Host: Jin-Peng Liu 刘锦鹏

Abstract: Quantum algorithms for estimating the ground state energy of a quantum system often operate by preparing a classically accessible quantum state and then applying quantum phase estimation. Whether this approach yields quantum advantage hinges on the state's energy spectrum, that is, the sequence of the state's overlaps with the energy eigenstates of the system Hamiltonian. For any entanglement-compressed quantum state with minimal expected energy, it is shown that its energy spectrum decays at most with the inverse-squared energy eigenvalues. This explains the main empirical finding of Silvester, Carleo, and White (Physical Review Letters, 2025) that the energy spectra of matrix product states do not decay exponentially. It also reduces the question of quantum advantage to the energy and entanglement profile of the Hamiltonian's eigenstates.

Bio: Daochen Wang is an Assistant Professor of Computer Science at the University of British Columbia. He received his PhD from the University of Maryland, and his BA and MMath degrees from the University of Cambridge. His research focuses on the structure, design, and application of quantum algorithms, as well as quantum cryptography. More information, including a list of publications, is available at https://wdaochen.com/.