Scalable Ellipsoidal Classification for Bipartite Quantum States

The Separability Problem is approached from the perspective of Ellipsoidal Classification. A Density Operator of dimension N can be represented as a vector in a real vector space of dimension $N^{2}- 1$, whose components are the projections of the matrix onto some selected basis. We suggest a method to test separability, based on successive optimization programs. First, we find the Minimum Volume Covering Ellipsoid that encloses a particular set of properly vectorized bipartite separable states, and then we compute the Euclidean distance of an arbitrary vectorized bipartite Density Operator to this ellipsoid. If the vectorized Density Operator falls inside the ellipsoid, it is regarded as separable, otherwise it will be taken as entangled. Our method is scalable and can be implemented straightforwardly in any desired dimension. Moreover, we show that it allows for detection of Bound Entangled StatesComment: 8 pages, 5 figures, 3 tables. Revised version, to appear in Physical Review

A Photonic Implementation for the Topological Cluster State Quantum Computer

A new implementation of the topological cluster state quantum computer is suggested, in which the basic elements are linear optics, measurements, and a two-dimensional array of quantum dots. This overcomes the need for non-linear devices to create a lattice of entangled photons. We give estimates of the minimum efficiencies needed for the detectors, fusion gates and quantum dots, from a numerical simulation

Policy Gradient Approach to Compilation of Variational Quantum Circuits

We propose a method for finding approximate compilations of quantum unitary transformations, based on techniques from policy gradient reinforcement learning. The choice of a stochastic policy allows us to rephrase the optimization problem in terms of probability distributions, rather than variational gates. In this framework, finding the optimal configuration is done by optimizing over distribution parameters, rather than over free angles. We show numerically that this approach can be more competitive than gradient-free methods, for comparable amounts of resources (i.e. quantum circuit runs). Another interesting feature of this approach to variational compilation is that it does not need a separate register and long-range interactions to estimate the end-point fidelity, which is an improvement over methods which rely on the Hilbert-Schmidt test. We expect these techniques to be relevant for training variational circuits in other contexts

Entanglement-Enhanced Classical Communication

This thesis will be focused on the classical capacity of quantum channels, one of the first areas treated by quantum information theorists. The problem is fairly solved since some years. Nevertheless, this work will give me a reason to introduce a consistent formalism of the quantum theory, as well as to review fundamental facts about quantum non-locality and how it can be used to enhance communication. Moreover, this reflects my dwelling in the spirit of classical information theory, and it is intended to be a starting point towards a thorough study of how quantum technologies can help to shape the future of telecommunications. Whenever it was possible, heuristic reasonings were introduced instead of rigorous mathematical proofs. This finds an explanation in that I am a self-taught neophyte in the field, and just about every time I came across a new concept, physical arguments were always more compelling to me than just maths. The technical content of the thesis is twofold. On one hand, a quadratic classification based on optimization programs that I devised for distinguishing entangled states is presented in Chapter 4. In second place, a less difficult yet I hope equally interesting technical part consists of versions of some proofs throughout the text.Comment: M.Sc. Thesis, 103 page

Periodic skyrmionic textures via conformal cartographic projections

We find periodic skyrmionic textures via conformal cartographic projections that map either an entire spherical parameter space or a hemisphere onto every regular polygon that provides regular tessellations of the plane. These maps preserve the sign of the Skyrme density throughout the entire space. We implement these textures in the polarization state of a laser beam, and demonstrate that paraxial fields where a periodic texture preserving the sign of the Skyrme density is implemented in the polarization state distribution unavoidably exhibit zeros

Remote lab experiments: opening possibilities for distance learning in engineering fields

Remote experimentation laboratories are systems based on real equipment, allowing students to perform practical work through a computer connected to the internet. In engineering fields lab activities play a fundamental role. Distance learning has not demonstrated good results in engineering fields because traditional lab activities cannot be covered by this paradigm. These activities can be set for one or for a group of students who work from different locations. All these configurations lead to considering a flexible model that covers all possibilities (for an individual or a group). An inter-continental network of remote laboratories supported by both European and Latin American institutions of higher education has been formed. In this network context, a learning collaborative model for students working from different locations has been defined. The first considerations are presented.Education for the 21 st century - impact of ICT and Digital Resources ConferenceRed de Universidades con Carreras en Informática (RedUNCI

Implementations of Fault-tolerant Quantum Devices

Accurate control and addressability of quantum devices will come with the promise of improvement in a wide variety of theoretical and applied fields, such as chemistry, condensed matter physics, theoretical computer science, foundational physics, communications, metrology and others. Decoherence of quantum states and the loss of quantum systems have adverse effects and deter a satisfactory usage of quantum devices. This is the main problem to be overcome, which is the goal of quantum fault tolerance. In this thesis we present a series of works that contribute to some of the fields mentioned above, in the direction of fighting decoherence and loss. These works fall in two categories: on one hand, we looked at computer architectures which can be used to combat errors, using techniques of quantum error correcting codes. In a first project we found decoherence and loss probability thresholds below which quantum computing is provably possible. We assumed a very particular error model tailored specially to quantum dots as single photon sources and linear optics. Subsequently we looked at the problem of loss, both of heralded and unheralded, and devised some ways to fight it. The framework under which this work was done was used to develop theory which is currently being tested in a quantum optics experimental group and will be reported in an article later this year. On the other hand, we studied how the error probability can be reduced at the physical level, thanks exclusively to the properties of the system in which information is stored, as opposed to making use of quantum codes. We looked at a particular superconducting circuit, which is potentially very well protected against some types of decoherence. In particular, we observed that the interaction with the environment become weaker for certain values of the circuit external parameters

Hamiltonian Forging of a Thermofield Double

We address the variational preparation of Gibbs states as the ground state of a suitably engineered Hamiltonian acting on the doubled Hilbert space. The construction is exact for quadratic fermionic Hamiltonians and gives excellent approximations up to fairly high quartic deformations. We provide a variational circuit whose optimization returns the unitary diagonalizing operator, thus giving access to the whole spectrum. The problem naturally implements the entanglement forging ansatz, allowing the computation of Thermofield Doubles with a higher number of qubits than in competing frameworks.Comment: 11 pages, 6 figure