Quantum Physics

Defining a generic quantum system requires, together with a Hilbert space and a Hamiltonian, the introduction of an algebra of observables, or equivalently a tensor product structure. Assuming a background time variable, Cotler, Penington and Ranard showed that the Hamiltonian selects an almost-unique tensor product structure. This result has been advocated by Carrol and collaborators as supporting the Everettian interpretation of quantum mechanics and providing a pivotal tool for quantum gravity. In this talk I argue against this, on the basis of the fact that the Cotler-Penington-Ranard result does not hold in the generic background-independent case where the Hamiltonian is replaced by a Hamiltonian constrain. This reinforces the understanding that entropy and entanglement, that in the quantum theory depend on the tensor product structure, are quantities that are observable dependent. To conclude, I would like to pose the question of whether clocks can be thought as a resource, and how thinking of time in terms of physical clocks can inform our interpretation of quantum mechanics

Causal reasoning is vital for effective reasoning in science and medicine. In medical diagnosis, for example, a doctor aims to explain a patient’s symptoms by determining the diseases causing them. This is because causal relations---unlike correlations---allow one to reason about the consequences of possible treatments. However, all previous approaches to machine-learning assisted diagnosis, including deep learning and model-based Bayesian approaches, learn by association and do not distinguish correlation from causation. I will show that these approaches systematically lead to incorrect diagnoses. I will outline a new diagnostic algorithm, based on counterfactual inference, which captures the causal aspect of diagnosis overlooked by previous approaches and overcomes these issues. I will additionally describe recent algorithms from my group which can discover causal relations from uncontrolled observational data and show how these can be applied to facilitate effective reasoning in medical settings such as deciding how to treat certain diseases.

Last fall, a team at Google announced the first-ever demonstration of "quantum computational supremacy"---that is, a clear quantum speedup over a classical computer for some task---using a 53-qubit programmable superconducting chip called Sycamore.  In addition to engineering, Google's accomplishment built on a decade of research in quantum computing theory.  This talk will discuss questions like: what exactly was the contrived computational problem that Google solved?  How does one verify the outputs using a classical computer?  And how confident are we that the problem really is classically hard---especially in light of subsequent counterclaims by IBM?  I'll end with a proposed application for Google's experiment---namely, the generation of certified random bits, for use (for example) in proof-of-stake cryptocurrencies---that I've been developing and that Google is now working to demonstrate.