oruganti, Powers, and NYH, arXiv: 2404.02965 (2024).