Efficient Characterisation and Optimal Control of Open Quantum Systems - Mathematical Foundations and Physical Applications

Since no physical system can ever be completely isolated from its environment, the study of open quantum systems is pivotal to reliably and accurately control complex quantum systems. In practice, reliability of the control field needs to be confirmed via certification of the target evolution while accuracy requires the derivation of high-fidelity control schemes in the presence of decoherence. In the first part of this thesis an algebraic framework is presented that allows to determine the minimal requirements on the unique characterisation of arbitrary unitary gates in open quantum systems, independent on the particular physical implementation of the employed quantum device. To this end, a set of theorems is devised that can be used to assess whether a given set of input states on a quantum channel is sufficient to judge whether a desired unitary gate is realised. This allows to determine the minimal input for such a task, which proves to be, quite remarkably, independent of system size. These results allow to elucidate the fundamental limits regarding certification and tomography of open quantum systems. The combination of these insights with state-of-the-art Monte Carlo process certification techniques permits a significant improvement of the scaling when certifying arbitrary unitary gates. This improvement is not only restricted to quantum information devices where the basic information carrier is the qubit but it also extends to systems where the fundamental informational entities can be of arbitary dimensionality, the so-called qudits. The second part of this thesis concerns the impact of these findings from the point of view of Optimal Control Theory (OCT). OCT for quantum systems utilises concepts from engineering such as feedback and optimisation to engineer constructive and destructive interferences in order to steer a physical process in a desired direction. It turns out that the aforementioned mathematical findings allow to deduce novel optimisation functionals that significantly reduce not only the required memory for numerical control algorithms but also the total CPU time required to obtain a certain fidelity for the optimised process. The thesis concludes by discussing two problems of fundamental interest in quantum information processing from the point of view of optimal control - the preparation of pure states and the implementation of unitary gates in open quantum systems. For both cases specific physical examples are considered: for the former the vibrational cooling of molecules via optical pumping and for the latter a superconducting phase qudit implementation. In particular, it is illustrated how features of the environment can be exploited to reach the desired targets.

Exploiting non-Markovianity for quantum control

Quantum technology, exploiting entanglement and the wave nature of matter, relies on the ability to accurately control quantum systems. Quantum control is often compromised by the interaction of the system with its environment since this causes loss of amplitude and phase. However, when the dynamics of the open quantum system is non-Markovian, amplitude and phase flow not only from the system into the environment but also back. Interaction with the environment is then not necessarily detrimental. We show that the back-flow of amplitude and phase can be exploited to carry out quantum control tasks that could not be realized if the system was isolated. The control is facilitated by a few strongly coupled, sufficiently isolated environmental modes. Our paradigmatic example considers a weakly anharmonic ladder with resonant amplitude control only, restricting realizable operations to SO(N). The coupling to the environment, when harnessed with optimization techniques, allows for full SU(N) controllability.

Hybrid optimization schemes for quantum control

Optimal control theory is a powerful tool for solving control problems in quantum mechanics, ranging from the control of chemical reactions to the implementation of gates in a quantum computer. Gradient-based optimization methods are able to find high fidelity controls, but require considerable numerical effort and often yield highly complex solutions. We propose here to employ a two-stage optimization scheme to significantly speed up convergence and achieve simpler controls. The control is initially parametrized using only a few free parameters, such that optimization in this pruned search space can be performed with a simplex method. The result, considered now simply as an arbitrary function on a time grid, is the starting point for further optimization with a gradient-based method that can quickly converge to high fidelities. We illustrate the success of this hybrid technique by optimizing a geometric phase gate for two superconducting transmon qubits coupled with a shared transmission line resonator, showing that a combination of Nelder-Mead simplex and Krotov’s method yields considerably better results than either one of the two methods alone.

A Computational Model for Observation in Quantum Mechanics

A computational model of observation in quantum mechanics is presented. The model provides a clean and simple computational paradigm which can be used to illustrate and possibly explain some of the unintuitive and unexpected behavior of some quantum mechanical systems. As examples, the model is used to simulate three seminal quantum mechanical experiments. The results obtained agree with the predictions of quantum mechanics (and physical measurements), yet the model is perfectly deterministic and maintains a notion of locality.

Room-temperature continuous-wave operation of GaInNAs/GaAs quantum dot laser with GaAsN barrier grown by solid source molecular beam epitaxy

We present the results of GaInNAs/GaAs quantum dot structures with GaAsN barrier layers grown by solid source molecular beam epitaxy. Extension of the emission wavelength of GaInNAs quantum dots by ~170nm was observed in samples with GaAsN barriers in place of GaAs. However, optimization of the GaAsN barrier layer thickness is necessary to avoid degradation in luminescence intensity and structural property of the GaInNAs dots. Lasers with GaInNAs quantum dots as active layer were fabricated and room-temperature continuous-wave lasing was observed for the first time. Lasing occurs via the ground state at ~1.2μm, with threshold current density of 2.1kA/cm[superscript 2] and maximum output power of 16mW. These results are significantly better than previously reported values for this quantum-dot system.

Java Applets for teaching quantum mechanics: Particle in a box

These Java Applets help to illustrate some of the difficult to grasp concepts of quantum mechanics. To run this Applet, use the 'Download as zip files' option. Make sure you extract the files first, then double click on the .html file to run the Applet. These are released as open access resources for the purpose of testing, and are to be deployed at the users own risk. Please report any errors you find.

