Related papers: Non-Abelian geometric phases in a system of couple…
We propose an approach to measure the quantum phase of an electron in a non-Abelian system using the algorithm of Quantum Phase Estimation (QPE). The discrete-path systems were previously studied in the context of square or rectangular…
Geometric phases, which are ubiquitous in quantum mechanics, are commonly more than only scalar quantities. Indeed, often they are matrix-valued objects that are connected with non-Abelian geometries. Here we show how generalized,…
The geometric aspects of quantum mechanics are underlined most prominently by the concept of geometric phases, which are acquired whenever a quantum system evolves along a closed path in Hilbert space. The geometric phase is determined only…
We introduce a self-consistent framework for the analysis of both Abelian and non-Abelian geometric phases associated with open quantum systems, undergoing cyclic adiabatic evolution. We derive a general expression for geometric phases,…
Adiabatic $U(2)$ geometric phases are studied for arbitrary quantum systems with a three-dimensional Hilbert space. Necessary and sufficient conditions for the occurrence of the non-Abelian geometrical phases are obtained without actually…
Steering a quantum harmonic oscillator state along cyclic trajectories leads to a path-dependent geometric phase. Here we describe an experiment observing this geometric phase in an electronic harmonic oscillator. We use a superconducting…
The concept of off-diagonal geometric phase (GP) has been introduced in order to recover interference information about the geometry of quantal evolution where the standard GPs are not well-defined. In this Letter, we propose a physical…
We present a superconducting circuit in which non-Abelian geometric transformations can be realized using an adiabatic parameter cycle. In contrast to previous proposals, we employ quantum evolution in the ground state. We propose an…
Recent discoveries in semi-metallic multi-gap systems featuring band singularities have galvanized enormous interest in particular due to the emergence of non-Abelian braiding properties of band nodes. This previously uncharted set of…
Abelian and Non-Abelian evolution of a quantum system manifests differently in the geometric phase acquired by the system under such evolutions. In this work we develop and study, using dressed state techniques, an experimentally realizable…
Non-Abelian and non-adiabatic variants of Berry's geometric phase have been pivotal in the recent advances in fault tolerant quantum computation gates, while Berry's phase itself is at the heart of the study of topological phases of matter.…
We consider a periodically driven quantum system described by a Hamiltonian which is the product of a slowly varying Hermitian operator $V\left(\boldsymbol{\lambda}\left(t\right)\right)$ and a dimensionless periodic function with zero…
Geometric quantum computation is the idea that geometric phases can be used to implement quantum gates, i.e., the basic elements of the Boolean network that forms a quantum computer. Although originally thought to be limited to adiabatic…
Geometric phases have stimulated researchers for its potential applications in many areas of science. One of them is fault-tolerant quantum computation. A preliminary requisite of quantum computation is the implementation of controlled…
We generalise our previous results of universal linear manipulations [Phys. Rev. A63, 032304 (2001)] to investigate three types of nonlinear qubit transformations using measurement and quantum based schemes. Firstly, nonlinear rotations are…
We use the theory of dynamical invariants to yield a simple derivation of noncyclic analogues of the Abelian and non-Abelian geometric phases. This derivation relies only on the principle of gauge invariance and elucidates the existing…
We propose a scheme for detecting noncommutative feature of the non-Abelian geometric phase in circuit QED, which involves three transmon qubits capacitively coupled to an one-dimensional transmission line resonator. By controlling the…
The properties of the geometric phases between three quantum states are investigated in a high-dimensional Hilbert space using the Majorana representation of symmetric quantum states. We found that the geometric phases between the three…
We discuss the basic theoretical framework for non-Hermitian quantum systems with particular emphasis on the diagonalizability of non-Hermitian Hamiltonians and their $GL(1,\mathbb{C})$ gauge freedom, which are relevant to the adiabatic…
Quantum operations by utilizing the underlying geometric phases produced in physical systems are favoured due to its potential robustness. When a system in a non-degenerate eigenstate undergoes an adiabatically cyclic evolution dominated by…