Efficiently preparing quantum samples
Benjamin Wong
Given a classical probability distribution $p(x),$ we consider the task of preparing the quantum sample $\sum_x\sqrt{p(x)}|x\rangle$ efficiently on a quantum computer. Quantum samples arise naturally in the study of thermal states, in existing quantum algorithms for volume estimation and sampling, and in the design of quantum new algorithms. We give two new algorithms for preparing quantum samples within the Grover-Rudolph framework. The first algorithm prepares thermal states for a large family of ferromagnetic Hamiltonians. The second algorithm, when provided with quasipolynomial-sized classical data, prepares any state for which the corresponding generating polynomial satisfies a strong zero-free condition.
This talk is based on work from my upcoming master's thesis and the preprint https://arxiv.org/abs/2602.03605
Location
QNC 1201