Diagonal-Budgeted Trotterization for Efficient Quantum Hamiltonian Simulation

2026-06-15

AI Summary

This work addresses the computational bottlenecks in simulating classical quantum Hamiltonian dynamics, which are hindered by exponential state-space growth and the high overhead of generic sparse linear algebra. The authors propose a diagonal-budget Trotterization method that introduces, for the first time, a structure-aware diagonal sparsity decomposition strategy, achieving near-perfect fidelity without requiring an exponential number of steps. Efficiency is substantially enhanced through a compact diagonal-sparse data layout, specialized C++/CUDA kernels, and aggressive optimization via SIMD vectorization, multithreading, and GPU acceleration. On the HamLib benchmark suite, the implementation demonstrates speedups of 4.8–1269× over Qiskit-Aer on CPU and up to 178× on GPU for 12–16 qubit problems.

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.

Problem

• quantum Hamiltonian simulation
• classical simulation
• exponential state growth
• sparse linear algebra
• Trotterization

Innovation

• diagonal-budgeted Trotterization
• Hamiltonian simulation
• diagonal sparsity
• high-fidelity classical simulation
• GPU acceleration