Southwest Quantum Information and Technology

Query-optimal estimation of unitary channels in diamond distance

Presenting Author: Ewin Tang, University of Washington

We will present an algorithm to learn an unknown unitary channel acting on a d-dimensional qudit to diamond-norm error \(\varepsilon\), using \(O(d^2/\varepsilon)\) applications of the unknown channel and only one qudit. This algorithm uses the optimal number of qudits and number of queries up to a sub-logarithmic factor, even if one has access to the inverse or controlled versions of the unknown unitary. This improves over prior work, which achieves entanglement infidelity \(\delta\) using \(O(d^2/\sqrt{\delta})\) applications in parallel, thereby requiring \(\Omega(d^2)\) qudits. Based on joint work with Jeongwan Haah, Robin Kothari, and Ryan O'Donnell.

(Session 3 : Thursday from 1:30 pm - 2:15 pm)