Mermin's inequalities of multiple qubits with orthogonal measurements onIBMQ 53‐qubit system

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

doi:10.1002/que2.45

Ching‐Ray Chang, Wei‐Jia Huang + Show 4 more

Open Access

https://doi.org/10.1002/que2.45

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Abstract

Entanglement properties of IBM Q 53 qubit quantum computer are carefully examined with the noisy intermediate-scale quantum (NISQ) technology. We study GHZ-like states with multiple qubits (N=2 to N=7) on IBM Rochester and compare their maximal violation values of Mermin 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 (LR). 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.

Highlights

Entanglement is a very unique feature of the quantum sciences and cannot be observed in the classical world
To study robustness of entanglement for the IBM Rochester 53-qubit system, we propose an orthogonal measurement to study the entanglement strength for systems with local realism (LR) below the maximal value
We have used GHZ-like states to study the entangled pairs on the IBM Rochester 53 quits quantum computer and most of the pairs we have studied either had the orthogonal properties between ⟨Mn⟩ and ⟨Mn′ ⟩ or violated LR of Mermin’s inequalities two qubits are entangled under noisy intermediate-scale quantum (NISQ) and the IBM Rochester quantum computer performs reasonably well with 2-qubit entanglement

Summary

Introduction

Entanglement is a very unique feature of the quantum sciences and cannot be observed in the classical world Coherence is another general property of waves and describes the correlation between the constituent parts. The full understanding of the entanglement properties of a large number of qubits within state-of-art quantum computers, e.g., IBM Rochester, becomes critical for the real applications. We propose to use orthogonal measurements of Mermin’s inequalities[2] to study the influence of phase angles and the correlations of orthogonal measurements in GHZ-like states[7]. The goal of experimental test on IBM Rochester is to characterize the entanglement behavior of N-qubits, and GHZ-like state[7] can assure the Mermin’s polynomials will be maximum. For Mn and Mn′ , the orthogonal measurements within an entangled system are strongly correlated, this unique quantum sum rule is very different from the independent and isotropy nature of a classical system

Method

Discussion and conclusion