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arXiv:2505.21243

Empirical Demonstration of Quantum Contextuality on NISQ Computers

Colm Kelleher, Frédéric Holweck

Published May 27, 2025• 0 citations
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Abstract

We present definitive violations of non-contextual hidden variable bounds in the latest generation of IBM noisy intermediate-scale quantum computers (NISQ). These violations are based on known tests for contextuality such as the Rio Negro inequality and pseudo-telepathic Mermin games. These are the first violations of the classical Mermin game on IBM NISQ computers, and the largest such violations for the Rio Negro inequality. The use of finite geometries proves instrumental in the development of more effective tests, with larger geometries providing sizeable datasets from which multiple distinct experiments can be compared.

DOI
10.48550/arxiv.2505.21243

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We present definitive violations of non-contextual hidden variable bounds in the latest generation of IBM noisy intermediate-scale quantum computers (NISQ). These violations are based on known tests for contextuality such as the Rio Negro inequality and pseudo-telepathic Mermin games. These are the first violations of the classical Mermin game on IBM NISQ computers, and the largest such violations for the Rio Negro inequality. The use of finite geometries proves instrumental in the development of more effective tests, with larger geometries providing sizeable datasets from which multiple distinct experiments can be compared.
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Abstract It is known that Mermin-Peres like proofs of quantum contextuality can furnish non-local games with a guaranteed quantum strategy, when classically no such guarantee can exist. This phenomenon, also called quantum pseudo-telepathy, has been studied in the case of the so-called Mermin Magic square game. In this paper we review in detail two different ways of implementing on a quantum computer such a game and propose a new Doily game based on the geometry of 2-qubit Pauli group. We show that the quantumness of these games are almost revealed when we play them on the IBM Quantum Experience, however the inherent noise in the available quantum machines prevents a full demonstration of the non-classical aspects.
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.
The contextuality of quantum mechanics can be shown by the violation of inequalities based on measurements of well chosen observables. These inequalities have been designed separately for both discrete and continuous variables. Here we unify both strategies by introducing general conditions to demonstrate the contextuality of quantum mechanics from measurements of observables of arbitrary dimensions. Among the consequences of our results is the impossibility of having a maximal violation of contextuality in the Peres-Mermin scenario with discrete observables of odd dimensions. In addition, we show how to construct a large class of observables with a continuous spectrum enabling the realization of contextuality tests both in the Gaussian and non-Gaussian regimes.
Quantum games embody non-intuitive consequences of quantum phenomena, such as entanglement and contextuality. The Mermin-Peres game is a simple example, demonstrating how two players can utilise shared quantum information to win a no - communication game with certainty, where classical players cannot. In this paper we look at the geometric structure behind such classical strategies, and borrow ideas from the geometry of symplectic polar spaces to maximise this quantum advantage. We introduce a new game called the Eloily game with a quantum-classical success gap of 0.26‾0.2\overline{6}0.26, larger than that of the Mermin-Peres and doily games. We simulate this game in the IBM Quantum Experience and obtain a success rate of 111, beating the classical bound of 0.73‾0.7\overline{3}0.73 demonstrating the efficiency of the quantum strategy.
Soon after the dawn of quantum error correction, DiVincenzo and Peres observed that stabilizer codewords could give rise to simple proofs of quantumness via contextuality. This discovery can be recast in the language of nonlocal games: every nnn-qubit stabilizer state defines a specific "stabilizer-testing" nnn-player nonlocal game, which quantum players can win with probability one. If quantum players can moreover outperform all possible classical players, then the state is contextual. However, the classical values of stabilizer-testing games are largely unknown for scalable examples beyond the nnn-qubit GHZ state. We introduce several new methods for upper-bounding the classical values of these games. We first prove a general coding-theory bound for all stabilizer-testing games: if the classical value pcl∗<1p_{\mathrm{cl}}^* < 1pcl∗​<1, then pcl∗≤7/8p_{\mathrm{cl}}^* \leq 7/8pcl∗​≤7/8, i.e., there is no classical strategy that can perform as well as the optimal quantum strategy even in an asymptotic sense. We then show how to tighten this bound for the most common scalable examples, namely GHZ, toric-code and cyclic cluster states. In particular, we establish an asymptotically tight upper bound for cyclic cluster states using transfer-matrix methods. This leads to the striking conclusion that measuring an exponentially small fidelity to the cyclic cluster state will suffice to witness its contextuality.