With quantum computing’s potential to be exponentially more powerful than classical computing, due to superposition and entanglement, several companies including IBM have started to develop quantum computers. Since 2016, IBM has developed publicly accessible cloud-based quantum computers. While the development of quantum computing can revolutionize decryption, optimization, and the simulation of quantum systems, quantum computers must maintain a high level of accuracy as they are scaled up. This paper introduces the fundamental gates used on IBM’s quantum computers and provides visualizations of each gate. A thought experiment involving two quantum entangled particles is used to explain the Einstein-Podolsky-Rosen Paradox, and two potential explanations are introduced: violation of locality and the Hidden Variable Theory. Experimental results are reported for the quality of entanglement created on IBM’s publicly accessible 5-qubit quantum computers by creating entanglement between 2 qubits and then measuring both qubits along a set combination of axes, and demonstrating the violation of the Bell-CHSH Inequality. Six out of seven 5-qubit quantum computers violated the Bell-CHSH Inequality, thus demonstrating strong quantum entanglement between 2 qubits, a standard crucial for scaling up quantum computers to harness their exponentially scaling power.
With quantum computing’s potential to be exponentially more powerful than classical computing, due to superposition and entanglement, several companies including IBM have started to develop quantum computers. Since 2016, IBM has developed publicly accessible cloud-based quantum computers. While the development of quantum computing can revolutionize decryption, optimization, and the simulation of quantum systems, quantum computers must maintain a high level of accuracy as they are scaled up. This paper introduces the fundamental gates used on IBM’s quantum computers and provides visualizations of each gate. A thought experiment involving two quantum entangled particles is used to explain the Einstein-Podolsky-Rosen Paradox, and two potential explanations are introduced: violation of locality and the Hidden Variable Theory. Experimental results are reported for the quality of entanglement created on IBM’s publicly accessible 5-qubit quantum computers by creating entanglement between 2 qubits and then measuring both qubits along a set combination of axes, and demonstrating the violation of the Bell-CHSH Inequality. Six out of seven 5-qubit quantum computers violated the Bell-CHSH Inequality, thus demonstrating strong quantum entanglement between 2 qubits, a standard crucial for scaling up quantum computers to harness their exponentially scaling power.
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.
This work provides quantitative tests of the extent of violation of two inequalities applicable to qubits coupled into Bell states, using IBM's publicly accessible quantum computers. Violations of the inequalities are well established. Our purpose is not to test the inequalities, but rather to determine how well quantum mechanical predictions can be reproduced on quantum computers, given their current fault rates. We present results for the spin projections of two entangled qubits, along three axes A, B, and C, with a fixed angle θ between A and B and a range of angles θ' between B and C. For any classical object that can be characterized by three observables with two possible values, inequalities govern relationships among the probabilities of outcomes for the observables, taken pairwise. From set theory, these inequalities must be satisfied by all such classical objects; but quantum systems may violate the inequalities. We have detected clear-cut violations of one inequality in runs on IBM's publicly accessible quantum computers. The Clauser-Horne-Shimony-Holt (CHSH) inequality governs a linear combination S of expectation values of products of spin projections, taken pairwise. Finding S > 2 rules out local, hidden variable theories for entangled quantum systems. We obtained values of S greater than 2 in our runs prior to error mitigation. To reduce the quantitative errors, we used a modification of the error-mitigation procedure in the IBM documentation. We prepared a pair of qubits in the state |00〉, found the probabilities to observe the states |00〉, |01〉, |10〉, and |11〉 in multiple runs, and used that information to construct the first column of an error matrix M. We repeated this procedure for states prepared as |01〉, |10〉, and |11〉 to construct the full matrix M, whose inverse is the filtering matrix. After applying filtering matrices to our averaged outcomes, we have found good quantitative agreement between the quantum computer output and the quantum mechanical predictions for the extent of violation of both inequalities as functions of θ'.
