Quantum Information Journal Club: ‘Optimal strategies for near-term simulation of fermionic systems with scalable local fermion-to-qubit mappings’

Abstract: Quantum simulation of interacting fermions remains one of the most compelling applications of quantum computing, but its practical realization depends on more than the asymptotic promise of fault-tolerant quantum algorithms. To bridge the gap with current NISQ devices, we derive a strategy for growing the corresponding code distance of local fermion-to-qubit mappings, which is otherwise fixed. Building upon the extended error detection properties of these mappings we present a quantum error mitigation (QEM) technique tailored for fermionic systems which outperforms other widely used techniques such as Post-selection, Virtual Distillation, and Probabilistic Error Cancellation in regimes of practical interest. We then study the performance of different combinations of QEM and fermion-to-qubit mappings and identify the best combination of mapping and QEM. This study enables us to derive minimal hardware requirements for the simulation of Fermi-Hubbard models of various sizes in near-term devices.