Quantum simulations of Fermionic Hamiltonians with efficient encoding and ansatz schemes

Abstract

We propose a computational protocol for quantum simulations of Fermionic Hamiltonians on a quantum computer, enabling calculations which were previously not feasible with conventional encoding and ansatses of variational quantum eigensolvers (VQE). We combine a qubit-efficient encoding scheme mapping Slater determinants onto qubits with a modified qubit-coupled cluster ansatz and noise-mitigation techniques. Our strategy leads to a substantial improvement in the scaling of circuit gate counts and to a decrease in the number of required variational parameters, thus increasing the resilience to noise. We present results for spin defects of interest for quantum technologies, going beyond minimum models for the negatively charged nitrogen vacancy center in diamond and the double vacancy in 4H silicon carbide (4H-SiC) and tackling a defect as complex as negatively charged silicon vacancy in 4H-SiC for the first time.