Quantum Matter

I’ll talk about two independent works on classical and quantum neural networks connected by information theory. In the first part of the talk, I’ll treat sequence models as one-dimensional classical statistical mechanical systems and analyze the scaling behavior of mutual information. I'll provide a new perspective on why recurrent neural networks are not good at natural language processing. In the second part of the talk, I’ll study information scrambling dynamics when quantum neural networks are trained by classical gradient descent algorithm. For many problems, this hybrid quantum-classical training process consists of two stages where information scrambles very differently in the network. 

I propose [1] to use the residual anyons of overscreened Kondo physics for quantum computation. A superconducting proximity gap of Δ<TK can be utilized to isolate the anyon from the continuum of excitations and stabilize the non-trivial fixed point. We use the dynamical large-N technique [2] and bosonization to show that the residual entropy survives in a superconductor and suggest a charge Kondo setup for isolating and detecting the Majorana fermion in the two-channel Kondo impurity.
I will then conjecture that topological defects in a multichannel Kondo lattice carry anyons. Motivated by this, we look at a two-channel SU(N) Kondo lattice in the large-N limit [3].  In this model, the continuous channel-symmetry is spontaneously broken, forming a “channel ferromagnet” and realizing the so-called fractionalized order parameter [4]. By integrating out the fermions we derive an effective action that describes the symmetry breaking and its emergent collective modes. Remarkably, topological defects in the order parameter carry a U(1) flux, manifested in the Aharonov-Bohm phase picked by electrons that orbit the defect. We argue that the phase diagram contains a non-magnetic transition between a large and a small Fermi surface.
I will also briefly highlight our recent results [5] on a magnetically frustrated Kondo-screened triangle which contains two symmetry-preserving phases, transcending the Landau-Ginzburg paradigm. The quantum phase transition is driven by the proliferation of instantons of the emergent gauge theory and can be regarded as a toy model for the deconfined criticality.

Meta-learning involves learning mathematical devices using problem instances as training data. In this talk, we first describe recent meta-learning approaches involving the learning of objects such as: initial weights, parameterized losses, hyper-parameter search strategies, and samplers. We then discuss learned optimizers in further detail and their applications towards optimizing variational circuits. This talk also covers some lessons learned starting a spin-off from academia.