Classical simulation of parity-preserving quantum circuits

We present a classical simulation method for fermionic quantum systems which, without loss of generality, can be represented by parity-preserving circuits made of two-qubit gates in a brick-wall structure. We map such circuits to a fermionic tensor network and introduce a novel decomposition of non-Matchgate gates into a Gaussian fermionic tensor and a residual quartic term, inspired by interacting fermionic systems. The quartic term is independent of the specific gate, which allows us to precompute intermediate results independently of the exact circuit structure and leads to significant speedups when compared to other methods. Our decomposition suggests a natural perturbative expansion which can be turned into an algorithm to compute measurement outcomes and observables to finite accuracy when truncating at some order of the expansion. For particle number conserving gates, our decomposition features a unique truncation cutoff reducing the computational effort for high precision calculations. Our algorithm significantly lowers resource requirements for simulating parity-preserving circuits while retaining high accuracy, making it suitable for simulations of interacting systems in quantum chemistry and material science. Lastly, we discuss how our algorithm compares to other classical simulation methods for fermionic quantum systems.