Marin Soljacic

We investigate two-dimensional spinless systems in which the fundamental domain in momentum space takes the form of a non-orientable closed manifold known as the real projective plane (RP2), in contrast to the usual case of a torus. We construct Wilson loops on RP2 to define a Z2 invariant that identifies topologically distinct phases. We find that the transition between the trivial and topological phases is mediated by an odd number of Weyl points within the fundamental domain, and that these Weyl points cannot all be annihilated. The topological phase is characterized by the presence of gapless bi-directional edge states, a feature attributed to the Fermi-arc connectivity of the Weyl points. Lastly, we demonstrate that these systems are examples of" momentum quadrupole insulators" that exhibit a linear response of momentum current to a translation gauge field.

Quantum optimization, a key application of quantum computing, has traditionally been stymied by the linearly increasing complexity of gradient calculations with an increasing number of parameters. This work bridges the gap between Koopman operator theory, which has found utility in applications because it allows for a linear representation of nonlinear dynamical systems, and natural gradient methods in quantum optimization, leading to a significant acceleration of gradient-based quantum optimization. We present Quantum-circuit Alternating Controlled Koopman learning (QuACK), a novel framework that leverages an alternating algorithm for efficient prediction of gradient dynamics on quantum computers. We demonstrate QuACK's remarkable ability to accelerate gradient-based optimization across a range of applications in quantum optimization and machine learning. In fact, our empirical studies, spanning quantum chemistry, quantum condensed matter, quantum machine learning, and noisy environments, have shown accelerations of more than 200x speedup in the overparameterized regime, 10x speedup in the smooth regime, and 3x speedup in the non-smooth regime. With QuACK, we offer a robust advancement that harnesses the advantage of gradient-based quantum optimization for practical benefits.

N02. 00012: Weyl points on non-orientable Brillouin zones: Nielsen-Ninomiya, Fermi arcs and Z2 topological charge*

Inspired by the Kolmogorov-Arnold representation theorem, we propose Kolmogorov-Arnold Networks (KANs) as promising alternatives to Multi-Layer Perceptrons (MLPs). While MLPs have fixed activation functions on nodes ("neurons"), KANs have learnable activation functions on edges ("weights"). KANs have no linear weights at all -- every weight parameter is replaced by a univariate function parametrized as a spline. We show that this seemingly simple change makes KANs outperform MLPs in terms of accuracy and interpretability. For accuracy, much smaller KANs can achieve comparable or better accuracy than much larger MLPs in data fitting and PDE solving. Theoretically and empirically, KANs possess faster neural scaling laws than MLPs. For interpretability, KANs can be intuitively visualized and can easily interact with human users. Through two examples in mathematics and physics, KANs are shown to be useful collaborators helping scientists (re)discover mathematical and physical laws. In summary, KANs are promising alternatives for MLPs, opening opportunities for further improving today's deep learning models which rely heavily on MLPs.

Plasmons, collective excitations of electrons in solids, are associated with strongly confined electromagnetic fields, with wavelengths far below the wavelength of photons in free space. Such strong confinement nominally holds the potential to enable optoelectronic technologies that bridge the size difference between photonic and electronic devices. However, despite decades of research in plasmonics, many applications remain limited by plasmonic losses, thus motivating a search for new engineered plasmonic materials with lower losses. Among the promising candidates for low-loss plasmonic materials are solid-state lattices with flat and energetically isolated metallic bands—with commensurately small phase spaces for phonon-assisted optical losses, a major contributor to short plasmonic lifetimes. Such electronic band structures may be created by judiciously introducing an ordered lattice of defects in an …

G38. 00002: Geometry of contact: contact planning for multi-legged robots via spin models

Partial differential equations (PDEs) are instrumental for modeling dynamical systems in science and engineering. The advent of neural networks has initiated a significant shift in tackling these complexities though challenges in accuracy persist, especially for initial value problems. In this paper, we introduce the $\textit{Time-Evolving Natural Gradient (TENG)}$, generalizing time-dependent variational principles and optimization-based time integration, leveraging natural gradient optimization to obtain high accuracy in neural-network-based PDE solutions. Our comprehensive development includes algorithms like TENG-Euler and its high-order variants, such as TENG-Heun, tailored for enhanced precision and efficiency. TENG's effectiveness is further validated through its performance, surpassing current leading methods and achieving machine precision in step-by-step optimizations across a spectrum of PDEs, including the heat equation, Allen-Cahn equation, and Burgers' equation.

Studying the dynamics of open quantum systems can enable breakthroughs both in fundamental physics and applications to quantum engineering and quantum computation. Since the density matrix ρ is high-dimensional, customized deep generative neural networks have been instrumental in modeling ρ. However, the complex-valued nature and normalization constraints of ρ, as well as its complicated dynamics, prohibit a seamless connection between open quantum systems and the recent advances in deep generative modeling. Here, we lift that limitation by utilizing a reformulation of open quantum system dynamics to a partial differential equation (PDE) for a corresponding quasiprobability distribution Q, the Husimi Q function. Thus, we model the Q function seamlessly with off-the-shelf deep generative models such as normalizing flows. Additionally, we develop novel methods for learning normalizing flow …