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What is Bell’s nonlocal connectivity? Bell Nonlocality via Machine Learning 

What is Bell’s nonlocal connectivity? Bell Nonlocality via Machine Learning 

Artificial Intelligence & Machine Learning

In our research at Fordham University, we explore the application of symbolic regression, a machine learning tool, to derive a symbolic form for the CHSH inequality, a fundamental concept in quantum mechanics and Bell nonlocality.

Our approach combines elements from various fields of machine learning and quantum physics to address a complex problem in a novel way.

Understanding Bell Nonlocality

We begin by discussing Bell nonlocality, delving into local theory and its assumptions. This concept is pivotal in understanding quantum mechanics and how it challenges traditional notions of locality. We focus on the Bell Scenario, where observers (like Alice and Bob in our paper) perform measurements on a shared physical system, such as an entangled pair. In addition, we delve into the complexities of these measurements and outcomes, setting the stage for our exploration of the CHSH inequality.

Machine Learning and Symbolic Regression

In the realm of machine learning, our research leverages symbolic regression, a powerful tool that generates models based on data availability, operator selection, and complexity constraints. We specifically selected PySR, a Python package with a Julia backend, for its efficiency in tree-search codes and flexibility in scientific computing. This choice allowed us to effectively generate and process data for our symbolic regression model.

Research Methodology and Data Generation

Our methodology involved generating a dataset that represents all possible probabilities in various experimental iterations performed by Alice and Bob. We used libraries like Numpy and Pandas for this purpose and applied symbolic regression to this dataset. Our goal was to find a symbolic equation that could represent the relationships in our data, particularly focusing on the left-hand side of the Bell inequality.

Results and Implications

The results of our experiment were promising. Our model successfully predicted the exact left-hand side of the Bell inequality, demonstrating low loss with a reasonable level of complexity. This outcome indicates the potential of symbolic regression in uncovering complex relationships in quantum physics data.

Future Directions

While our current work focuses on the Bell inequality and its implications in quantum theory, we see several potential directions for future research. Furthermore, these include exploring other expressions in quantum computing using machine learning techniques. Thus, examining quantum behaviors at different hierarchy levels, and applying symbolic regression to quantum data generated using open-source libraries like Qiskit or Cirq.

Our work demonstrates the efficacy of symbolic regression in tackling complex quantum mechanics problems and paves the way for further exploration in this intriguing intersection of machine learning and quantum physics.

Written by Faruque Khan

What is Bell’s nonlocal connectivity?