Abstract This laboratory work presents a practical implementation of the CHSH game using the Qiskit framework and IBM quantum hardware. The material is based on educational resources developed by the International Quantum Center at CERN (Switzerland) and aims to provide an experimental demonstration of quantum nonlocality and Bell inequality violation. In Laboratory Work No. 4, participants implement a simplified version of the Clauser–Horne–Shimony–Holt (CHSH) game to test whether IBM quantum processors exhibit genuinely quantum behavior. The CHSH game is a fundamental protocol in quantum information theory that distinguishes classical correlations from quantum correlations through statistical violation of Bell inequalities. Using Qiskit, a two-qubit entangled state is prepared and measurement settings corresponding to different basis choices are applied. By executing the circuit multiple times on a simulator and real quantum hardware, participants collect measurement statistics and compute the CHSH correlation parameter. If the experimentally obtained value exceeds the classical bound, the results provide empirical evidence of quantum entanglement and nonlocal correlations. This laboratory exercise demonstrates how foundational concepts of quantum mechanics—entanglement, superposition, and measurement basis dependence—can be directly tested using cloud-accessible quantum processors. The experiment not only reinforces theoretical understanding of Bell inequalities but also introduces practical skills in circuit construction, parameterized measurements, statistical analysis, and noise considerations in real quantum devices.
Quantum entanglement has gained significant attention in recent years owing to its diverse application in quantum informatics. Its nonlocal nature makes it a crucial resource in quantum information, especially in quantum communication and networking. Entanglement plays a vital role in advancing quantum computation and technology.This study discusses the creation of entangled quantum states using photon pairs and the measurement of entanglement, utilizing the IBM Q Experience the first industrial initiative to develop universal quantum computers and provide widespread access to these technologies through cloud platforms. The introduction of the Qiskit tool has enabled researchers, educators, developers, and enthusiasts to write code and conduct experiments on quantum machines. In this study, we implemented and tested circuits on the IBM Q quantum computing platform using Qiskit to execute quantum computing programs such as the Bell Inequality, CHSH Inequality, and Five-Qubit GHZ States, with two successful programming presented, these tools, along with the associated Jupyter Notebook pages, serve as additional resources for users of the IBM Q Experience. We present the results which will help evaluate these prototypes’ performance. Where quantum computers are designed to process information units that go beyond mere abstract mathematical entities, as suggested by Shannon’s theory; instead, they represent real physical objects defined by one of the two fundamental physical theories—quantum mechanics.
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.
The aim of this paper is to attract the attention of experimenters to the original Bell (OB) inequality that was shadowed by the common consideration of the Clauser-Horne-Shimony-Holt (CHSH) inequality. There are two reasons to test the OB inequality and not the CHSH inequality. First of all, the OB inequality is a straightforward consequence to the Einstein-Podolsky-Rosen (EPR) argumentation. In addition, only this inequality is directly related to the EPR-Bohr debate. The second distinguishing feature of the OB inequality was emphasized by Itamar Pitowsky. He pointed out that the OB inequality provides a higher degree of violations of classicality than the CHSH inequality. For the CHSH inequality, the fraction of the quantum (Tsirelson) bound Q CHSH = 2 2 to the classical bound C CHSH = 2 , i.e., F CHSH = Q CHSH C CHSH = 2 is less than the fraction of the quantum bound for the OB inequality Q OB = 3 2 to the classical bound C OB = 1 , i.e., F OB = Q OB C OB = 3 2 . Thus, by violating the OB inequality, it is possible to approach a higher degree of deviation from classicality. The main problem is that the OB inequality is derived under the assumption of perfect (anti-) correlations. However, the last few years have been characterized by the amazing development of quantum technologies. Nowadays, there exist sources producing, with very high probability, the pairs of photons in the singlet state. Moreover, the efficiency of photon detectors was improved tremendously. In any event, one can start by proceeding with the fair sampling assumption. Another possibility is to use the scheme of the Hensen et al. experiment for entangled electrons. Here, the detection efficiency is very high.