Related papers: Generalized quantum geometric tensor for excited s…
The quantum geometric tensor (QGT) reveals local geometric properties and associated topological information of quantum states. Here a generalization of the QGT to mixed quantum states at finite temperatures based on the…
Quantum geometry governs a wide range of transport and optical phenomena in quantum materials. Recent works have explored analogue electromagnetism and gravity in terms of the quantum geometric tensor, whose real and imaginary parts…
Geometric quantum mechanics, through its differential-geometric underpinning, provides additional tools of analysis and interpretation that bring quantum mechanics closer to classical mechanics: state spaces in both are equipped with…
Quantum geometry, which describes the geometry of Bloch wavefunctions in solids, has become a cornerstone of modern quantum condensed matter physics. The quantum geometrical tensor encodes this geometry through two fundamental components:…
We propose a generalized quantum geometric tenor to understand topological quantum phase transitions, which can be defined on the parameter space with the adiabatic evolution of a quantum many-body system. The generalized quantum geometric…
The geometric formulation of quantum mechanics is a very interesting field of research which has many applications in the emerging field of quantum computation and quantum information, such as schemes for optimal quantum computers. In this…
The quantum geometric tensor (QGT) characterizes the Hilbert space geometry of the eigenstates of a parameter-dependent Hamiltonian. In recent years, the QGT and related quantities have found extensive theoretical and experimental utility,…
Geometric quantum mechanics aims to express the physical properties of quantum systems in terms of geometrical features preferentially selected in the space of pure states. Geometric characterisations are given here for systems of one, two,…
The quantum geometric tensor (QGT) is a fundamental concept for characterizing the local geometry of quantum states. After casting the geometry of pure quantum states and extracting the QGT, we generalize the geometry to mixed quantum…
Tensor networks impose a notion of geometry on the entanglement of a quantum system. In some cases, this geometry is found to reproduce key properties of holographic dualities, and subsequently much work has focused on using tensor networks…
We propose a generic protocol to experimentally measure the quantum metric tensor, a fundamental geometric property of quantum states. Our method is based on the observation that the excitation rate of a quantum state directly relates to…
We study the quantum metric tensor and its scalar curvature for a particular version of the Lipkin-Meshkov-Glick model. We build the classical Hamiltonian using Bloch coherent states and find its stationary points. They exhibit the presence…
Geometric Quantum Mechanics is a novel and prospecting approach motivated by the belief that our world is ultimately geometrical. At the heart of that is a quantity called Quantum Geometric Tensor (or Fubini-Study metric), which is a…
We consider graph states generated by the action of controlled phase shift operators on a separable state of a multi-qubit system. The case when all the qubits are initially prepared in arbitrary states is investigated. We obtain the…
This article proposes an efficient way of calculating the geometric measure of entanglement using tensor decomposition methods. The connection between these two concepts is explored using the tensor representation of the wavefunction.…
Parametrically driven nonlinear resonators represent a building block for realizing fault-tolerant quantum computation and are useful for critical quantum sensing. From a fundamental viewpoint, the most intriguing feature of such a system…
Geometrical methods in quantum information are very promising for both providing technical tools and intuition into difficult control or optimization problems. Moreover, they are of fundamental importance in connecting pure geometrical…
The quantum geometric tensor (QGT) fundamentally encodes the geometry and topology of quantum states in both Hermitian and non-Hermitian regimes. While adiabatic perturbation theory links its real part (quantum metric) and imaginary part…
The geometric properties of quantum states is fully encoded by the quantum geometric tensor. The real and imaginary parts of the quantum geometric tensor are the quantum metric and Berry curvature, which characterize the distance and phase…
This paper introduces a formalism that aims to describe the intricacies of quantum computation by establishing a connection with the mathematical foundations of tensor theory and multilinear maps. The focus is on providing a comprehensive…