This talk will review our recent work on classical and quantum glasses. I will start with a discussion of spin glasses from the perspective of chaos theory.

The Thouless-Anderson-Palmer (TAP) formalism will be introduced to "visualize" the landscape of metastable energy minima in such systems. The quantization of the TAP equations will be introduced and used to explore the spectral form factor (SFF)—a key metric of quantum chaos—in certain models of quantum glasses. It will be shown that the hallmark of quantum chaos—a ramp in the SFF—is rescaled by the exponential of complexity compared to the standard chaotic (random matrix) model. I will briefly mention the realization of such models in glassy quantum circuits, which exhibit slow thermalization.

Next, a one-to-one correspondence between classical spin models and neural networks (NNs) will be established. Training a NN in this mapping corresponds to a family of spin Hamiltonians parameterized by training time. TAP equations will be used to show that training a NN on a classification task physically implies the destruction of the spin glass and the emergence of hidden order, whose melting temperature increases as a power law with training time. This provides an appealing physical picture of training neural networks as a search for hidden order associated with the task.

Finally, a natural quantization of neural networks will be introduced, and I will argue that some test cases are readily deployable on present-day quantum computers.

*We strongly encourage attendees to use their full name (and if possible, their UMD credentials) to join the zoom session.*