Post-Processing Electronic Configuration Measurements with Probability Estimation

We present ExtraFerm, an open-source simulator for quantum circuits composed of particle-number conserving matchgates and controlled-phase gates. Given such a circuit and a list of bitstrings, ExtraFerm computes the Born-rule probabilities of these bitstrings with respect to the circuit. ExtraFerm supports both exact and approximate probability calculations, allowing users to trade accuracy for efficiency as needed. Notably, ExtraFerm's performance is polynomial in the number of qubits and matchgates gates in the circuit, at the cost of a runtime exponential in a quantity which measures how far the system is from being Gaussian. This makes ExtraFerm useful for simulating systems beyond the reach of state vector methods. We demonstrate ExtraFerm's utility by simulating the local unitary cluster Jastrow (LUCJ) ansatz and integrating it with sample-based quantum diagonalization (SQD) to improve the accuracy of molecular ground-state energy estimates. For a nitrogen molecule described by a 52-qubit quantum circuit, we observe accuracy improvements of up to 46% over the baseline SQD implementation relative to the heat-bath configuration interaction (HCI) reference energy. As an efficient and flexible tool for extended matchgate simulation, ExtraFerm enables new opportunities for enhancing near-term quantum algorithms in chemistry and related domains.