The charge-singlet measurement toolbox

Symmetry is fundamental to physical laws across different scales$\unicode{x2014}$from spacetime structure in general relativity to particle interactions in quantum field theory. Local symmetries, described by gauge theories, are central to phenomena such as superconductivity, topological phases, and the Standard Model of particle physics. Emerging simulation techniques using tensor network states or quantum computers offer exciting new possibilities of exploring the physics of these gauge theories, but require careful implementation of gauge symmetry and charge-neutrality constraints. This is especially challenging for non-Abelian gauge theories such as quantum chromodynamics (QCD), which governs the strong interaction between quarks and gluons. In a recent article (arXiv:2501.00579), we introduced "charge-singlet measurements" for quantum simulations, consisting of a projection based technique from group representation theory that allowed us to probe for the first time the phase diagram of (1+1)-dimensional QCD on a quantum computer. In this article, we show more broadly how to apply charge-singlet measurements as a flexible tool for both classical and quantum simulations of discrete and continuous gauge theories. Our approach extends the use of charge-singlet measurements beyond state preparation in the charge neutral (charge-singlet) sector to include noise mitigation in symmetry-preserving time-evolution circuits. We further demonstrate how this method enables the computation of thermodynamic observables$\unicode{x2014}$such as entropy$\unicode{x2014}$within the charge-singlet subspace, providing a new tool for exploring the connection between quantum thermodynamics and gauge symmetry.