Purdue–UMich Quantum Algorithms Seminar
November 6, 2026
Quantum Spectral Estimation with Multiple Initial States
Lingwei Zhang (University of Michigan)
4:10PM–5:10PM EST · Online
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Multiple initial states provide access to spectral information that a single state cannot reveal, including eigenvalue degeneracies and observable spectra within eigenspaces. In this talk, I will introduce QFAMES, a Gaussian-filtering framework for recovering this information from matrix-valued quantum signals. I will explain how cross amplitudes between initial states encode eigenspace structure and how QFAMES uses this structure to estimate energies, multiplicities, and observables. Then, I will present our recent work on improving its sampling efficiency. By sampling evolution times independently across state pairs, we obtain better error and cost scaling with the number of initial states under suitable assumptions, while retaining Heisenberg scaling for energy estimation.