[Paper Review] Measuring the Mermin-Peres magic square using an online quantum computer

A. Dikme, N. Reichel+2 more|arXiv (Cornell University)|Sep 22, 2020

Quantum Mechanics and Applications1 references4 citations

TL;DR

This paper demonstrates the first implementation of the Mermin-Peres magic square contextuality test on a publicly accessible, online five-qubit quantum computer. Using sequential, non-demolition measurements on a two-qubit system, the experiment violates realistic and non-contextual models by approximately 28 standard deviations, confirming quantum mechanics' non-classical nature despite significant noise in current NISQ devices.

ABSTRACT

We have implemented the six series of three commuting measurement of the Mermin-Peres magic square on an online, five qubit, quantum computer. The magic square tests if the measurements of the system can be described by physical realism (in the EPR sense) and simultaneously are non-contextual. We find that our measurement results violate any realistic and non-contextual model by almost 28 standard deviations. We also find that although the quantum computer we used for the measurements leaves much to be desired in producing accurate and reproducible results, the simplicity, the ease of re-running the measurement programs, and the user friendliness compensates for this fact.

Motivation & Objective

• To test quantum contextuality and realism using the Mermin-Peres magic square on a publicly accessible quantum computer.
• To assess the feasibility and accuracy of performing complex quantum contextuality experiments via online quantum computing platforms.
• To evaluate the performance of current noisy intermediate-scale quantum (NISQ) devices in realizing state-independent contextuality tests.
• To demonstrate that user-friendly, remote access to quantum hardware enables advanced foundational quantum physics experiments without specialized lab infrastructure.

Proposed method

• The Mermin-Peres magic square, a 3×3 matrix of two-qubit Pauli observables, was implemented on a five-qubit online quantum computer using sequential, non-demolition measurements.
• Six series of three commuting measurements were performed, each corresponding to a row or column of the magic square, with outcomes restricted to ±1.
• Quantum non-demolition (QND) measurement techniques were employed to preserve the state between sequential measurements, relying on entanglement with ancilla qubits.
• Measurement outcomes were collected over multiple runs (typically 8000–10000 shots per circuit), and statistical analysis was performed to compute mean outcome vectors and standard deviations.
• A convex hull of all classically allowed outcome vectors under realism and non-contextuality was constructed using Delaunay triangulation and constrained nonlinear optimization to find the closest point to the measured result vector.
• The Euclidean distance between the measured result vector and the nearest point on the convex hull was computed, and the result was normalized by a standard deviation sphere to determine the statistical significance of the violation.

Experimental results

Research questions

• RQ1 Can the Mermin-Peres magic square contextuality test be successfully implemented on a publicly available, online quantum computer?
• RQ2 To what extent do current noisy intermediate-scale quantum (NISQ) devices produce results consistent with quantum mechanical predictions for contextuality?
• RQ3 How significant is the statistical violation of realistic and non-contextual models in a real-world, noisy quantum computing environment?
• RQ4 Can the simplicity and accessibility of online quantum computers compensate for hardware imperfections in foundational quantum experiments?

Key findings

• The experiment achieved a statistical violation of any realistic and non-contextual model by approximately 27.8 standard deviations, with a measured distance of 0.4029 from the classical convex hull.
• The standard deviation sphere radius was calculated as 0.0145, providing a conservative error estimate for the measurement uncertainty.
• Approximately 10–30% of program runs produced results inconsistent with quantum predictions due to decoherence, gate infidelities, and readout errors, highlighting the noise in current NISQ devices.
• Despite hardware imperfections, the results strongly support quantum mechanics and rule out local, realistic, and non-contextual models.
• The study confirms that online quantum computers, though noisy, are sufficient for testing foundational quantum phenomena like contextuality.
• The user-friendliness, reusability, and remote accessibility of online quantum platforms significantly offset their technical limitations for foundational physics experiments.