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Accurate control of quantum states is crucial for quantum computing and other quantum technologies. In the basic scenario, the task is to steer a quantum system towards a target state through a sequence of control operations. Determining…
This thesis explores the use of entangled states in quantum computation and quantum information science. Entanglement, a quantum phenomenon with no classical counterpart, has been identified as an important and quantifiable resource in many…
Effective quantum computation relies upon making good use of the exponential information capacity of a quantum machine. A large barrier to designing quantum algorithms for execution on real quantum machines is that, in general, it is…
Quantum machine learning algorithms have emerged to be a promising alternative to their classical counterparts as they leverage the power of quantum computers. Such algorithms have been developed to solve problems like electronic structure…
One of the potential applications of a quantum computer is solving quantum chemical systems. It is known that one of the fastest ways to obtain somewhat accurate solutions classically is to use approximations of density functional theory.…
Quantum computing is the process of performing calculations using quantum mechanics. This field studies the quantum behavior of certain subatomic particles for subsequent use in performing calculations, as well as for large-scale…
Quantum machine learning, as an extension of classical machine learning that harnesses quantum mechanics, facilitates effiient learning from data encoded in quantum states. Training a quantum neural network typically demands a substantial…
Learning quantum states from measurement data is a central problem in quantum information and computational complexity. In this work, we study the problem of learning to generate mixed states on a finite-dimensional lattice. Motivated by…
In recent years, the entanglement spectra of quantum states have been identified to be highly valuable for improving our understanding on many problems in quantum physics, such as classification of topological phases, symmetry-breaking…
The aim of this paper is to introduce a new graphic representation of quantum states by means of a specific application: the analysis of two models of quantum copying machines. The graphic representation by diagrams of states offers a clear…
State transformation problems such as compressing quantum information or breaking quantum commitments are fundamental quantum tasks. However, their computational difficulty cannot easily be characterized using traditional complexity theory,…
The famous no-cloning principle has been shown recently to enable a number of uncloneable functionalities. Here we address for the first time unkeyed quantum uncloneablity, via the study of a complexity-theoretic tool that enables a…
The vast complexity is a daunting property of generic quantum states that poses a significant challenge for theoretical treatment, especially in non-equilibrium setups. Therefore, it is vital to recognize states which are locally less…
The goal of generative machine learning is to model the probability distribution underlying a given data set. This probability distribution helps to characterize the generation process of the data samples. While classical generative machine…
Understanding the power and limitations of quantum access to data in machine learning tasks is primordial to assess the potential of quantum computing in artificial intelligence. Previous works have already shown that speed-ups in learning…
The linearity of quantum operations puts many fundamental constraints on the information processing tasks we can achieve on a quantum system whose state is not exactly known, just as we observe in quantum cloning and quantum discrimination.…
One advantage of quantum algorithms over classical computation is the possibility to spread out, process, analyse and extract information in multipartite configurations in coherent superpositions of classical states. This will be discussed…
We investigate unitary and state $t$-designs from a computational complexity perspective. First, we address the problems of computing frame potentials that characterize (approximate) $t$-designs. We present a quantum algorithm for computing…
We describe a quantum algorithm to prepare an arbitrary pure state of a register of a quantum computer with fidelity arbitrarily close to 1. Our algorithm is based on Grover's quantum search algorithm. For sequences of states with suitably…
Complexity theory typically focuses on the difficulty of solving computational problems using classical inputs and outputs, even with a quantum computer. In the quantum world, it is natural to apply a different notion of complexity, namely…