



01443nas a2200121   4500008004100000245004000041210004000081260001400121520110400135100002401239700002101263856003701284       2023                        eng d00aBell sampling from quantum circuits0 aBell sampling from quantum circuits  c6/19/20233 a<p>A central challenge in the verification of quantum computers is benchmarking their performance as a whole and demonstrating their computational capabilities. In this work, we find a model of quantum computation, Bell sampling, that can be used for both of those tasks and thus provides an ideal stepping stone towards fault-tolerance. In Bell sampling, we measure two copies of a state prepared by a quantum circuit in the transversal Bell basis. We show that the Bell samples are classically intractable to produce and at the same time constitute what we call a circuit shadow: from the Bell samples we can efficiently extract information about the quantum circuit preparing the state, as well as diagnose circuit errors. In addition to known properties that can be efficiently extracted from Bell samples, we give two new and efficient protocols, a test for the depth of the circuit and an algorithm to estimate a lower bound to the number of T gates in the circuit. With some additional measurements, our algorithm learns a full description of states prepared by circuits with low T-count.</p>1 aHangleiter, Dominik1 aGullans, Michael  uhttps://arxiv.org/abs/2306.00083