Quantum Physics

While originally motivated by quantum computation, quantum error correction (QEC) is currently providing valuable insights into many-body quantum physics such as topological phases of matter. Furthermore, mounting evidence originating from holography research (AdS/CFT), indicates that QEC should also be pertinent for conformal field theories. With this motivation in mind, we introduce quantum source-channel codes, which combine features of lossy-compression and approximate quantum error correction, both of which are predicted in holography. Through a recent construction for approximate recovery maps, we derive guarantees on its erasure decoding performance from calculations of an entropic quantity called conditional mutual information. As an example, we consider Gibbs states of the transverse field Ising model at criticality and provide evidence that they exhibit non-trivial protection from local erasure. This gives rise to the first concrete interpretation of a bona fide conformal field theory as a quantum error correcting code. We argue that quantum source-channel codes are of independent interest beyond holography.

What can machine learning teach us about quantum mechanics? I will begin with a brief overview of attempts to bring together the two fields, and the insights this may yield. I will then focus on one particular framework, Projective Simulation, which describes physics-based agents that are capable of learning by themselves. These agents can serve as toy models for studying a wide variety of phenomena, as I will illustrate with examples from quantum experiments and biology.

We construct a hidden variable model for the EPR correlations using a Restricted Boltzmann Machine. The model reproduces the expected correlations and thus violates the Bell inequality, as required by Bell's theorem. Unlike most hidden-variable models, this model does not violate the locality assumption in Bell's argument. Rather, it violates measurement independence, albeit in a decidedly non-conspiratorial way.