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Quantum information science has leaped forward with the exploration of high-dimensional quantum systems, offering greater potential than traditional qubits in quantum communication and quantum computing. To advance the field of…

We develop a novel approach to Quantum Mechanics that we call Curved Quantum Mechanics. We introduce an infinite-dimensional K\"ahler manifold ${\cal M}$, that we call the state manifold, such that the cotangent space $T_z^*{\cal M}$ is a…

Quantum simulation provides quantum systems under study with analogous controllable quantum systems and has wide applications from condensed-matter physics to high energy physics and to cosmology. The quantum system of a homogeneous and…

Graph states are computationally powerful quantum states with many applications including use as resource states for measurement-based quantum computing (MBQC). We demonstrate construction of graph states on a Rydberg atom quantum analogue…

We develop a means of simulating the evolution and measurement of a multipartite quantum state under discrete or continuous evolution using another quantum system with states and operators lying in a real Hilbert space. This extends…

In dense neutrino gases, which exist for instance in supernovae, the flavour states of different neutrinos may become entangled with one another. The theoretical description of such systems may therefore call for simulations on a quantum…

We develop an action formulation of stochastic dynamics in the Hilbert space. By generalizing the Wiener process into 1+3-dimensional spacetime, we define a Lorentz-invariant random field. By coupling the random to quantum fields, we obtain…

Fast entangling gate operations are a fundamental prerequisite for quantum simulation and computation. We propose an entangling scheme for arbitrary pairs of ions in a linear crystal, harnessing the high electric polarizability of highly…

Quantum Mechanics and Signal Processing in the line R, are strictly related to Fourier Transform and Weyl-Heisenberg algebra. We discuss here the addition of a new discrete variable that measures the degree of the Hermite functions and…

As a toy model for the microscopic description of matter in de Sitter space, we consider a Hamiltonian acting on the spin-j representation of SU(2). This is a model with a finite-dimensional Hilbert space, from which quasinormal modes…

We present a scheme to generate steady-state atomic spin squeezing in a cavity QED system using cavity-mediated Raman transitions to engineer effective atom-photon interactions, which include both linear and nonlinear (dispersive)…

Quantum algorithms operate on quantum states through unitary transformations in high dimensional complex Hilbert space. In this work, we propose a machine learning approach to create the quantum circuit using a single-layer complex-valued…

We implement arbitrary maps between pure states in the 16-dimensional Hilbert space associated with the ground electronic manifold of Cs. This is accomplished by driving atoms with phase modulated rf and {\mu}w fields, using modulation…

The strong interaction between Rydberg atoms can be used to control the strength and character of the interatomic interaction in ultracold gases by weakly dressing the atoms with a Rydberg state. Elaborate theoretical proposals for the…

Recent advances in laser interactions with coherent free electrons have enabled to shape the electron's quantum state. Each electron becomes a superposition of energy levels on an infinite quantized ladder, shown to contain up to thousands…

It is shown that quantum walks on one-dimensional arrays of special linear-optical units allow the simulation of discrete-time Hamiltonian systems with distinct topological phases. In particular, a slightly modified version of the…

We propose a scheme to generate spin cat states, i.e., superpositions of maximally separated quasiclassical states on a single high-dimensional nuclear spin in a solid-state device. We exploit a strong quadrupolar nonlinearity to drive the…

In the past few years there has been a tumultuous activity aimed at introducing novel conceptual schemes for quantum computing. The approach proposed in (Marzuoli A and Rasetti M 2002, 2005a) relies on the (re)coupling theory of SU(2)…

A powerful method to interface quantum light with matter is to propagate the light through an ensemble of atoms. Recently, a number of such interfaces have emerged, most prominently Rydberg ensembles, that enable strong nonlinear…

By periodical two-step modulation, we demonstrate that the dynamics of multilevel system can still evolve even in multiple large detunings regime, and provide the effective Hamiltonian (of interest) for this system. We then illustrate this…