Host: Jin-Peng Liu 刘锦鹏

Abstract: Estimating thermal expectation values of observables is a fundamental task in quantum physics, quantum chemistry, and materials science. While recent quantum algorithms have enabled efficient quantum preparation of thermal states, observable estimation via sampling remains costly: a straightforward implementation separates successive measurements by a full mixing time in order to ensure samples are approximately independent. In this work, we show that the sampling cost can be substantially reduced by using a single Gibbs-sampling trajectory. After a single burn-in period, we interleave coherent measurements that satisfy detailed balance with respect to the target Gibbs state. The efficiency of this approach rests on the fact that, in many settings, the autocorrelation time can be significantly shorter than the mixing time. For energy estimation (and more generally for observables commuting with the Hamiltonian), we implement the required measurements using Gaussian-filtered quantum phase estimation with only logarithmic overhead. We also introduce a weighted operator Fourier transform technique to mitigate measurement-induced disturbance for general observables.

Bio: Jiaqing Jiang is a Quantum Postdoctoral Fellow at the Simons Institute for the Theory of Computing, hosted by Umesh Vazirani. She got her PhD from Caltech in 2025, advised by Thomas Vidick, Urmila Mahadev, and John Preskill . She is broadly interested in quantum algorithm and quantum complexity, especially in understanding potential quantum advantage for solving quantum many-body systems, like estimating ground energy and preparing ground states / Gibbs states.