#Winning at CHSH with Parameterized Quantum Circuits and Bayesian Optimization
In this experiment I've tried to "win" a formulation of the CHSH game 1 in the formulation proposed by Mark Wilde 2 (Sec. 3.6.2 : Entanglement in the CHSH Game) and Ronald de Wolf 3 (Sec. 15.2: CHSH: Clauser-Horne-Shimony-Holt).
This was done through the combined usage of cirq and bayesian optimization, as the goal is to find the optimal set of parameters that show the ability of winning at the CHSH game.
Starting from a small parameterized quantum circuit (7 parameterized gates and 3 Hadamard gates) randomly initialized, a global black-box optimization strategy was employed searching for the optimal parameters.
The goal is to maximize the probability of winning the CHSH game and this is done alternating two phases: the first one is the simulation of the circuit, which leads us to a performance metric (the #wins/#runs ratio). This metric guides the optimizer in the second phase, searching for the set of parameters that maximize this ratio.
You can read my blog post for a few more details or look at my slides.