2D lattice gauge theory simulations on superconducting qubits: technical implementation

Given today's noisy quantum processors, the details of how an algorithm is implemented can make a significant difference in performance. For example, how the circuit is compiled, what error mitigation techniques are used, and which quantities are measured all affect performance. I will present aspects of two recent works by the Google Quantum AI team and collaborators: arXiv:2409.17142 and arXiv:2410.06557, both of which use an array of superconducting qubits to simulate 2D lattice gauge theories. The former work demonstrates the confinement and deconfinement of gauge excitations whereas the latter work demonstrates localization for a typical initial state even though the initial state and the generator of dynamics do not have disorder. We show how implementing the dynamics using ancilla qubits reduces the circuit depth and reduces noise in the local observables while also adding degrees of freedom on which we post select for further error mitigation. We also show that post-selecting on the gauge charges and rescaling assuming a global depolarizing channel are effective error mitigation techniques in certain cases. Time permitting, we discuss how well-tailored techniques allowed us to measure certain observables that would have otherwise remained elusive, such as the Renyi entropy of relatively large subsystems and two-time correlators.