2026/04/07 by Nhat A. Nghiem, Tzu-Chieh Wei · 1 voice
Physics and Astronomy · #quant-ph
We introduce a hybrid classical-quantum algorithm for simulating a Hamiltonian of the form H= ∑i=1K Hi = ∑i=1K Hi1 ⊗ Hi2 ⊗ ⋯ ⊗ HiM. Given that the entries of all \ Hi1, Hi2 , ⋯ , HiM\ (for all i) are classically known, we present a procedure (with three variants) in which these operators are classically diagonalized, and then this information is fed into three possible quantum procedures to obtain the block-encoding of H. The evolution operator exp(-iHt) is then obtained using the standard block-encoding/quantum singular value transformation framework. In the case where \Hi\i=1K commute pairwise, our method can be trivially extended to the case with time-dependent coefficients. We provide a detailed discussion of the efficient regime of our hybrid framework and compare it with existing quantum simulation algorithms. Our algorithm can serve as a useful complement to existing quantum simulation algorithms, thereby expanding the reach of quantum computers for practically simulating physical systems. As a side contribution, we will show how the recent technique called randomized truncation to a quantum state developed by Harrow, Lowe, and Witteveen [arXiv preprint arXiv:2510.08518, 2025] can be applied to the context of quantum simulation and particularly quantum state preparation, for which the latter can be of independent interest.