Year: 2026
Type: preprint
Abstract: We study quantum spectrum and eigenstate property estimation using multiple initial states and generalized Hadamard tests. Building on the QFAMES (quantum filtering and analysis of multiplicities in eigenvalue spectra) framework, we introduce a new method that samples evolution times independently for each initial-state pair. Under the stated assumptions, when statistical error determines the sampling cost, the total Hamiltonian simulation cost required for fixed-accuracy eigenvalue and observable estimation is independent of the number of initial states, up to logarithmic factors. This improves scalability when many initial states are needed to explore the target eigenspaces. The method also reduces the cost of multiplicity recovery and retains Heisenberg-limited scaling for eigenvalue estimation. Numerical experiments support the predicted statistical error scalings.
Source: arXiv (Cornell University)
Authors: Zhang, Lingwei, Ding, Zhiyan
Institution: University of Michigan
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7222211884