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In this thesis we present new results relevant to two important problems in quantum information science: the development of a theory of entanglement and the exploration of the use of controlled quantum systems to the simulation of quantum…
We discuss encodings of fermionic many-body systems by qubits in the presence of symmetries. Such encodings eliminate redundant degrees of freedom in a way that preserves a simple structure of the system Hamiltonian enabling quantum…
An algorithm for quantum computing Hamiltonian cycles of simple, cubic, bipartite graphs is discussed. It is shown that it is possible to evolve a quantum computer into an entanglement of states which map onto the set of all possible paths…
Simple constructions and protocols are demonstrated to allow the implementation of universal quantum computation on an arbitrarily large quantum system by controlling a fixed number of spins, vastly reducing the engineering requirements in…
Resonant systems emerge as weakly nonlinear approximations to problems with highly resonant linearized perturbations. Examples include nonlinear Schroedinger equations in harmonic potentials and nonlinear dynamics in Anti-de Sitter…
We present an adaptation of the so-called structural method \cite{CMM23} for Hamiltonian systems, and redesign the method for this specific context, which involves two coupled differential systems. Structural schemes decompose the problem…
We introduce a scheme for the quantum simulation of many-body decoherence based on the unitary evolution of a stochastic Hamiltonian. Modulating the strength of the interactions with stochastic processes, we show that the noise-averaged…
Accurate modeling of driven light-matter interactions is essential for quantum technologies, where natural and synthetic atoms are used to store and process quantum information, mediate interactions between bosonic modes, and enable…
We develop a quantum computing scheme utilizing McLachlan variational principle in a hybrid quantum-classical algorithm to accurately calculate the transition dynamics of a closed quantum system with many excited states subject to a strong…
We propose a (theoretical ;-) model for quantum computation where the result can be read out from the time average of the Hamiltonian dynamics of a 2-dimensional crystal on a cylinder. The Hamiltonian is a spatially local interaction among…
The characterization of Hamiltonians and other components of open quantum dynamical systems plays a crucial role in quantum computing and other applications. Scientific machine learning techniques have been applied to this problem in a…
Integrability is a cornerstone of classical mechanics, where it has a precise meaning. Extending this notion to quantum systems, however, remains subtle and unresolved. In particular, deciding whether a quantum Hamiltonian - viewed simply…
Quantum simulation is a promising near term application for mesoscale quantum information processors, with the potential to solve computationally intractable problems at the scale of just a few dozen interacting quantum systems. Recent…
Many-body entangled systems, in particular topologically ordered spin systems proposed as resources for quantum information processing tasks, often involve highly non-local interaction terms. While one may approximate such systems through…
An input-output model of a two-level quantum system in the Heisenberg picture is of bilinear form with constant system matrices, which allows the introduction of the concepts of controllability and observability in analogy with those of…
The fundamental question of how to best simulate quantum systems using conventional computational resources lies at the forefront of condensed matter and quantum computation. It impacts both our understanding of quantum materials and our…
We develop a workflow to use current quantum computing hardware for solving quantum many-body problems, using the example of the fermionic Hubbard model. Concretely, we study a four-site Hubbard ring that exhibits a transition from a…
We present a recursive formula for the computation of the static effective Hamiltonian of a system under a fast-oscillating drive. Our analytical result is well-suited to symbolic calculations performed by a computer and can be implemented…
Classical simulation of quantum systems plays an important role in the study of many-body phenomena and in the benchmarking and verification of quantum technologies. Exact simulation is often limited to small systems because the dimension…
Simulation of the time-dynamics of fermionic many-body systems has long been predicted to be one of the key applications of quantum computers. Such simulations -- for which classical methods are often inaccurate -- are critical to advancing…