Related papers: Adjoint computation of Berry phase gradients

We propose a general method by which experiments on ultracold gases can be used to determine the topological properties of the energy bands of optical lattices, as represented by the map of the Berry curvature across the Brillouin zone. The…

The Berry phase is a fundamental quantity in the classification of topological phases of matter. In this paper, we present a new quantum algorithm and several complexity-theoretical results for the Berry phase estimation (BPE) problems. Our…

We study topological properties of phase transition points of two topologically non-trivial $\mathbb{Z}_2$ classes (D and DIII) in one dimension by assigning a Berry phase defined on closed circles around the gap closing points in the…

We derive closed analytical expressions for the complex Berry phase of an open quantum system in a state which is a superposition of resonant states and evolves irreversibly due to the spontaneous decay of the metastable states. The…

The Berry phase is a geometric phase acquired during adiabatic evolution over a closed loop in parameter space. It plays an essential role in geometric quantum gates and other phase-based protocols. In non-Hermitian systems, the Berry phase…

We unveil the existence of a non-trivial Berry phase associated to the dynamics of a quantum particle in a one dimensional box with moving walls. It is shown that a suitable choice of boundary conditions has to be made in order to preserve…

Here, we introduce and apply non-Abelian tensor Berry connections to topological phases in multi-band systems. These gauge connections behave as non-Abelian antisymmetric tensor gauge fields in momentum space and naturally generalize…

We show the presence of a topological (Berry) phase in the time evolution of a mixed state. For the case of mixed neutrinos, the Berry phase is a function of the mixing angle only.

We design an adiabatic quantum algorithm for the counting problem, i.e., approximating the proportion, $\alpha$, of the marked items in a given database. As the quantum system undergoes a designed cyclic adiabatic evolution, it acquires a…

The properties that quantify photonic topological insulators (PTIs), Berry phase, Berry connection, and Chern number, are typically obtained by making analogies between classical Maxwell's equations and the quantum mechanical…

As more and more multiphysics effects are entering the field of CFD simulations, this raises the question how they can be accurately captured in gradient computations for shape optimization. The latter has been successfully enriched over…

The electronic dispersion of a graphene bilayer is highly dependent on rotational mismatch between layers and can be further manipulated by electrical gating. This allows for an unprecedented control over electronic properties and opens up…

Despite the extensive studies of topological states, their characterization in strongly nonlinear classical systems has been lacking. In this work, we identify the proper definition of Berry phase for nonlinear bulk modes and characterize…

First-order optimization algorithms, often preferred for large problems, require the gradient of the differentiable terms in the objective function. These gradients often involve linear operators and their adjoints, which must be applied…

The development of inverse design, where computational optimization techniques are used to design devices based on certain specifications, has led to the discovery of many compact, non-intuitive structures with superior performance. Among…

Geometric or Berry phases are fundamental manifestations that appear in many areas of physics. They arise from the geometry of the space describing the properties of multi-component wave fields. An important example for electromagnetic…

The Moebius strip, as a fascinating loop structure with one-sided topology, provides a rich playground for manipulating the non-trivial topological behavior of spinning particles, such as electrons, polaritons, and photons in both real and…

Recent discoveries have demonstrated that matter can be distinguished on the basis of topological considerations, giving rise to the concept of topological phase. Introduced originally in condensed matter physics, the physics of topological…

We introduce an adjoint-based aerodynamic shape optimization framework that integrates a diffusion model trained on existing designs to learn a smooth manifold of aerodynamically viable shapes. This manifold is enforced as an equality…

Gradient-based inverse design in photonics has already achieved remarkable results in designing small-footprint, high-performance optical devices. The adjoint variable method, which allows for the efficient computation of gradients, has…