Dissertations / Theses on the topic 'Quantum computing'

Quantum holonomies are investigated in different contexts.

A geometric phase is proposed for decomposition dependent evolution, where each component of a given decomposition of a mixed state evolves independently. It is shown that this geometric phase only depends on the path traversed in the space of decompositions.

A holonomy is associated to general paths of subspaces of a Hilbert space, both discrete and continuous. This opens up the possibility of constructing quantum holonomic gates in the open path setting. In the discrete case it is shown that it is possible to associate two distinct holonomies to a given path. Interferometric setups for measuring both holonomies are

provided. It is further shown that there are cases when the holonomy is only partially defined. This has no counterpart in the Abelian setting.

An operational interpretation of amplitudes of density operators is provided. This allows for a direct interferometric realization of Uhlmann's parallelity condition, and the possibility of measuring the Uhlmann holonomy for sequences of density operators.

Off-diagonal geometric phases are generalized to the non-Abelian case. These off-diagonal holonomies are undefined for cyclic evolution, but must contain members of non-zero rank if all standard holonomies are undefined. Experimental setups for measuring the off-diagonal holonomies are proposed.

The concept of nodal free geometric phases is introduced. These are constructed from gauge invariant quantities, but do not share the nodal point structure of geometric phases and off-diagonal geometric phases. An interferometric setup for measuring nodal free geometric phases is provided, and it is shown that these phases could be useful in geometric quantum computation.

A holonomy associated to a sequence of quantum maps is introduced. It is shown that this holonomy is related to the Uhlmann holonomy. Explicit examples are provided to illustrate the general idea.

Quantum information science has made significant progress over the last several decades, but the eventual form a quantum computer will take has yet to be determined. Several physical systems have been shown to operate as quantum bits, or qubits, but each faces a central challenge: the qubit must be sufficiently isolated from its environment to maintain quantum coherence while simultaneously having sufficient coupling to the environment to allow quantum mechanical interactions for manipulation and measurement. An approach to achieve these conflicting requirements is to create qubits that are insensitive to small perturbing interactions within their environment by using topological properties of the physical system in which the qubits are formed. This dissertation presents studies on low-dimensional semiconductor heterostructures of InAs, GaSb and AlSb fabricated by molecular beam epitaxy with focus on relevant properties for their utilization in forming a topologically protected (TP) qubit.

The theoretical basis regarding the semiconductor characteristics suitable for realizing TP qubits stipulates the need for strong spin-orbit coupled semiconductors with high carrier mobility. A comparative study of InAs/AlSb heterostructures wherein structure parameters were systematically varied led to a greater understanding of the limits to mobility in InAs quantum wells. Magnetotransport measurements using a dual-gated device geometry and a comparison of experiment to models of carrier mobility as a function of carrier density were used to identify dominant scattering mechanisms in these heterostructures.

The development of dual-gated devices and high quality InAs channels with AlSb barriers led to a demonstration of the gate control of spin-orbit coupling in a high mobility InAs/AlSb quantum well in which the gate-tuned electron mobility exceeded 700,000 cm²/V·s. Analysis of low temperature magnetoresistance oscillations indicated the zero field spin-splitting could be tuned via the Rashba effect while keeping the two-dimensional electron gas charge density constant.

Findings from the work on InAs quantum wells were applied to investigations on InAs/GaSb bilayers, a system predicted to be a two-dimensional topological insulator (TI). The temperature and magnetic field dependence of the resistance in dual-gated InAs/GaSb heterostructures gate-tuned to the predicted TI regime were found consistent with conduction through a disordered two-fluid system. The impact of disorder on the formation of topologically protected edge states and an insulating bulk was considered. Potential fluctuations in the band structure for realistic levels of disorder in state-of-the-art heterostructures were calculated using a gated heterostructure model. Potential fluctuations were estimated to be sufficiently large such that conduction in the predicted TI regime was likely dominated by tunneling between localized electron and hole charge fluctuations, corresponding to a symplectic metallic phase rather than a topological insulator. The implications are that future efforts must address defects and disorder in this system if the TI regime is to be achieved.

