The TopMath Elite Graduate Program regularly invites current TopMath students to its Alumni Speaker Series to give them an insight into their work and careers after completing their doctorates. Dr. Matthi-as C. Caro, currently a postdoc at Freie Universität Berlin, was invited to give a lecture on "Classical Verification of Quantum Learning".
In the past ten years, machine learning has taken the world by storm. This is partly due to high-profile events such as the Go matches between Google DeepMind's AlphaGo and Lee Sedol, one of the world's best Go players, in 2016 – reminiscent of the chess showdown between Deep Blue and Garry Kasparov in 1997. Since the advent of ChatGPT, many people worldwide have been using a machine learning model in their daily lives. However, from a user's perspective, such models are often black boxes whose internal workings are not transparent. The process through which these black boxes emerge – the training of the model – requires such vast amounts of data and computing time that it is achievable for only a few companies globally. This raises the question: Can the reliability of machine learning be verified? Recently, a work provided a positive answer to this question. Using an important paradigm from theoretical computer science, known as Interactive Proofs, they demonstrated within the framework of classical learning theory that verifying machine learning can be possible with significantly fewer resources than would be required for actually solving the learning problem.
In contrast to machine learning, which is already of great importance today, quantum computers – computers that operate based on the principles of quantum physics – are, in many ways, still a thing of the future. However, there are already results in theoretical computer science showing that quantum learning algorithms, using quantum data, can efficiently solve specific classically intractable learning problems. In addition to the resource requirements of machine learning, such quantum learners would also rely on quantum computers, which, at least in the medium term, will only be accessible to a few. Thus, the question of verification becomes even more pressing. In the work, we build upon ideas, translate them into scenarios involving quantum learners, and identify classically hard learning problems that can be efficiently verified by delegating them to a quantum learner. We see this as a theoretical foundation upon which a theory of quantum learning with classically verifiable quantum advantages can be developed.
Text: Dr. Matthias C. Caro, Alumnus Elite Graduate Program "TopMath"
