The development of a quantum computer presents one of the greatest challenges in science and engineering to date. The promise of more efficient computing based on entangled quantum states and the superposition principle has led to a worldwide explosion of interest in the fields of quantum information and computation. Among the number of hurdles which must first be cleared before we witness a physical realization are problems associated with environment-induced decoherence and noise more generally. However, the discovery of quantum error correction and the establishment of the accuracy threshold theorem provide us with the hope of someday harnessing the potential power a functioning fault-tolerant quantum information processor has to offer. This dissertation contributes to this effort by investigating a particular class of quantum error correcting codes, namely noiseless subsystem encodings. The passive approach to error correction taken by these encodings provides an efficient means of protection from symmetrically coupled system-environment interactions. Here I will present methods for determining the subsystem-preserving evolutions for noiseless subsystem encodings supported by arbitrary-dimensional physical quantum systems. Implications for universal, collective decoherence-free quantum computation using the derived operations are discussed. Moreover, I will present a proposal for an optical device which is capable of preparing a variety of these noiseless subsystem encodings through a postselection strategy.

The theory of decoherence aims to explain how macroscopic quantum objects become effectively classical. Understanding this process could help in the search for the quantum theory underlying gravity, and suggest new schemes for preserving the coherence of technological quantum devices. The process of decoherence is best understood in terms of information flow within a quantum system, and between the system and its environment. We develop a novel way of characterizing this information, and give a sufficient condition for its classicality. These results generalize previous models of decoherence, clarify the process by which a phase-space based on non-commutative quantum variables can emerge, and provide a possible explanation for the universality of the phenomenon of decoherence. In addition, the tools developed in this approach generalize the theory of quantum error correction to infinite-dimensional Hilbert spaces. We characterize the nature of the information preserved by a quantum channel by the observables which exist in its image (in the Heisenberg picture). The sharp observables preserved by a channel form an operator algebra which can be characterized in terms of the channel's elements. The effect of the channel on these observables can be reversed by another physical transformation. These results generalize the theory of quantum error correction to codes characterized by arbitrary von Neumann algebras, which can represent hybrid quantum-classical information, continuous variable systems, or certain quantum field theories. The preserved unsharp observables (positive operator-valued measures) allow for a finer characterization of the information preserved by a channel. We show that the only type of information which can be duplicated arbitrarily many times consists of coarse-grainings of a single POVM. Based on these results, we propose a model of decoherence which can account for the emergence of a realistic classical phase-space. This model supports the view that the quantum-classical correspondence is given by a quantum-to-classical channel, which is another way of representing a POVM.

The theory of decoherence aims to explain how macroscopic quantum objects become effectively classical. Understanding this process could help in the search for the quantum theory underlying gravity, and suggest new schemes for preserving the coherence of technological quantum devices. The process of decoherence is best understood in terms of information flow within a quantum system, and between the system and its environment. We develop a novel way of characterizing this information, and give a sufficient condition for its classicality. These results generalize previous models of decoherence, clarify the process by which a phase-space based on non-commutative quantum variables can emerge, and provide a possible explanation for the universality of the phenomenon of decoherence. In addition, the tools developed in this approach generalize the theory of quantum error correction to infinite-dimensional Hilbert spaces. We characterize the nature of the information preserved by a quantum channel by the observables which exist in its image (in the Heisenberg picture). The sharp observables preserved by a channel form an operator algebra which can be characterized in terms of the channel's elements. The effect of the channel on these observables can be reversed by another physical transformation. These results generalize the theory of quantum error correction to codes characterized by arbitrary von Neumann algebras, which can represent hybrid quantum-classical information, continuous variable systems, or certain quantum field theories. The preserved unsharp observables (positive operator-valued measures) allow for a finer characterization of the information preserved by a channel. We show that the only type of information which can be duplicated arbitrarily many times consists of coarse-grainings of a single POVM. Based on these results, we propose a model of decoherence which can account for the emergence of a realistic classical phase-space. This model supports the view that the quantum-classical correspondence is given by a quantum-to-classical channel, which is another way of representing a POVM.

Quantum computers can theoretically perform certain tasks which classical computers at realistic times could not. Operating a quantum computer requires precise control over the system, for instance achieved by adiabatic evolution, and isolation from the environment to retain coherence. This report combines these two, somewhat contradicting, error preventing techniques. To reduce the run-time a transitionless quantum driving algorithm, or, adiabatic shortcut, is employed. The notion of Noiseless Subsystems (NS), a generalization of decoherence free subspaces, are used for robustness against environmental decoupling, by creating logical qubits which act as a noiseless code. Furthermore, the adiabatic shortcut for the NS code is applied to a refocusing scheme (spin-echo) in order to remove the dynamical phase, sensitive to error propagation, so that only the Berry phase is effectively picked up. The corresponding Hamiltonian is explicitly derived for the only two cases of two-dimensional NS: N=3,4 qubits with total spin of j=1/2,0, respectively. This constitutes geometric quantum computation (GQC) enacting a universal single-qubit gate, which is also explicitly derived. / Kvantdatorer kan teoretiskt utföra vissa uppgifter som klassiska datorer vid realistiska tider inte kan. Att köra en kvantdator kräver exakt kontroll över systemet, till exempel genom adiabatisk utvecking, och isolering från omgiviningen för att behålla koherens. Denna rapport kombinerar dessa två, något motsägelsefulla, tekniker för felhantering. För att minska körtiden används en övergångsfri kvantkörningsalgoritm, också kallad adiabatisk genväg. Konceptet brusfria delsystem, en generalisering av dekoherensfria underrum, används för robusthet mot sammanflätning med omgivningen genom att skapa logiska kvantbitar som fungerar som en brusfri kod. Vidare tillämpas den adiabatiska genvägen för den brusfria koden på ett spinn-eko för att eliminera den dynamiska fasen, som är känslig för felpropagering, så att endast Berrys fas, som är okänslig för felpropagering, effektivt plockas upp. Motsvarande Hamiltonian härleds uttryckligen för de enda två fallen av tvådimensionella brusfria delsystem: 3 eller 4 kvantbitar med respektive totalspinn j = 1/2 och 0. Detta möjliggör beräkning med en geometrisk kvantdator baserad på en universell en-kvantbitsgrind, som också härleds explicit.