Related papers: Quantum thermodynamics and semi-definite optimizat…
We consider a generic framework of optimization algorithms based on gradient descent. We develop a quantum algorithm that computes the gradient of a multi-variate real-valued function $f:\mathbb{R}^d\rightarrow \mathbb{R}$ by evaluating it…
This thesis addresses problems in the field of quantum information theory. The first part of the thesis is opened with concrete definitions of general quantum source models and their compression, and each subsequent chapter addresses the…
We study the thermodynamics of various physical systems in the framework of the Generalized Uncertainty Principle that implies a minimal length uncertainty proportional to the Planck length. We present a general scheme to analytically…
Optimizing over separable quantum objects is challenging for two key reasons: determining separability is NP-hard, and the dimensionality of the problem grows exponentially with the number of qubits. We address both challenges by…
Quantum computation is one of the most promising new paradigms for the simulation of physical systems composed of electrons and atomic nuclei, with applications in chemistry, solid-state physics, materials science, and molecular biology.…
Thermodynamics relies on the possibility to describe systems composed of a large number of constituents in terms of few macroscopic variables. Its foundations are rooted into the paradigm of statistical mechanics, where thermal properties…
Quantum machines are among the most promising technologies expected to provide significant improvements in the following years. However, bridging the gap between real-world applications and their implementation on quantum hardware is still…
A nonperturbative theory is developed, aiming at an exact and efficient evaluation of a general quantum system interacting with arbitrary bath environment at any temperature and in the presence of arbitrary time-dependent external fields.…
We consider the reduced dynamics in a bipartite quantum system (consisting of a central system and an intermediate environment) coupled to a heat bath at finite temperature. To describe this situation, in the simplest possible -- yet…
Local master equations are a widespread tool to model open quantum systems, especially in the context of many-body systems. These equations, however, are believed to lead to thermodynamic anomalies and violation of the laws of…
The gradient descent approach is the key ingredient in variational quantum algorithms and machine learning tasks, which is an optimization algorithm for finding a local minimum of an objective function. The quantum versions of gradient…
We set up a framework for quantum stochastic thermodynamics based solely on experimentally controllable, but otherwise arbitrary interventions at discrete times. Using standard assumptions about the system-bath dynamics and insights from…
Quantum thermodynamics is a research field that aims at fleshing out the ultimate limits of thermodynamic processes in the deep quantum regime. A complete picture of quantum thermodynamics allows for catalysts, i.e., systems facilitating…
Quantum coherence is one of the fundamental properties of quantum mechanics and also acts as a valuable resource for a variety of practical applications, which includes quantum computing and quantum information processing. Evaluating the…
This is a set of lecture notes for a graduate-level course on quantum algorithms, with an emphasis on quantum optimization algorithms. It is developed for applied mathematicians and engineers, and requires no previous background in quantum…
A widely used strategy to reduce the computational cost in quantum-chemical calculations is to partition the system into an active subsystem, which is the focus of the computational efforts and an environment that is treated at a lower…
For a closed bi-partite quantum system partitioned into system proper and environment we interprete the microcanonical and the canonical condition as constraints for the interaction between those two subsystems. In both cases the possible…
Recently, several approaches to solving linear systems on a quantum computer have been formulated in terms of the quantum adiabatic theorem for a continuously varying Hamiltonian. Such approaches enabled near-linear scaling in the condition…
Simulating the time evolution of a physical system at quantum mechanical levels of detail -- known as Hamiltonian Simulation (HS) -- is an important and interesting problem across physics and chemistry. For this task, algorithms that run on…
While most work on the quantum simulation of chemistry has focused on computing energy surfaces, a similarly important application requiring subtly different algorithms is the computation of energy derivatives. Almost all molecular…