IQC Colloquium featuring Mark M. Wilde

Machina Ex Quanta: Rise of the Quantum Boltzmann Machines

Mark M. Wilde | Cornell University

Boltzmann machines are a well established model for classical machine learning, based on ideas rooted in physics like thermal distributions. Roughly eight years ago now, quantum Boltzmann machines were proposed as a generalization of their classical counterparts and can be understood as parameterized thermal states of local Hamiltonians. While this generalization allows for non-commuting Hamiltonians inaccessible in the classical case, training them for various optimization tasks had remained an obstacle.

In this talk, I'll discuss how my coauthors and I have overcome this obstacle by deriving analytical expressions for the gradient and providing quantum algorithms that can estimate it. The algorithms make use of standard primitives such as the Hadamard test, classical sampling, and Hamiltonian simulation.

I'll also show how to train quantum Boltzmann machines using a metric-aware gradient descent algorithm, which makes use of analytical expressions we have derived for quantum generalizations of the Fisher information matrix and quantum algorithms we have constructed for estimating information matrix elements.

Finally, I'll introduce a new model called evolved quantum Boltzmann machines, which uses parameterized time-evolved thermal states as an ansatz, extending the conventional model of quantum Boltzmann machines. Evolved quantum Boltzmann machines incorporate real and imaginary time evolution according to two different non-commuting parameterized Hamiltonians, and they can also be trained using metric-aware gradient descent.

If time permits, I'll mention applications of our findings to estimating time-evolved thermal states. Based on joint work with Daniel Koch, Michele Minervini, Dhrumil Patel, Saahil Patel, and available at

Quantum Boltzmann machine learning of ground-state energies; arXiv:2410.12935

Natural gradient and parameter estimation for quantum Boltzmann machines; arXiv:2410.24058

Evolved Quantum Boltzmann Machines; arXiv:2501.03367

Biography

Mark M. Wilde received the Ph.D. degree in electrical engineering from the University of Southern California, Los Angeles, California. He is an Associate Professor of Electrical and Computer Engineering at Cornell University. He is an IEEE Fellow, he is a recipient of the National Science Foundation Career Development Award, he is a co-recipient of the 2018 AHP-Birkhauser Prize, awarded to “the most remarkable contribution” published in the journal Annales Henri Poincare, and he is an Outstanding Referee of the American Physical Society. His current research interests are in quantum Shannon theory, quantum computation, quantum optical communication, quantum computational complexity theory, and quantum error correction.

Location

• QNC 0101