Braiding transformation, entanglement swapping and Berry phase in entanglement space

Non-Abelian Berry phase for open quantum systems: Topological protection vs geometric dephasing

We provide a detailed theoretical analysis of the adiabatic evolution of degenerate open quantum systems, where the dynamics is induced by time-dependent fluctuating loop paths in control parameter space. For weak system-bath coupling, the fluctuations around a deterministic base path obey Gaussian statistics, where we assume that the quantum adiabatic theorem is also satisfied for fluctuating paths. We show that universal non-Abelian geometric dephasing (NAGD) contributions are contained in the fluctuation-averaged evolution operator. This operator plays a key role in all experimental protoco…

Observing a Topological Transition in Weak-Measurement-Induced Geometric Phases

Measurement plays a quintessential role in the control of quantum systems. Beyond initialization and readout which pertain to projective measurements, weak measurements in particular, through their back-action on the system, may enable various levels of coherent control. The latter ranges from observing quantum trajectories to state dragging and steering. Furthermore, just like the adiabatic evolution of quantum states that is known to induce the Berry phase, sequential weak measurements may lead to path-dependent geometric phases. Here we measure the geometric phases induced by sequences of w…

Topological Quantum Computing and 3-Manifolds

In this paper, we will present some ideas to use 3D topology for quantum computing. Topological quantum computing in the usual sense works with an encoding of information as knotted quantum states of topological phases of matter, thus being locked into topology to prevent decay. Today, the basic structure is a 2D system to realize anyons with braiding operations. From the topological point of view, we have to deal with surface topology. However, usual materials are 3D objects. Possible topologies for these objects can be more complex than surfaces. From the topological point of view, Thurston'…

分子取向的量子理论

Quantum theory of molecular orientations

本文提出了一种分子取向的量子理论，通过构建量子相空间，探讨了刚性分子的旋转和核自旋状态，并揭示了周期性旋转对称态空间中旋转-自旋纠缠和纤维自由度的特性，为量子纠错和容错量子门提供了新思路。

Observation of topological Euler insulators with a trapped-ion quantum simulator

Symmetries play a crucial role in the classification of topological phases of matter. Although recent studies have established a powerful framework to search for and classify topological phases based on symmetry indicators, there exists a large class of fragile topology beyond the description. The Euler class characterizing the topology of two-dimensional real wave functions is an archetypal fragile topology underlying some important properties, such as non-Abelian braiding of crossing nodes and higher-order topology. However, as a minimum model of fragile topology, the two-dimensional topolog…