Related papers: Hilbert-Space Ergodicity in Driven Quantum Systems…
Discrete and continuous variables oftentimes require different treatments in many learning tasks. Identifying the Hamiltonian governing the evolution of a quantum system is a fundamental task in quantum learning theory. While previous works…
This thesis, explores the quantum entanglement and evolution through both a geometric and dynamical perspective. The first part focuses on classical phase space and its central role in Hamiltonian mechanics, emphasizing the importance of…
We consider a closed macroscopic quantum system in a pure state $\psi_t$ evolving unitarily and take for granted that different macro states correspond to mutually orthogonal subspaces $\mathcal{H}_\nu$ (macro spaces) of Hilbert space, each…
Using a model Hamiltonian for a single-mode electromagnetic field interacting with a nonlinear medium, we show that quantum expectation values of subsystem observables can exhibit remarkably diverse ergodic properties even when the dynamics…
Topological quantum computation has been extensively studied due to its robustness against decoherence. A conventional way to realize it is by adiabatic operations---it requires relatively long time to accomplish so that the speed of…
The nature of the behaviour of an isolated many-body quantum system periodically driven in time has been an open question since the beginning of quantum mechanics. After an initial transient, such a system is known to synchronize with the…
Developing measures of quantum ergodicity and chaos stands as a foundational task in the study of quantum many-body systems. In this work, we propose metrics for these effects based on Hamiltonian learning that unify multiple advantages of…
The construction of exactly-solvable models has recently been advanced by considering integrable $T\bar{T}$ deformations and related Hamiltonian deformations in quantum mechanics. We introduce a broader class of non-Hermitian Hamiltonian…
It is widely accepted that the states of any quantum system are vectors in a Hilbert space. Not everyone agrees, however. The recent paper ``The unphysicality of Hilbert spaces'' by Carcassi, Calder\'on and Aidala is a thoughtful dissection…
We derive the theory of open quantum system dynamics intervened by a series of nonselective measurements. We analyze the cases of time independent and time dependent Hamiltonian dynamics in between the measurements and find the approximate…
The simulation of quantum systems has been a key aim of quantum technologies for decades, and the generalisation to open systems is necessary to include physically realistic systems. We introduce an approach for quantum simulations of open…
Non-Hermitian dynamics in quantum systems preserves the rank of the state density operator. Using this insight, we develop a geometric framework to describe its time evolution. In particular, we identify mutually orthogonal coherent and…
We propose a new model for a measurement of a characteristic of a microscopic quantum state by a large system that selects stochastically the different eigenstates with appropriate quantum weights. Unlike previous works which formulate a…
We introduce a geometrical framework to construct a large class of time-dependent quantum systems, in which the position of a classical particle moving autonomously on a smooth connected manifold is used to steer a quantum Hamiltonian over…
We present a model of discrete quantum evolution based on quantum correlations between the evolving system and a reference quantum clock system. A quantum circuit for the model is provided, which in the case of a constant Hamiltonian is…
The evolution of an isolated quantum system inevitably exhibits recurrence: the state returns to the vicinity of its initial condition after finite time. Despite its fundamental nature, a rigorous quantitative understanding of recurrence…
This thesis explores the concept of realizing quantum gates using physical systems like atoms and oscillators perturbed by electric and magnetic fields. The basic idea is that if a time-independent Hamiltonian $H_0$ is perturbed by a…
We study dynamics of isolated quantum many-body systems under periodic driving. We consider a driving protocol in which the Hamiltonian is switched between two different operators periodically in time. The eigenvalue problem of the…
We introduce a class of quantum Markov semigroups describing the evolution of interacting quantum lattice systems, specified either as generic qudits or as fermions. The corresponding generators, which include both conservative and…
We present a mapping of potentially chaotic time-dependent quantum kicked systems to an equivalent effective time-independent scenario, whereby the system is rendered integrable. The time-evolution is factorized into an initial kick,…