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The quantum simulation of fermionic gauge field theories is one of theanticipated uses of quantum computers in the NISQ era. Recently work has beendone to simulate properties of the fermionic Z2 gauge field theory in (1+1) Dand the pure gauge theory in (2+1) D. In this work, we investigate variousoptions for simulating the fermionic Z2 gauge field theory in (2+1) D. Tosimulate the theory on a NISQ device it is vital to minimize both the number ofqubits used and the circuit depth. In this work we propose ways to optimizeboth criteria for simulating time dynamics. In particular, we develop a new wayto simulate this theory on a quantum computer, with minimal qubit requirements.We provide a quantum circuit, simulating a single first order Trotter step,that minimizes the number of 2-qubit gates needed and gives comparable resultsto methods requiring more qubits. Furthermore, variational approaches areinvestigated that allow to further decrease the circuit depth.

Quantum Simulation of Z2 Lattice Gauge theory with minimal resources