Empirical Demonstration of Quantum Contextuality on NISQ Computers

TL;DR

The paper addresses empirical quantum contextuality on NISQ devices by adopting a geometry-based framework that links contextual constraints to finite geometries, enabling tests via the Rio Negro inequality and Mermin-like games. It formalizes contextuality as a geometric property within structures such as the symplectic polar space $\mathcal{W}(5,2)$ and related quadrics, using the bound $\chi \le L - 2d$ to distinguish noncontextual models. Key contributions include the first Mermin-game victory on modern IBM backends and improved Rio Negro violations across larger operator geometries, demonstrating robust contextuality on noisy hardware. The work provides a scalable approach for hardware-aware contextuality benchmarking and offers open-source resources to reproduce and extend these tests on future quantum processors.

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.

Figures (3)

• Figure 1: The Peres-Mermin Magic Square (left) consisting of 9 operators (points) and 6 contexts (lines) of 3 operators each. The doily (right) with 15 points, 15 lines. Each context line gives a constraint on measurement outcome products, with black lines indicating $+1$ and red $-1$. The square has degree $d=1$, the doily $d=3$.
• Figure 2: Distributions for geometries squares, doilies, elliptic quadrics $E_{p}$ and hyperbolic quadrics $H_{p}$ vs. $\chi_{\text{NISQ}}$ values, from data computing $\langle{\mathcal{C}}\rangle$ for each context in $\mathcal{W}(5,2)$. NCHV upper bounds shown in red, with each geometry clearly violating its bound.
• Figure 3: Distributions for squares, doilies vs. $\sigma_{\text{NISQ}}$ values from $E_{YYY}$$ll$ game. NCHV upper bounds shown in red, with all but one square violating its bound.