Talks

Provably efficient machine learning for quantum many-body problems

Classical machine learning (ML) provides a potentially powerful approach to solving challenging quantum many-body problems in physics and chemistry. However, the advantages of ML over traditional methods have not been firmly established. In this work, we prove that classical ML algorithms **can** efficiently learn to predict important properties of a quantum many-body system. In particular, ML can provably predict ground-state properties of gapped Hamiltonians after learning from other Hamiltonians in the same quantum phase of matter. Our proof technique combines signal processing with quantum many-body physics and also builds upon the recently developed framework of classical shadows. I will try to convey the ideas and also present numerical experiments that confirm our theoretical findings. This colloquium talk is based on joint work with Hsin-Yuan (Robert) Huang, Giacomo Torlai, Victor Albert and John Preskill, see [Huang et al., Provably efficient machine learning for quantum many-body problems, Science 2022]

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Multipolar Approach to Nanophotonics

Electromagnetic fields have an inherently vectorial nature. Often, many problems are described by reducing a vector problem to a scalar one. However, in many cases, this reduction is unnecessary, and a more insightful approach is to consider vector fields as a whole. For analyzing individual nanostructures and nanoparticles, a convenient basis for expanding electromagnetic fields is provided by vector spherical harmonics. These harmonics are divided into magnetic and electric ones and possess unique symmetry properties, being eigenfunctions of both the total angular momentum operator and its projection onto the z-axis. Moreover, certain combinations of these harmonics have well-defined helicity values. By leveraging these properties along with group representation theory, we classify the eigenmodes of nanostructures and derive multipole selection rules for linear scattering processes and harmonic generation. This framework provides a powerful tool for predicting and controlling scattered and generated light, enabling applications in chiral sensing, refractive index sensing, structured light shaping, vortex beam generation, optical trapping, image processing, and biophysics.

Quantum trajectories, quantum potential, superoscillations: Madelung, de Broglie, Newton

The wave counterparts of classical particle paths and geometrical-optics rays are families of trajectories – patterns of streamlines – modified by a ‘quantum potential’. Wave interference corresponds to undulations in these trajectories, as envisaged by Isaac Newton. Streamline patterns are dominated by singularities at wave vortices and stagnation points. The local momentum (phase gradient of the wave), can exceed the values classically allowed. Regions of such ‘superoscillations’ are bounded by manifolds where the quantum potential is zero. Some classical ‘curl forces’ – not the gradient of a potential – are associated with Hamiltonians (dispersion relations) anisotropic in momentum components, with unusual group velocity field singularities, and eigenfunctions with unfamiliar classical counterparts. For simple dispersion relations, some singularities coincide; for general cases, they are separate.

Gutzwiller Colloquium