Hardware‐Efficient Hamiltonian Simulation via Trotter‐Initialized Variational Optimization With Native Placement

ABSTRACT

Compiling time‐evolution operators into hardware‐native gate sequences is a bottleneck for digital quantum simulation on noisy intermediate‐scale quantum (NISQ) devices. Generic transpilation treats as an arbitrary unitary, discarding the structure of Hamiltonian dynamics and producing circuits exceeding hardware coherence limits.

We introduce a structure‐aware compilation framework that treats product‐formula decompositions as synthesis primitives rather than simulation approximations. The method combines (1) native placement of Hamiltonian terms onto the hardware coupling map, (2) adaptive selection of Trotter blocks via a greedy discretization procedure, and (3) variational refinement using a Trotter‐initialized ansatz.

Across Heisenberg, Ising, and XY models with – qubits, compiled circuits achieve fidelities with near‐linear scaling in entangling gates, while generic synthesis produces circuits orders of magnitude deeper. On IBM Torino hardware, shorter approximate circuits outperform deeper exact decompositions: a 27‐CX circuit achieves higher hardware fidelity futher () than a 187‐CX exact circuit.

These results demonstrate that structure‐aware approximate compilation outperforms exact structure‐agnostic synthesis, providing a practical pathway for executing Hamiltonian dynamics without pulse‐level control.