Related papers: Quantum geometry of the parameter space: a proposa…
We propose quantum-mechanical systems in which the number of spatial dimensions is promoted to a dynamical quantum variable, making the effective dimension state-dependent. Interestingly, systems of this form can exhibit enhanced symmetries…
An alternative model to describe the electronic and thermal properties of quantum dot based on triangle geometry is proposed. The model predicts characteristics and limitations of the system by controlling the magnetic field and…
Quantum materials are characterized by electromagnetic responses intrinsically linked to the geometry and topology of electronic wavefunctions, encoded in the quantum metric and Berry curvature. Whereas Berry curvature-mediated transport…
The application of geometry to physics has provided us with new insightful information about many physical theories such as classical mechanics, general relativity, and quantum geometry (quantum gravity). The geometry also plays an…
We review some geometrical aspects pertaining to the world of monotone quantum metrics in finite dimensions. Particular emphasis is given to an unfolded perspective for quantum states that is built out of the spectral theorem and is…
The experimental realisation of the basic constituents of quantum information processing devices, namely fault-tolerant quantum logic gates, requires conditional quantum dynamics, in which one subsystem undergoes a coherent evolution that…
Geometric phases, arising from cyclic evolutions in a curved parameter space, appear in a wealth of physical settings. Recently, and largely motivated by the need of an experimentally realistic definition for quantum computing applications,…
Quantum computers are known to provide speedups over classical state-of-the-art machine learning methods in some specialized settings. For example, quantum kernel methods have been shown to provide an exponential speedup on a learning…
The covariant derivative capable of differentiating and parallel transporting tangent vectors and other geometric objects induced by a parameter-dependent quantum state is introduced. It is proved to be covariant under gauge and coordinate…
Quantum kernel methods are a promising method in quantum machine learning thanks to the guarantees connected to them. Their accessibility for analytic considerations also opens up the possibility of prescreening datasets based on their…
The quantum geometric properties of typical diamond-type (C, Si, Ge) and zincblende-type (GaAs, InP, etc) semiconductors are investigated by means of the $sp^{3}s^{\ast}$ tight-binding model, which allows to calculate the quantum metric of…
We introduce the perturbative aspects of noncommutative quantum mechanics. Then we study the Berry's phase in the framework of noncommutative quantum mechanics. The results show deviations from the usual quantum mechanics which depend on…
The possibilities of curvature of space-time in the metric of quantum states are investigated. The curvature of the metric corresponding to a wave function of Hydrogen atom is determined. Also, Einstein tensor is described for a given…
Consider a set of quantum states $| \psi(x) \rangle$ parameterized by $x$ taken from some parameter space $M$. We demonstrate how all geometric properties of this manifold of states are fully described by a scalar gauge-invariant Bargmann…
We find relations between quantities defining geometry and quantities defining the length of a curve in geometries underlying Electromagnetism and unified model of Electromagnetism and Gravitation. We show that the length of a vector…
The coupling between internal degrees of freedom of quantum systems and their overall motion in an external gravitational field plays a central role in multiple extensions of Einstein's equivalence principle to quantum physics. While…
We describe an approach for characterizing the process of quantum gates using quantum process tomography, by first modeling them in an extended Hilbert space, which includes non-qubit degrees of freedom. To prevent unphysical processes from…
A family of finite-dimensional quantum systems with a non-degenerate ground state gives rise to a closed 2-form on the parameter space: the curvature of the Berry connection. Its cohomology class is a topological invariant of the family. We…
Recently, there has been considerable interest in the application of information geometry to quantum many body physics. This interest has been driven by three separate lines of research, which can all be understood as different facets of…
Over the last two years, the canonical approach to quantum gravity based on connections and triads has been put on a firm mathematical footing through the development and application of a new functional calculus on the space of gauge…