Year: 2024
Type: preprint
Abstract: We describe a simple method for simulating time-independent Hamiltonian $H$ that could be decomposed as $H = \sum_{i=1}^m H_i$ where each $H_i$ can be efficiently simulated. Approaches relying on product formula generally work by splitting the evolution time into segments, and approximate the evolution in each segment by the evolution of composing Hamiltonian $H_i$. This key step incur a constraint, that prohibits a (poly)logarithmic scaling on approximation error. We employ the recently introduced quantum singular value transformation framework to utilize the ability to simulate $H_i$ in an alternative way, which then allows us to construct and simulate the main Hamiltonian $H$ with polylogarithmical scaling on the inverse of desired error, which is a major improvement with respect to product formula approaches.
Source: arXiv (Cornell University)
Author: Nghiem, Nhat A.
Institutions: State University of New York, Stony Brook University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: Stony Brook University
OpenAlex ID: W4404088489