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arXiv:2005.12504 · Quantum Engineering

Mermin's inequalities of multiple qubits with orthogonal measurements on IBM Q 53‐qubit system

Wei‐Jia Huang, Wei‐Chen Chien, Chien‐Hung Cho, Che‐Chun Huang, Tsung‐Wei Huang, Ching‐Ray Chang

Published May 28, 2020• 32 citations
arXivHTMLPDF

Abstract

Entanglement properties of IBM Q 53-qubit quantum computer are carefully examined with the noisy intermediate-scale quantum technology. We study Greenberger-Horne-Zeilinger-like states with multiple qubits (N = 2 to N = 7) on IBM Rochester and compare their maximal violation values of Mermin's polynomials with analytic results. A rule of N-qubits orthogonal measurements is taken to further justify the entanglement less than maximal values of local realism. The orthogonality of measurements is another reliable criterion for entanglement except the maximal values of LR. Our results indicate that the entanglement of IBM 53 qubits is reasonably good when N ≤ 4, while for the longer entangle chains, the entanglement is only valid for some special connectivity.

DOI
10.1002/que2.45

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Entanglement properties of IBM Q 53-qubit quantum computer are carefully examined with the noisy intermediate-scale quantum technology. We study Greenberger-Horne-Zeilinger-like states with multiple qubits (N = 2 to N = 7) on IBM Rochester and compare their maximal violation values of Mermin's polynomials with analytic results. A rule of N-qubits orthogonal measurements is taken to further justify the entanglement less than maximal values of local realism. The orthogonality of measurements is another reliable criterion for entanglement except the maximal values of LR. Our results indicate that the entanglement of IBM 53 qubits is reasonably good when N ≤ 4, while for the longer entangle chains, the entanglement is only valid for some special connectivity.
The difference between a quantum computer and a classical computer is that the classical computer one bit has zero and one states with only 2^n states for n bits, while the quantum computer has the nature that phase and entanglement, so the quantum computer has more variations and can have nearly infinite possibilities. Therefore, the two principal axes of this paper are to observe the entangled state characteristics of multiple qubits (N=2 to N=7) on the IBM Q 53 qubit quantum computer and the influence of phase on the entangled state properties. The first part, which has been published in Quantum Engineering, is the GHZ-like states of multiple qubits (N = 2 to N = 7) in IBM Rochester, and compares the maximum violation values of Mermin orthogonal polynomials with the analytic results among each other. In another experiment, two qubits with different phase angles were used to analyze the phase trajectory, and the effect on the improved Mermin polynomial in the GHZ-like states was studied. Our results in the first part show that the entanglement nature of IBM Rochester is fairly good when N ≤ 4, while for longer chains, entanglement is only valid for certain special connections. In the other experimental phase trajectory analysis, most of the trajectories are stable circular trajectories, and under certain circumstances the GHZ-like state and its excited state will produce the evolution of resurgence and reignition.
There are different families of inequalities that can be used to characterize the entanglement of multiqubit entangled states by the violation of quantum mechanics prediction versus local realism prediction. In a noisy environment, the violation of different inequalities distinguishes a direct from a noise-free environment. That is, each inequality has a different robustness against noise. We investigate theoretically and experimentally this proposition with the Mermin inequality, Bell inequality, and Svetlichny inequality using three-qubit GHZ states for different levels of noise. Our purpose is to determine which one of the inequalities is more robust against noise and thus more suitable to characterize entanglement of states. Our results show that the Mermin inequality is the most robust against stronger noise and is, thus, more suitable for characterizing the entanglement of three-qubit GHZ states in a noisy environment.
Quantum computers have tremendous potential of simulating large quantum systems that classical computers can’t. In the theoretical verification of quantum non-locality principle, Bell’s and Mermin’s inequalities stood out, which proved to be valid in multiple empirical experiments. In this paper we report the tests of Bell and Mermin’s inequalities carried out on the 2- qubit and 3-qubit IBM quantum computer respectively. By comparing the result we obtained and the pattern predicted by the inequalities, our experimental results indicate clear violations of the two inequalities; thereby, we validate postulates in quantum mechanics and disprove the local realism argument in classical hidden variable theories proposed by Einstein, Podolsky, and Rosen on quantum circuits.
We have studied carefully the behaviors of entangled qubits on the IBM Rochester with various connectivities and under a "noisy" environment. A phase trajectory analysis based on our measurements of the GHZ-like states is performed. Our results point to an important fact that entangled qubits are "protected" against environmental noise by a scaling property that impacts only the weighting of their amplitudes. The reproducibility of most measurements has been confirmed within a reasonably short gate operation time. But there still are a few combinations of qubits that show significant entanglement evolution in the form of transitions between quantum states. The phase trajectory of an entangled evolution, and the impact of the sudden death of GHZ-like states and the revival of newly excited states are analyzed in details. All observed trajectories of entangled qubits arise under the influences of the newly excited states in a "noisy" intermediate-scale quantum (NISQ) computer.
We have studied carefully the behaviors of entangled qubits on the IBM Rochester with various connectivities and under a "noisy" environment. A phase trajectory analysis based on our measurements of the GHZ-like states is performed. Our results point to an important fact that entangled qubits are "protected" against environmental noise by a scaling property that impacts only the weighting of their amplitudes. The reproducibility of most measurements has been confirmed within a reasonably short gate operation time. But there still are a few combinations of qubits that show significant entanglement evolution in the form of transitions between quantum states. The phase trajectory of an entangled evolution, and the impact of the sudden death of GHZ-like states and the revival of newly excited states are analyzed in details. All observed trajectories of entangled qubits arise under the influences of the newly excited states in a "noisy" intermediate-scale quantum (NISQ) computer.
Violation of Mermin inequalities is tested on the five-qubit IBM quantum computer. For three, four, and five parties, quantum states that violate the corresponding Mermin inequalities are constructed using quantum circuits on superconducting qubits. Measurements on different bases are included as additional final gates in the circuits. The experimental results obtained using the quantum computer show violation of all Mermin inequalities, with a clear degradation of the results in the five-qubit case. Though this quantum computer is not competitive to test Mermin inequalities as compared to other techniques when applied to a few qubits, it does offer the opportunity to explore multipartite entanglement for four and five qubits beyond the reach of other alternative technologies.