Efficient Representation for Simulating U(1) Gauge Theories on Digital Quantum Computers at All Values of the Coupling

We derive a representation for a lattice U(1) gauge theory with exponential convergence in the number of states used to represent each lattice site that is applicable at all values of the coupling. At large coupling, this representation is equivalent to the Kogut-Susskind electric representation, which is known to provide a good description in this region. At small coupling, our approach adjusts the maximum magnetic field that is represented in the digitization as in this regime the low-lying eigenstates become strongly peaked around zero magnetic field. Additionally, we choose a representation of the electric component of the Hamiltonian that gives minimal violation of the canonical commutation relation when acting upon low-lying eigenstates. For <math display="inline"><mrow><mo stretchy="false">(</mo><mn>2</mn><mo>+</mo><mn>1</mn><mo stretchy="false">)</mo></mrow></math> dimensions with 4 lattice sites the expectation value of the plaquette operator can be calculated with only 7 states per lattice site with per-mille level accuracy for all values of the coupling constant.