What I've been reading lately

Continuity Equation for the Flow of Fisher Information in Wave Scattering

We can get an intuitive understanding of a wide variety of wave systems ranging including photonics, acoustics, and electronic condensed matter by visualizing the flow of intensity, energy, or probability density through them. These flows are useful for understanding the behaviour of conserved quantities, since they can be decomposed into sources, sinks, and solenoidal components. This paper shows that the Fisher information, a measure which bounds the precision with which parameters of interest can be measured, similarly obeys a conservation law enabling its visualization in terms of information flow. Remarkably, the Fisher information flow gives distinct insights into wave propagation in complex media and is complementary to more standard analysis methods based on the energy flow. This work raises many interesting questions and opens new possibilities!

Energy and Power requirements for alteration of the refractive index

This is another paper in a series of perspectives on estimating the capabilities and potential limits to the performance of photonic devices using relatively simple classical oscillator models and sharp physical insights. The take home message is that the power required to achieve a given level of optical modulation depends primarily on the interaction time, which depends on the device geometry (e.g. resonator vs travelling wave), without substantial variation among different materials. This suggests that improvements in power efficiency are more likely to come from improvements in fabrication methods and device design, rather than the discovery of some new material with substantially better physical properties.

Quantum Algorithm for Computing Distances Between Subspaces

There's growing evidence that the best place to look for a quantum advantage for classical machine learning will be geometrical or topological problems that have a natural connection to quantum systems. One example is the Betti number problem, which maps to computing the ground state of supersymmetric many-body Hamiltonians. This work shows that computing distances between k-dimensional subspaces of an n-dimensional space can be done exponentially faster using a fault-tolerant quantum computer. The algorithm exploits the ability to efficiently encode subspaces into quantum states combined with quantum signal processing. Subspace distances have to large scale machine learning and computer vision problems, suggesting the asymptotic exponential advantage promised by a fault-tolerant quantum computer could lead to practical speedups.