NQCP - Life in Quantum - Postdoc Marek L. Miller, Quantum for Life Centre, University of Copenhagen

Large-scale distributed simulation of quantum algorithms for quantum time evolution

Abstract: The ability to efficiently simulate Hamiltonian time evolution lies at the heart of many quantum algorithms, and it naturally encapsulates the computational complexity of quantum computers. Various methods are known to implement time evolution in polynomial time on a quantum computer, with their applicability depending on concrete problem instances. Trotter product formulas are widely used for this purpose; their performance guarantees, however, rely on accurate bounds of the Trotter error. We extend our numerical simulation approach [1] to calculate the quantum time evolution of a model system (the ruthenium complex NKP-1339) with up to 40 qubits, using the Trotter product formula with stochastic sampling. By randomly sampling low-weight terms in the Hamiltonian, we avoid implementing all terms in each Trotter step, which for the 18 orbital system reduces the number of terms per step by a factor of five. By Fourier analysis of the time signal, we can obtain numerical spectroscopy of a given initial state. The results provide insight into Trotter errors, the distribution of excited-state energies, and ground-state overlaps. With a simulation algorithm highly optimized for large distributed workloads, we have achieved nearly perfect strong and weak scaling, as well as record-breaking performance on a distributed system comprising 512 NVIDIA H100 GPUs on Gefion supercomputer (DCAI). The Trotter product formula for Hamiltonian time evolution is amenable to HPC simulation, and the results exhibit a substantial speedup for realistic Hamiltonians when our “common-suffix strategy” is implemented. We expect that our method of large-scale simulation of quantum systems, along with the error estimates we have derived, will guide the advancement of both quantum software and quantum hardware by offering precise resource and accuracy assessments.

[1] Miller, M., Günther, J., Witteveen, F., Teynor, M.S., Erakovic, M., Reiher, M., Solomon, G.C. and Christandl, M., 2025. phase2: Full-State Vector Simulation of Quantum Time Evolution at Scale. arXiv preprint arXiv:2504.17881.