Java Applets for teaching quantum mechanics: Particle in a 2D box

These Java Applets help to illustrate some of the difficult to grasp concepts of quantum mechanics. To run this Applet, use the 'Download as zip files' option. Make sure you extract the files first, then double click on the .html file to run the Applet. These are released as open access resources for the purpose of testing, and are to be deployed at the users own risk.

Java Applets for teaching quantum mechanics: Particle in a well

These Java Applets help to illustrate some of the difficult to grasp concepts of quantum mechanics. To run this Applet, use the 'Download as zip files' option. Make sure you extract the files first, then double click on the .html file to run the Applet. These are released as open access resources for the purpose of testing, and are to be deployed at the users own risk.

QLM Quantum Light and Matter Logo

The new Physics dept Quantum Light and Matter group logo designed by Alexey Kavokin in vector format. Re-traced original bitmap logo for high quality printing. Created in inkscape and exported to PDF, EPS and high resolution PNG

Propostes d'ambientalització dels centres educatius de les Illes Balears : ambientalització de bars i menjadors. 'Propuestas de ambientalización de los centros educativos de las Islas Baleares : ambientalización de bares y comedores'.

Documento en formato electrónico (PDF). Resumen tomado de la propia innovación

Los valores en la LOGSE : un análisis de documentos a través de la metodología de Hall-Tonna.

Estudio sobre el tema de los valores en la educación, cuyo objetivo general es conocer los valores implícitos y explícitos contenidos en la LOGSE, tanto en su conjunto como de cada una de las partes que la integran. Pretende proporcionar un conocimiento más profundo de la ley. El informe comienza con una exposición de las bases teóricas y la metodología empleada en el estudio. A continuación expone los resultados del análisis del Preámbulo y de cada uno de los títulos de la LOGSE, seguida de la ley completa. El último capítulo hace una recapitulación de los principales resultados del análisis del texto, seguida de comentarios y reflexiones finales.

La metodolog??a de an??lisis de valores Hall-Tonna aplicada al texto de la LOGSE

Analizar la representaci??n y tratamiento de los valores relativos a la educaci??n en la LOGSE, tanto en conjunto como en las partes que la integran.. Se realiza una introducci??n a la Teor??a de los Valores de Hall y Tonna, presentando el cuestionario de opci??n m??ltiple, para conocer los valores del sujeto y su prioridad, y el an??lisis de documentos como m??todo para la detecci??n de valores institucionales. Se presentan las pautas para el an??lisis de los datos y las gu??as para la interpretaci??n del perfil obtenido, formado por cuatro apartados: 1. Mapa de valores, 2. Ciclo de desarrollo y liderazgo, 3. Destrezas, tiempo y orientaci??n, 4. Prioridades de valor. Se separa la LOGSE seg??n los apartados de la estructura interna y se obtienen perfiles para cada secci??n y uno global, comparando los resultados obtenidos.. Porcentajes.. En el mapa de valores de la LOGSE se observa un equilibrio entre metas y medios y ausencias relacionadas con el autocontrol, el placer sensorial o la fantas??a. El estilo de liderazgo que se deriva de los valores del perfil de la Ley es el permisivo. Los porcentajes menores son los de destrezas imaginativas e interpersonales y los valores de tiempo de recuperaci??n, de descanso y de ocio se presentan con escasa relevancia. Se observa un grado de coherencia acptable entre los ciclos de desarrollo y los niveles educacionales.. En la relaci??n entre la LOGSE y la sociedad actual se observa un predominio de lo institucional y las complejidades burocr??ticas. Los valores con mayor protagonismo son el trabajo, la dignidad humana y la justicia social. Se recomienda la ampliaci??n de la investigaci??n a los Decretos de implantaci??n de la Reforma y el Curr??culo..

Automatic generation of active coordinates for quantum dynamics calculations: application to the dynamics of benzene photochemistry

A new practical method to generate a subspace of active coordinates for quantum dynamics calculations is presented. These reduced coordinates are obtained as the normal modes of an analytical quadratic representation of the energy difference between excited and ground states within the complete active space self-consistent field method. At the Franck-Condon point, the largest negative eigenvalues of this Hessian correspond to the photoactive modes: those that reduce the energy difference and lead to the conical intersection; eigenvalues close to 0 correspond to bath modes, while modes with large positive eigenvalues are photoinactive vibrations, which increase the energy difference. The efficacy of quantum dynamics run in the subspace of the photoactive modes is illustrated with the photochemistry of benzene, where theoretical simulations are designed to assist optimal control experiments

A quantum molecular similarity analysis of changes in molecular electron density caused by basis set flotation and electric field application

Quantum molecular similarity (QMS) techniques are used to assess the response of the electron density of various small molecules to application of a static, uniform electric field. Likewise, QMS is used to analyze the changes in electron density generated by the process of floating a basis set. The results obtained show an interrelation between the floating process, the optimum geometry, and the presence of an external field. Cases involving the Le Chatelier principle are discussed, and an insight on the changes of bond critical point properties, self-similarity values and density differences is performed

A comparative analysis by means of quantum molecular similarity measures of density distributions derived from conventional ab initio and density functional methods

A procedure based on quantum molecular similarity measures (QMSM) has been used to compare electron densities obtained from conventional ab initio and density functional methodologies at their respective optimized geometries. This method has been applied to a series of small molecules which have experimentally known properties and molecular bonds of diverse degrees of ionicity and covalency. Results show that in most cases the electron densities obtained from density functional methodologies are of a similar quality than post-Hartree-Fock generalized densities. For molecules where Hartree-Fock methodology yields erroneous results, the density functional methodology is shown to yield usually more accurate densities than those provided by the second order Møller-Plesset perturbation theory