1) HeH+, a species of great astrochemical importance which is thought to be the first molecular species to have formed in the universe;

2) CO2+, a metastable dication of particular interest in quantum control experiments due to its long-lived lowest vibrational level;

3) 41K87Rb, a polar molecule that can be formed at very low temperature and trapped, making it a good candidate for quantum computing schemes.

First, we use ab initio methods to compute accurate potential energy curves for the lowest singlet and triplet states of HeH+ as well as the potential energy curves, transition dipole moments and nonadiabatic radial couplings of the ground 3Π state of CO2+ and of its 11 lowest 3Σ- states.

In a second step, we use this ab initio data to compute the photodissociation and radiative association cross sections for the a and b 3Σ+ states of HeH+, as well as the values of the corresponding rate constants for astrophysical environments. The photodissociation cross sections from the lowest vibrational level of CO2+ is also determined.

Going one step further, we optimize laser control fields that drive the photodissociation dynamics of HeH+ and CO2+ towards specific channels. We compare two field optimization methods: a Møller operator-based Local Control approach and Optimal Control Theory. In both cases, we add a constraint that minimizes the area of the optimized fields.

Finally, we focus on one of the potential applications of high-fidelity laser control: the use of small molecular systems as quantum computers. We more specifically study the potential implementation of both intra- and intermolecular logic gates on data encoded in hyperfine states of trapped ultracold polar 41K87Rb molecules, opening interesting perspectives in terms of extensibility.

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Dans cette thèse, nous étudions théoriquement les propriétés de molécules diatomiques, leur dynamique de réaction ainsi que le contrôle de cette dynamique à l'aide de champs laser. Notre travail porte plus spécifiquement sur trois espèces :

1) HeH+, un composé-clé en astrochimie considéré comme la première espèce moléculaire qui s'est formée dans l'univers ;

2) CO2+, un dication métastable qui se prête bien à des expériences de contrôle quantique en raison du relativement long temps de vie de son état vibrationnel le plus bas ;

3) 41K87Rb, une molécule polaire qui présente la particularité de pouvoir être formée à très basse température et piégée, ce qui en fait un bon support physique potentiel pour la réalisation d'un ordinateur quantique moléculaire.

Nous utilisons tout d'abord des méthodes de calcul ab initio afin d'obtenir les courbes d'énergie potentielle des premiers états singulets et triplets de HeH+ avec un haut de degré de précision, ainsi que les courbes d'énergie potentielle, les moments dipolaires de transition et les couplages non-adiabatiques radiaux de l'état fondamental 3Π de CO2+ et de ses 11 premiers états 3Σ-.

Ensuite, nous utilisons ces données ab initio pour calculer les sections efficaces de photodissociation et d'association radiative des états a et b 3Σ+ de HeH+, ainsi que les constantes cinétiques associées à ces processus dans les conditions rencontrées dans des environnements astrophysiques. Les sections efficaces de photodissociation du niveau vibrationnel le plus bas de CO2+ sont également calculées.

Nous allons ensuite un cran plus loin en optimisant des champs laser qui guident la dynamique de photodissociation de HeH+ et CO2+ vers des canaux de dissociation spécifiques. Nous comparons deux méthodes d'optimisation de ces champs: une approche de contrôle local basée sur les opérateurs de Møller et la théorie du contrôle optimal. Dans le deux cas, nous incluons une contrainte qui minimise l'aire des champs.

Enfin, nous nous concentrons sur l'une des applications possibles du contrôle laser à haute fidélité :l'utilisation de petits systèmes moléculaires comme ordinateurs quantiques. Nous étudions plus spécifiquement l'implémentation possible d'opérations logiques intra- et intermoléculaires sur des données encodées dans des états hyperfins de molécules de 41K87Rb piégées, ce qui ouvre des perspectives intéressantes en terme d'extensibilité.
Doctorat en Sciences
info:eu-repo/semantics/nonPublished