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The study of real-time evolution of lattice quantum field theories usingclassical computers is known to scale exponentially with the number of latticesites. Due to a fundamentally different computational strategy, quantumcomputers hold the promise of allowing for detailed studies of these dynamicsfrom first principles. However, much like with classical computations, it isimportant that quantum algorithms do not have a cost that scales exponentiallywith the volume. Recently, it was shown how to break the exponential scaling ofa naive implementation of a U(1) gauge theory in two spatial dimensions throughan operator redefinition. In this work, we describe modifications to howoperators must be sampled in the new operator basis to keep digitization errorssmall. We compare the precision of the energies and plaquette expectation valuebetween the two operator bases and find they are comparable. Additionally, weprovide an explicit circuit construction for the Suzuki-Trotter implementationof the theory using the Walsh function formalism. The gate count scaling isstudied as a function of the lattice volume, for both exact circuits andapproximate circuits where rotation gates with small arguments have beendropped. We study the errors from finite Suzuki-Trotter time-step, circuitapproximation, and quantum noise in a calculation of an explicit observableusing IBMQ superconducting qubit hardware. We find the gate count scaling forthe approximate circuits can be further reduced by up to a power of the volumewithout introducing larger errors.

Efficient quantum implementation of 2+1 U(1) lattice gauge theories with Gauss law constraints