Testing Scalable Bell Inequalities for Quantum Graph States on IBM Quantum Devices

Abstract

Testing and verifying imperfect multi-qubit quantum devices are important as such noisy quantum devices are widely available today. Bell inequalities are known to be 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.. The violations are obtained from the quantum states of path graphs up to 57 and 21 qubits on a 65-qubit and two 27-qubit IBM Quantum devices, respectively, and from those of star graphs up to 11 qubits with quantum readout error mitigation (QREM). We are able to show violations of the inequalities on various graph states by constructing low-depth quantum circuits and by applying the QREM technique. We also point out that quantum circuits for star graph states of size <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> can be realized with circuits of depth <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$O(\sqrt {N})$ </tex-math></inline-formula> 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 evidence on the benefit of scalable Bell inequalities for testing them.