Appears in collection : Combinatorics and Arithmetic for Physics

Analytical and classical numerical approaches can fail for significant regimes of certain physical systems, see, e.g., the sign problem in lattice Quantum Chromodynamics. Quantum computing presents a viable framework to perform calculations in such regimes. However, current quantum hardware is affected by noise, requiring quantum error mitigation (QEM). We present two QEM techniques: First, QEM driven by data obtained in classical simulations. This approach involves learning the properties of the quantum noise in a regime accessible by both noisy quantum and classical devices, and then using this for error mitigation in a regime accessible only by noisy quantum devices. Second, QEM driven by analytically computed evolution equations. This approach leverages the fact that the observables within the simulation of an evolved quantum system obey a system of coupled evolution equations. Using an appropriate subset of these equations allows to mitigate errors in the measurements obtained on noisy quantum hardware. We demonstrate the two QEM techniques on the example of the lattice Schwinger model with a topological θ term. Based on joint work with Theo Saporiti, Vasily Sazonov, and Mohamed Tamaazousti: [Phys. Rev. A 111 (2025) 6, 062202], [arXiv:2507.06601 (2025)] and [Phys. Rev. A 112 (2025) 3, 032409], work in progress, respectively.