Floquet-induced matrix models for quantum simulations of gauge theories on dynamical spacetimes

Inspired by the techniques used in classical simulations of large-N Yang-Mills matrix models, we investigate representations of Floquet sequences in terms of non-commutative manifolds, and in the process develop a new framework for quantum simulations of gauge theories. In particular, the method we propose uses no lattice discretizations, and is thus capable of representing dynamical spacetimes while preserving unitarity. The symmetries of a field's spacetime background are encoded in the dynamical Lie algebra of the quantum operators used in the computation. With the Yang-Mills matrix model Lagrangian, an analogue of gauge field path integrals can be generated on a variety of background spacetimes by applying specific sequences of high-dimensional Hermitian operators. Geometrically, the available background manifolds range from spheres and planes, to relativistic manifolds including flat Minkowski space and the cosmological FLRW metric. Using the Suzuki-Trotter formula, we translate the matrix operators found in classical simulations of matrix models into finite quantum Floquet sequences. We then study a selection of applications for these sequences in analog, digital, and hybrid quantum circuits, making use of variational algorithms and amplitude amplification. These results constitute a quantum-native framework for gauge theory simulations without lattice discretization, and offer a concrete step toward mathematically reconciling quantum theory with general relativity.