[CANCELLED] Path Signatures and Physics

I will talk about recent work on connections between kernel methods for time series in machine learning and Wilson lines in quantum field theory. Specifically, we formulate path signatures within the framework of matrix models in quantum field theory. Using tools from physics, we introduce a new family of randomized path developments, derive the corresponding loop equations, and examine the associated kernels. We then interpret unitary path developments as time evolution operators on a Hilbert space of qubits, leading to the definition of a quantum signature kernel through a quantum circuit construction. In the case of the Gaussian matrix model, we propose a quantum algorithm to compute this kernel.