Error mitigation for fermionic simulation

Simulation of fermionic systems is a promising application of noisy intermediate-scale quantum (NISQ) computers, with hopes of genuinely exciting problems being tackled on as few as 50 qubits. While the number of qubits in NISQ devices is already within the regime where we can execute classically challenging and theoretically interesting experiments, the noise present on these devices can be prohibitive. To solve this problem, over the last few years various error mitigation techniques have been developed, attempting to limit and reduce errors, with variable levels of practical success. Here I will present our work on an error mitigation strategy practically useful for fermionic systems. It relies on fermionic linear optical (FLO) circuits which are efficiently classically simulable, allowing us to find exact outcomes of these circuits using classical computers, and then inferring the relationship between exact and noisy outcomes from the NISQ device. This relationship can then be used to invert the noise on other circuits which are not classically simulable. First, we will see how the algorithm works and the promise it holds in simulation. We will look at its powerful error mitigation on two NISQ devices, the Rigetti Aspen chip and Google Quantum AI Sycamore chip, when applied to a Hamiltonian Variational ansatz solving for the ground state of the Fermi-Hubbard model. Finally, we will briefly look at other error mitigation strategies that made a real-world difference in our Fermi-Hubbard simulation.