Hardware-Efficient Hamiltonian Simulation via Trotter-Initialized Variational Optimization with Native Placement

• URL: http://arxiv.org/abs/2604.26663v1
• Date: Wed, 29 Apr 2026 13:26:54 GMT
• Title: Hardware-Efficient Hamiltonian Simulation via Trotter-Initialized Variational Optimization with Native Placement
• Abstract summary: We introduce a structure-aware compilation framework that treats product-formula decompositions as synthesis primitives.<n>Across Heisenberg, Ising, and XY models with $n$--$8$ qubits, the compiled circuits achieve fidelities $F>0.996$.<n>On IBM Torino hardware, we observe a regime in which shorter approximate circuits outperform deeper exact decompositions.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: Compiling time-evolution operators of the form $U(t)=e^{-iHt}$ into hardware-native gate sequences is a central bottleneck for digital quantum simulation on noisy intermediate-scale quantum (NISQ) devices. Generic transpilation treats $U(t)$ as an arbitrary unitary, discarding the structure of Hamiltonian dynamics and producing circuits whose depth exceeds 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 (i) native placement of Hamiltonian terms onto the hardware coupling map, (ii) adaptive selection of Trotter blocks via a greedy discretization procedure, and (iii) variational refinement using a Trotter-initialized ansatz. Across Heisenberg, Ising, and XY models with $n=3$--$8$ qubits, the compiled circuits achieve fidelities $F>0.996$ with approximately linear scaling in the number of entangling gates, while generic synthesis produces circuits that are orders of magnitude deeper. On IBM Torino hardware, we observe a regime in which shorter approximate circuits outperform deeper exact decompositions: a 27-CX circuit achieves higher hardware fidelity ($F_{\mathrm{hw}}=0.987$) than a 187-CX exact circuit. These results demonstrate that, in the NISQ regime, structure-aware approximate compilation can outperform exact structure-agnostic synthesis, providing a practical pathway for executing Hamiltonian dynamics without requiring pulse-level control.

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