Accordion: An End-to-end Approach for Fermionic Simulation in Quantum Devices

Abstract

Simulating fermionic systems on quantum hardware requires compiling fermionic Hamiltonians into executable quantum circuits through three stages: fermion-to-qubit mapping, circuit synthesis, and hardware routing. Existing approaches largely optimize these stages independently, relying on stage-specific heuristics that can lead to >> O(n4) scaling in gate count and circuit depth, as well as compilation times of several hours for large instances. We present SimP, an end-to-end compilation framework that vertically integrates fermion-to-qubit mapping, circuit synthesis, and hardware routing. SimP exploits the regular structure of two-body fermionic operators across these compilation stages to substantially reduce the complexity of the resulting circuits. For full-rank all-to-all two-body Hamiltonians, SimP achieves O(n4) gate count and circuit depth, with gate count matching the information-theoretic lower bound imposed by the ?(n4) terms in a two-body fermionic Hamiltonian. Across linear, IBM heavy-hex, and square-grid architectures, SimP reduces gate count by up to 80% and circuit depth by up to 77% relative to the state of the art, while reducing compilation time by up to 99% on large instances. The source code of SimP is publicly available at https://github.com/ruadapt/Accordion-Fermionic-Simulation.