Pentaquarks with one heavy antiquark

Treballs Finals de Grau de Física, Facultat de Física, Universitat de Barcelona, Curs: 2017, Tutor: Joan Soto i RieraThe aim of this project is to construct a complete classification of all possible ground wave functions of a pentaquark consisting of four light quarks and a heavy antiquark. The existence of such a particle has not been established yet, but the theoretical interest in studying properties of pentaquarks has raised since the discovery, in July 2015, of an exotic baryon consisting of three light quarks (two up and one down) and a heavy pair charm-anticharm. We will study the symmetries of the internal degrees of freedom of avour, colour and spin by computing the tensor product of irreducible representations of SU(3) and SU(2), and then identify which results correspond to particles that hold the quark model symmetry principles and thus could exist and might be discovered in the future

Lie groups and algebras in particle physics

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2017, Director: Laura Costa Farràs[en] The present document is a first introduction to the Theory of Lie Groups and Lie Algebras and their representations. Lie Groups verify the characteristics of both a group and a smooth manifold structure. They arise from the need to study continuous symmetries, which is exactly what is needed for some branches of modern Theoretical Physics and in particular for quantum mechanics. The main objectives of this work are the following. First of all, to introduce the notion of a matrix Lie Group and see some examples, which will lead us to the general notion of Lie Group. From there, we will define the exponential map, which is the link to the notion of Lie Algebras. Every matrix Lie Group comes attached somehow to its Lie Algebra. Next we will introduce some notions of Representation Theory. Using the detailed examples of SU(2) and SU(3), we will study how the irreducible representations of certain types of Lie Groups are constructed through their Lie Algebras. Finally, we will state a general classification for the irreducible representations of the complex semisimple Lie Algebras

Initial state preparation for quantum chemistry on quantum computers

Quantum algorithms for ground-state energy estimation of chemical systems require a high-quality initial state. However, initial state preparation is commonly either neglected entirely, or assumed to be solved by a simple product state like Hartree-Fock. Even if a nontrivial state is prepared, strong correlations render ground state overlap inadequate for quality assessment. In this work, we address the initial state preparation problem with an end-to-end algorithm that prepares and quantifies the quality of initial states, accomplishing the latter with a new metric -- the energy distribution. To be able to prepare more complicated initial states, we introduce an implementation technique for states in the form of a sum of Slater determinants that exhibits significantly better scaling than all prior approaches. We also propose low-precision quantum phase estimation (QPE) for further state quality refinement. The complete algorithm is capable of generating high-quality states for energy estimation, and is shown in select cases to lower the overall estimation cost by several orders of magnitude when compared with the best single product state ansatz. More broadly, the energy distribution picture suggests that the goal of QPE should be reinterpreted as generating improvements compared to the energy of the initial state and other classical estimates, which can still be achieved even if QPE does not project directly onto the ground state. Finally, we show how the energy distribution can help in identifying potential quantum advantage