Postdoctoral Position at Wave Transport in Complex Systems Lab—Wesleyan University

The Wave Transport in Complex Systems (WTICS) Lab at Wesleyan University is
opening a post-doctoral position on wave transport in theory or/and experiment
using microwave and RF analogue circuitry. The candidate must have a basic
knowledge of theory of metamaterials. A knowledge of software packages for
electronic design (such as COMSOL, SPICE etc) is desirable. Specific areas of research that are relevant to the current post include:

(a) Artificial Intelligence and Machine Learning;
(b) Non-Hermitian systems;
(c) Active topological structures;
(d) Asymmetric transport;
(e) Wavefront shaping techniques

The position is for two years with a possible extension of a third year. Information
about the WTICS group can be found here. Interested candidates should send a CV, a short statement of work and three recommendation letters to Prof. T. Kottos at tkottos@wesleyan.edu.

Squeezed states, squashed states, spoofing, and more

Rationalizing systematic discrepancies between election outcomes and opinion polls

This work analyzes an exactly-solvable Ising model of the Bradley effect, which refers to discrepancies between election results and opinion polls resulting from poll respondents hiding their true preference. The Ising model takes the form of a bipartite network composed of a hidden layer (corresponding to voter intentions) and a visible layer (the voters' declared preferences).

Quadrature nonreciprocity: unidirectional bosonic transmission without breaking time-reversal symmetry

The authors propose and experimentally demonstrate quadrature non-reciprocity, referring to unidirectional transport of mode quadratures arising due to the interplay between linear coupling (beam splitter operations) and two-mode squeezing. This platform promises to be an interesting playground for non-Hermitian physics, with potential applications for multi-mode bosonic quantum networks. 

When you can't count, sample! Computable entropies beyond equilibrium from basin volumes

A very clear and beginner-friendly perspective on the difficulty of estimating volumes and densities in high-dimensional configuration spaces, and how the problem can be efficiently solved using importance sampling and replicas. Verification of quantum supremacy experiments is tricky for similar reasons - estimation of the probability density function of a random quantum state requires an exponential number of measurements.

Fundamental constraints on the observability of non-Hermitian effects in passive systems

There is still huge interest in non-Hermitian phenomena including non-Hermitian topological phases. Authors on this subject would be wise to understand important caveats regarding commonly-used models. For example, when considering a model including gain terms, some kind of nonlinear term such as gain saturation is required to avoid an unphysical blow-up of energy. Analysis of nonlinear systems is of course much more difficult, making it hard to obtain rigorous general results in this case. One alternative is to consider purely passive non-Hermitian systems formed via inhomogeneous losses, such that one does not need to worry about the stability of the system. Interestingly, this is not the whole story. This preprint shows that when inevitable material dispersion is included into passive non-Hermitian Hamiltonians (which is required for the model to satisfy the fundamental constraint of causality), "some of the most widely studied features [exceptional points, non-Hermitian skin effect, and symmetry-protected edge states] are effectively disguised in the density of states, in particular to the signatures of drastic mode nonorthogonality. These findings highlight the essential role of active elements in devices that aim to exploit these signatures."

Solving the sampling problem of the Sycamore quantum supremacy circuits 

This preprint from last year was just accepted in PRL. The authors demonstrate a method to classically spoof the results of the Google quantum supremacy experiments. "If our algorithm could be implemented with high efficiency on a modern supercomputer with ExaFLOPS performance, we estimate that ideally, the simulation would cost a few dozens of seconds, which is faster than Google's quantum hardware."

Classical models are a better explanation of the Jiuzhang Gaussian Boson Samplers than their targeted squeezed light models

Nicolas Quesada (formerly of Xanadu) and collaborators show that mixtures of coherent states termed squashed states are capable of spoofing higher order correlations measured in Gaussian BosonSampling experiments, one of the (multiple) tests used to establish a potential quantum advantage. However, the results of another test (Heavy Output Generation), could not be classically reproduced using the squashed state. "This work thus provides a new adversary that should be considered against future GBS experiments and, perhaps more importantly, further motivates the need to identify proper metrics and optimal classical adversaries for quantum advantage in the context of threshold GBS"

arxiv highlights

Quantum persistent homology

A generalization of the quantum algorithm by Lloyd et al., which provides an exponential speed up for computing Betti numbers, enabling the computation of persistent Betti numbers. Like the original algorithm, however, it assumes the existences of a QRAM allowing the input data to be queried in a quantum superposition. It is an open question whether the exponential speedup remains when the data-encoding overhead is taken into account. See also the related arXiv:2111.00433.

