Testing Scalable Bell Inequalities for Quantum Graph States on IBM
  Quantum Devices
Testing and verifying imperfect multi-qubit quantum devices are important as
such noisy quantum devices are widely available today. Bell inequalities are
known useful for testing and verifying the quality of the quantum devices from
their nonlocal quantum states and local measurements. There have been many
experiments demonstrating the violations of Bell inequalities but they are
limited in the number of qubits and the types of quantum states. We report
violations of Bell inequalities on IBM Quantum devices based on the scalable
and robust inequalities maximally violated by graph states as proposed by
Baccari et al. (Ref.[1]). The violations are obtained from the quantum states
of path graphs up to 57 and 21 qubits on the 65-qubit and 27-qubit IBM Quantum
devices, respectively, and from those of star graphs up to 8 and 7 qubits with
error mitigation on the same devices. We are able to show violations of the
inequalities on various graph states by constructing low-depth quantum circuits
producing them, and by applying the readout error mitigation technique. We also
point out that quantum circuits for star graph states of size N can be realized
with circuits of depth $O(\sqrt n)$ on subdivided honeycomb lattices which are
the topology of the 65-qubit IBM Quantum device. Our experiments show
encouraging results on the ability of existing quantum devices to prepare
entangled quantum states, and provide experimental evidences on the benefit of
scalable Bell inequalities for testing them.
Bo Yang Rudy Raymond Hiroshi Imai Hyungseok Chang Hidefumi Hiraishi