Feature: Add Magic Square game for Contextuality demonstration

[alejogoogle]

This PR adds a new experimental module to the ReCirq repository that implements the Mermin-Peres Magic Square game (a form of quantum pseudo-telepathy).

Specifically, this code:

• Adds new functionality: It provides a framework to run the game using cirq on both simulators and quantum hardware.

• Implements three experimental variations:

  1. infer_3rd: Measuring two observables and calculating the third classically.

  2. measure_3rd_classical_multiplication: Measuring components and multiplying the outcomes.

  3. measure_3rd_quantum_multiplication: Using two-qubit interactions to directly measure the product observable.

• Provides analysis tools: Includes a ContextualityResult class to calculate win rates, agreement matrices, and parity check fractions to verify quantum non-locality.

Relevance to Contextuality Work
The Magic Square game is a cornerstone "warm-up" experiment for demonstrating quantum contextuality (https://arxiv.org/pdf/2512.02284). It proves that measurement outcomes cannot be pre-determined independently of their "context" (which other measurements are performed simultaneously).

No new external libraries are required.

[mhucka]

In addition to addressing Doug's comments about the code, I think also it's important to add a description to the pull request. Here are some points to address:

• What is this PR for? What does it actually do? From the title, one can infer it concerns a game, but that's about it – the title doesn't say if this PR adds code for a game, or fixes a problem with exiting code, or something else. (We shouldn't assume that the reader of the PR will take time to read the code in order to deduce these things.)

• What is the relevance to the contextuality work? Is this game mentioned in the paper, or is it just a fun supplement, or something else? (We shouln't assume that the reader will go look at the paper to figure that out.)

• Is this related to any other PR or issue in the ReCirq repo?

• Does this game require new libraries that aren't already in the project's requirements?

I realize it's more work to write a description, and I'm sorry for that. Perhaps an AI tool can help with this in some way.

[mhucka]

A number of these items are nit-picky details, and I tried to make it easy to accept or reject the changes using GitHub's interface for suggested edits. Hopefully that'll make this easier.

[mhucka]

Almost there! One

[mhucka]

Looks like something happened to the formatting of this docstring. Suggested fix:

Suggested change

	"""Find the fraction of the time that Alice and Bob
	Alice and Bob "agree" (in the intersection)
	and
	they "multiply correctly" (alice to -1 and bob to +1).
	"""Find the fraction of the time that Alice and Bob "agree" (in the intersection)
	and they "multiply correctly" (alice to -1 and bob to +1).

[mhucka]

Also, @alejogoogle should that really say alice to -1 and bob to +1? I thought Alice was +1 and Bob was -1.