Zenith Grant Awardee

Cristhiano Andre Gamarano Duarte Carneiro Silva

Chapman University

Co-Investigators

Matthew Leifer, Chapman University

Project Title

Reasoning in a Quantum World

Project Summary

Machine learning algorithms based on deep learning have achieved impressive feats in recent years, and are having a large effect on our daily life in applications from facial recognition to determining the news feed on Facebook. Many machine learning algorithms are based on the reasoning in the face of uncertainty using the tools of probability and statistics. However, the world we live in is fundamentally quantum mechanical, and quantum systems obey a different set of rules from those described by ordinary probability theory. Therefore, if we want machines to learn about the world we actually live in, then we need a different set of techniques and algorithms to reason about the quantum world. In this proposal, we ask whether conventional machine learning algorithms can learn about the difference between the classical and quantum worlds, how to reason about cause and effect in quantum theory, and whether a quantum agent (i.e. an entity with a quantum computer for a brain) would describe the world differently than us. Apart from improving our foundational understanding, we expect this to have applications in quantum computing and information.

Technical Abstract

We pose the question "How should an intelligent agent reason in a quantum world?" Our response is broken down into three parts. We first ask whether classical deep learning algorithms can distinguish between classicality and nonclassicality based on the raw data coming from experiments. We plan to do this for quantum contextuality, which is often thought to be the "most nonclassical" quantum phenomenon. Next, we ask how a classical agent should reason about cause and effect in quantum theory. We plan to extend quantum causal models to include influence diagrams, which provide a graphical calculus for optimizing decisions based on causal structure. We plan to do this by generalizing classical inference algorithms that involve reversing edges in an influence diagram using belief propagation and Bayes' rule to quantum edge reversal based on recent quantum generalizations of Bayesian probability. Finally, we will ask how a quantum agent (i.e. an entity with a quantum computer for a brain that may be correlated with the outside world) should describe the quantum world. We plan to do this by considering the set of operations that such an agent can perform on the world, which is larger than the set accessible to a classical agent.