 

Anomalous single-mode lasing induced by nonlinearity and the non-Hermitian skin effect

Highlighting a nice collaboration I was involved in. One limitation of many topological or PT-symmetric models for single mode lasers is that they require a structured pump. Such structured pumping will necessarily lower the device efficiency (in terms of output power / device size). Here we show counterintuitively how nonlinear gain saturation can lead to the emergence of stable single mode lasing in uniformly-pumped systems exhibiting the non-Hermitian skin effect. Due to the non-Hermitian skin effect, most of the linear modes become localized to the boundary of the system. However, a few (non-extensive) delocalized bulk modes remain and can be used as large volume lasing modes.

CAFQA: Clifford Ansatz For Quantum Accuracy

This is a neat approach for solving the barren plateau problem that makes quantum neural networks (and other variational quantum algorithms) expensive to train. The idea is to the initialize the circuit as a set of Clifford gates, which are efficiently simulable using classical computers. Therefore a classical computer can be used to find the best Clifford circuit approximation to the solution of the problem. The gate parameters are then allowed to deviate from those corresponding to Clifford gate, producing classically intractable states, and are optimized by running the quantum circuit. The better Clifford starting ansatz allows the quantum circuit optimization to converge more quickly, minimizing the number of expensive quantum circuit evaluations.

Physics-Informed Neural Networks for Quantum Eigenvalue Problems

Physics-informed neural networks are a new approach for solving partial differential equations, based on minimizing a cost function measuring the deviation from the equation being fulfilled at a set of points in the bulk and at the edges of the domain of interest. Once trained one can obtain the field value at any desired point x within the domain. Mesh-free solutions of Maxwell's equations are one promising application. This preprint applies the physics-informed neural network approach to solve the time-independent single particle Schrodinger equation. I wonder whether this approach will also be useful for the many-body problem, since it does not require storing all the wave function components in memory, one can instead query the wavefunction at the desired set of points.

Tying knots in energy bands

The generation of knots in optical systems has fascinated me since my PhD days. Influential early works focused on optical vortex knots. Optical vortices trace out curves in 3D space; in certain circumstances the curves trace out knotted trajectories. Influential early works include the generation of knotted vortices in light beams using a spatial light modulator, large-scale statistical analysis of the probability of knots forming in random optical beams, and the spontaneous formation of vortex knots in the tails of self-trapped nonlinear optical beams. 

More recently, with the surge in interest in topological photonics, interest has turned to the study of knots in other objects, including the energy bands of periodic systems.

An article just published in Nature reports the observation of braided energy bands using a pair of coupled modulated ring resonators. Braids are closely related to knots (knots can be obtained by connecting the ends of non-trivial braids). Braids are more natural to study in the context of band structures, owing to the periodicity of the Brillouin zone.

In order to generate knots or braids, one needs to consider curves in a 3D space. In this work, one of the dimensions is provided by the momentum (k) space, while the other two dimensions are played by the real and imaginary parts of the complex energy eigenvalues E. Using phase and amplitude modulators it is now possible to implement near-arbitrary non-Hermitian Hamiltonians using coupled ring resonators, allowing exquisite of the trajectories of the energy eigenvalues in the complex plane.

To observe the energy band braiding, the authors probed their ring resonator system using a continuous wave laser beam, measuring the time-dependent transmission, with time playing the role of k. Scanning the frequency of the probe beam, a peak in transition occurs at frequencies corresponding to resonances (real parts of the eigenvalues) of the system, with the linewidth of the resonance corresponding to the imaginary part of the eigenvalue. This allows the reconstruction of various braids, including those corresponding the simplest Hopf link (two threaded rings) and more complex objects such as trefoil knots.