Bell inequality violation on small NISQ computers
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.
H. W. L. Naus H. Polinder