Related papers: Quantum Surface of Section Method: Eigenstates and…
Topological and geometrical properties of the set of mixed quantum states in the N-dimensional Hilbert space are analysed. Assuming that the corresponding classical dynamics takes place on the sphere we use the vector SU(2) coherent states…
Quantum state tomography (QST) is the gold standard technique for obtaining an estimate for the state of small quantum systems in the laboratory. Its application to systems with more than a few constituents (e.g. particles) soon becomes…
We study the competing order and chaos in a first-order quantum phase transition with a high barrier. The boson model Hamiltonian employed, interpolates between its U(5) (spherical) and SU(3) (deformed) limits. A classical analysis reveals…
Semiclassical approximations for various representations of a quantum state are constructed on a single (Lagrangian) surface in phase space, but it is not available for chaotic systems. An analogous evolution surface underlies semiclassical…
A proof that minimum uncertainty states of the simplest periodic quantum system exist in a state space that is represented by a Colombeau algebra of generalised functions but not in Hilbert space or in the space of Schwartz distributions is…
We show that measuring any two quantum states by a random POVM, under a suitable definition of randomness, gives probability distributions having total variation distance at least a universal constant times the Frobenius distance between…
We investigate the effect that spatially modulated continuous conserved quantities can have on quantum ground states. We do so by introducing a family of one-dimensional local quantum rotor and bosonic models which conserve finite Fourier…
We introduce a unified framework -- Quantum Neural Ordinary and Partial Differential Equations (QNODEs and QNPDEs) -- which extends the continuous-time formalism of classical neural ordinary and partial differential equations into quantum…
This dissertation studies the statistics and modeling of a quantum system probed by a coherent laser field. We focus on an ensemble of qubits dispersively coupled to a traveling wave light field. The first research topic explores the…
We employ machine learning techniques to provide accurate variational wavefunctions for matrix quantum mechanics, with multiple bosonic and fermionic matrices. Variational quantum Monte Carlo is implemented with deep generative flows to…
We consider the problem of finding exact sums of squares (SOS) decompositions for certain classes of non-negative multivariate polynomials, relying on semidefinite programming (SDP) solvers. We start by providing a hybrid numeric-symbolic…
Poincare return maps are a fundamental tool for analyzing periodic orbits in hybrid dynamical systems, including legged locomotion, power electronics, and other cyber-physical systems with switching behavior. The Poincare return map…
We construct a class of exact eigenstates of the Hamiltonian obtained by projecting the Hubbard interaction term onto the flat band subspace of a generic lattice model. These exact eigenstates are many body states in which an arbitrary…
We demonstrate that the task of determining an unknown quantum state can be accomplished efficiently by making a sequential measurement of two observables $\hat{A}$ and $\hat{B}$, provided that the two observables are chosen in such a way…
The ability of matter to be superposed at two different locations while being intrinsically connected by a quantum phase is among the most counterintuitive predictions of quantum physics. While such superpositions have been created for a…
Typical eigenstates of quantum systems, whose classical limit is chaotic, are well approximated as random states. Corresponding eigenvalue spectra is modeled through appropriate ensemble of random matrix theory. However, a small subset of…
We extend the semiclassical theory of scarring of quantum eigenfunctions psi_{n}(q) by classical periodic orbits to include situations where these orbits undergo generic bifurcations. It is shown that |psi_{n}(q)|^{2}, averaged locally with…
We study how useful random states are for quantum metrology, i.e., surpass the classical limits imposed on precision in the canonical phase estimation scenario. First, we prove that random pure states drawn from the Hilbert space of…
We develop a systematic approach to determine and measure numerically the geometry of generic quantum or "fuzzy" geometries realized by a set of finite-dimensional hermitian matrices. The method is designed to recover the semi-classical…
Employing the algebraic framework of local quantum physics, vacuum states in Minkowski space are distinguished by a property of geometric modular action. This property allows one to construct from any locally generated net of observables…