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This research introduces diagonal-budgeted Trotterization to overcome the exponential scaling bottlenecks in classical quantum Hamiltonian simulation. The proposed HamSim implementation leverages specialized sparse data layouts and GPU acceleration, delivering massive speedups over generic solvers like Qiskit-Aer while maintaining high fidelity for optimization and physical models. This advancement establishes a scalable numerical foundation essential for validating near-term quantum hardware performance on complex problems.
Diagonal-Budgeted Trotterization for Efficient Quantum Hamiltonian Simulation
arXiv:2606.16959v1 Announce Type: new Abstract: Efficient classical simulation of quantum Hamiltonian dynamics is often bottlenecked by exponential state growth and the overhead of generic sparse linear algebra. We introduce diagonal-budgeted Trotterization, a structure-aware strategy that decomposes Hamiltonians into factors preserving diagonal sparsity while tightly controlling fidelity loss. Our implementation, HamSim, utilizes a compact diagonal-sparse data layout and specialized C++/CUDA kernels to bypass the overheads of generic formats like CSR. By leveraging SIMD vectorization, multithreading, and GPU acceleration, HamSim achieves high performance across heterogeneous architectures. Benchmarks on the HamLib suite show that HamSim significantly outperforms Qiskit-Aer. On CPUs, HamSim attains speedups of $182$--$1,269\times$ on optimization instances (TSP, MaxCut) and $4.8$--$841\times$ on physical models (TFIM, Heisenberg). On GPUs, it achieves up to $178\times$ speedup for $12$--$16$ qubit problems. Unlike traditional Trotterization, HamSim maintains near-perfect fidelity without requiring exponential steps. This demonstrates that diagonal-aware numerical kernels provide a scalable foundation for high-fidelity classical Hamiltonian simulation.
Abstract:Efficient classical simulation of quantum Hamiltonian dynamics is often bottlenecked by exponential state growth and the overhead of generic sparse linear algebra. We introduce diagonal-budgeted Trotterization, a structure-aware strategy that decomposes Hamiltonians into factors preserving diagonal sparsity while tightly controlling fidelity loss. Our implementation, HamSim, utilizes a compact diagonal-sparse data layout and specialized C++/CUDA kernels to bypass the overheads of generic formats like CSR. By leveraging SIMD vectorization, multithreading, and GPU acceleration, HamSim achieves high performance across heterogeneous architectures. Benchmarks on the HamLib suite show that HamSim significantly outperforms Qiskit-Aer. On CPUs, HamSim attains speedups of $182$--$1,269\times$ on optimization instances (TSP, MaxCut) and $4.8$--$841\times$ on physical models (TFIM, Heisenberg). On GPUs, it achieves up to $178\times$ speedup for $12$--$16$ qubit problems. Unlike traditional Trotterization, HamSim maintains near-perfect fidelity without requiring exponential steps. This demonstrates that diagonal-aware numerical kernels provide a scalable foundation for high-fidelity classical Hamiltonian simulation.
Extended version including appendix. Accepted to ACM ICS 2026
Quantum Physics (quant-ph); Distributed, Parallel, and Cluster Computing (cs.DC)
arXiv:2606.16959 [quant-ph]
(or arXiv:2606.16959v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2606.16959 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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