Bell inequality violation on small NISQ computers

TL;DR

This paper demonstrates Bell inequality violations using small NISQ quantum computers through specific quantum algorithms, avoiding detection and freedom-of-choice loopholes, and confirms results via simulations and real hardware experiments.

Contribution

It introduces new quantum algorithms for Bell tests on NISQ devices that address common loopholes and validate Bell violations with minimal measurements.

Findings

Bell inequality violation confirmed on NISQ simulators and hardware.

Algorithms effectively avoid detection and freedom-of-choice loopholes.

Results are robust even with added noise.

Abstract

Quantum computational experiments exploiting Noisy Intermediate-Scale Quantum (NISQ) devices to demonstrate violation of a Bell inequality are proposed. They consist of running specified quantum algorithms on few-qubit computers. If such a device assures entanglement and performs single-shot measurements, the detection loophole is avoided. Four concise quantum circuits determining the expectation values of the relevant observables are used for a two-qubit system. It is possible to add an ancilla qubit to these circuits and eventually only measure the ancilla to obtain the relevant information. For a four-qubit NISQ computer, two algorithms yielding the same averages, however also guaranteeing a random choice of the observable, are developed. A freedom-of-choice loophole is therefore avoided. Including an additional ancilla reduces the number of measurements by one since in this case only the ancillas need to be measured. Note that these methods, using the NISQ device, are intrinsically quantum mechanical. Locality loopholes cannot be excluded on present NISQ systems. Results of simulations on the QX simulator of Quantum Inspire are presented. The Bell inequality is indeed found to be violated, even if some additional noise is included by means of the depolarizing channel error model. The algorithms have been implemented on the IBM Q Experience as well. The results of these quantum computations support a violation of the Bell inequality by various standard deviations.