Error mitigation through partial Pauli twirling and layer-wise zero-noise extrapolation on a simulation of Fermi-Hubbard Hamiltonian

Error mitigation in noisy intermediate-scale quantum (NISQ) computers currently requires significant overhead. Specifically, Pauli twirling applied to two-qubit gates demands an overhead that scales exponentially with the two-qubit gate depth, severely burdening many error mitigation techniques designed to handle incoherent noise. To alleviate this overhead, we propose partial Pauli twirling. This technique applies only a select instance of Pauli twirling operations, effective within the local noise environment of a regime with sufficiently shallow circuit depth. This approach offers the advantage of achieving a beneficial error mitigation effect with a reduced overhead. Here, we constructed a Fermi-Hubbard circuit featuring noisy, local CZ gates arranged in a zigzag pattern within a moderately shallow depth regime. We benchmarked layered CZ gates and analyzed the extrapolation trend with respect to circuit depth for different layer types.