Math Physics Seminar
Lattice gauge theories are typically described in terms of local, redundant degrees of freedom, supplemented by appropriate gauge constraints, i.e. Gauss's law or its generalizations. The Hamiltonian is then a sum of gauge invariant operators acting on those degrees of freedom. Trotter-Suzuki decompositions employed for digital quantum simulation, however, do not necessarily implement any one of those individual operators exactly -- leading to the possible systematic breaking of gauge constraints. I will discuss how shear transformations in the space of electric quantum numbers of Abelian gauge theories facilitate Trotter-Suzuki approximation of the gauge invariant operators that exactly preserves the gauge constraints.