Bell sampling from quantum circuits

TL;DR

This paper introduces Bell sampling as a universal quantum computation model that enables efficient benchmarking, error diagnosis, and circuit analysis, demonstrating its potential for advancing quantum computer verification and fault-tolerance.

Contribution

It presents Bell sampling as a new universal model for quantum computation that facilitates benchmarking, error detection, and circuit property estimation.

Findings

Bell samples are classically intractable to produce.

Bell samples can be used to efficiently extract circuit information.

Protocols for fidelity estimation, circuit depth testing, and T-gate counting are introduced.

Abstract

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 universal 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 several new and efficient protocols: an estimator of state fidelity, 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.