AI summaryⓘ
The authors present a new method called diagonal-budgeted Trotterization to simulate quantum systems more efficiently on classical computers. Their approach keeps the important diagonal structure of the problem to reduce computational overhead and maintain accuracy without needing a lot of extra steps. They implemented this method in a program named HamSim, which uses smart data layouts and hardware tricks like GPU acceleration to run much faster than existing tools. Testing shows HamSim can speed up simulations by hundreds of times on various quantum problems while preserving accuracy. This work highlights how paying attention to problem structure can make classical quantum simulations more practical.
Quantum Hamiltonian DynamicsClassical SimulationTrotterizationDiagonal SparsitySparse Linear AlgebraSIMD VectorizationGPU AccelerationHamLib BenchmarkQiskit-Aer
Authors
Srikar Chundury, Blake Burgstahler, Jiajia Li, In-Saeng Suh, Frank Mueller
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.