Related papers: Higher Berry Connection for Matrix Product States
The Berry curvature is a fundamental concept describing topological order of quantum systems. While it can be analytically tractable in non-interacting systems, numerical simulations are necessary in interacting systems. We present a…
The Berry phase is a geometric phase of a pure state when the system is adiabatically transported along a loop in its parameter space. The concept of geometric phase has been generalized to mixed states by the so called Uhlmann phase.…
The topology of the non-adiabatic parameter space bundle is discussed for evolution of exact cyclic state vectors in Berry's original example of split angular momentum eigenstates. It turns out that the change in topology occurs at a…
Modern approaches to generative modeling of continuous data using tensor networks incorporate compression layers to capture the most meaningful features of high-dimensional inputs. These methods, however, rely on traditional Matrix Product…
In the era of noisy, intermediate-scale quantum (NISQ) devices, the efficient preparation of many-body resource states is a task of paramount importance. In this paper we focus on the deterministic preparation of matrix-product states (MPS)…
We briefly review the advanced mathematical language of fiber bundle structures and how they can be used to classify two-level quantum systems based on the analysis of the topological properties of their sets of state vectors. The…
The line bundles which arise in the holonomy interpretations of the geometric phase display curious similarities to those encountered in the statement of the Borel-Weil-Bott theorem of the representation theory. The remarkable relation of…
A generic method to investigate many-body continuous-variable systems is pedagogically presented. It is based on the notion of matrix product states (so-called MPS) and the algorithms thereof. The method is quite versatile and can be…
In the holonomic approach to quantum computation information is encoded in a degenerate eigenspace of a parametric family of Hamiltonians and manipulated by the associated holonomic gates. These are realized in terms of the non-abelian…
Recently, the notion of circuit complexity defined in symmetry group manifolds has been related to geometric actions which generally arise in the coadjoint orbit method in representation theory and play an important role in geometric…
The discovery of topological phases of matter and topological boundary states had tremendous impact on condensed matter physics and photonics, where topological phases are defined via energy bands, giving rise to topological band theory.…
We study a class of translational-invariant insulators with discrete rotational symmetry. These insulators have no spin-orbit coupling, and in some cases have no time-reversal symmetry as well, i.e., the relevant symmetries are purely…
The Berry phase in a composite system with only one subsystem being driven has been studied in this Letter. We choose two spin-$\frac 1 2 $ systems with spin-spin couplings as the composite system, one of the subsystems is driven by a…
Projected Entangled Pair States (PEPS) are recognized as a potent tool for exploring two-dimensional quantum many-body systems. However, a significant challenge emerges when applying conventional PEPS methodologies to systems with periodic…
Distinct from the dynamical phase, in a cyclic evolution, a system's state may acquire an additional component, a.k.a. geometric phase. The latter is a manifestation of a closed path in state space. Geometric phases underlie various…
Geometric phases in quantum mechanics play an extraordinary role in broadening our understanding of fundamental significance of geometry in nature. One of the best known examples is the Berry phase (M.V. Berry (1984), Proc. Royal. Soc.…
Subsystems of composite quantum systems are described by reduced density matrices, or quantum marginals. Important physical properties often do not depend on the whole wave function but rather only on the marginals. Not every collection of…
We develop a multi affine geometric framework to unify classical and quantum mechanical laws through the lens of information geometry. By combining the principle of stationary action with maximum entropy production, we show that divergences…
Topologically ordered phase has emerged as one of most exciting concepts that not only broadens our understanding of phases of matter, but also has been found to have potential application in fault-tolerant quantum computation. The direct…
We discuss the concept of connection states (or connection matrices) that describe posterior ensembles, post-selected according to the outcomes of a quantum measurement. Connection matrices allow one to obtain results of any weak and some…