Feynmanâ€™s Path Integral (PI) is the celebrated mathematical reformulation of operator Quantum Mechanics. Such reformulation offers both an intuitive classical interpretation of Quantum Mechanics, and a powerful computational approach to investigate Quantum fluctuations. However, less is known about its stochastic counterparts, whose PI representations enable alternative routes to investigate stochastic phenomena.

Feynmanâ€™s Path Integral (PI) is the celebrated mathematical reformulation of operator Quantum Mechanics. Such reformulation offers both an intuitive classical interpretation of Quantum Mechanics, and a powerful computational approach to investigate Quantum fluctuations. However, less is known about its stochastic counterparts, whose PI representations enable alternative routes to investigate stochastic phenomena.

In this special QTFT seminar, we will begin by reviewing the less familiar PI representations of stochastic processes, such as the Doi-Peliti PI and the Onsager-Machlup PI, and draw connections to standard Quantum Physics. We will then discuss how these alternative views of stochastic processes may offer new tools to tackle modern Machine Learning/Theoretical Neuroscience problems, as well as Quantum control problems.

In particular, through stochastic PI, we will first discuss why the spike-timing statistics in experimental neural spike-train data are typically and successfully described by an effective Poisson-like neuron model, despite the sophisticated underlying neural network architecture. The connection between our biologically plausible model of spiking neural networks and the well-known Hopfield neural network originated from statistical physics community will also be discussed.

In addition, turning back to quantum problems, we will discuss how the stochastic PI can be applied to quantum systems, but now including fluctuation from measurements and decoherence. The PI provides us a convenient way to derive optimal paths for qubit evolution, which could be useful for problems in quantum control.