This thesis is concerned with finding technologically useful quantum phenomena that are robust against real world imperfections. We examine three different areas covering techniques for spin measurement, photon preparation and error correction. The first research chapter presents a robust spin-measurement procedure, using an amplification approach: the state of the spin is propagated over a two-dimensional array to a point where it can be measured using standard macroscopic state mea- surement techniques. Even in the presence of decoherence, our two-dimensional scheme allows a linear growth in the total spin polarisation - an important increase over the √t obtainable in one-dimension. The work is an example of how simple propagation rules can lead to predictable macroscopic behaviour and the techniques should be applicable in other state propagation schemes. The next chapter is concerned with strategies for obtaining a robust and reliable single photon source. Using a microscopic model of electron-phonon interactions and a quantum master equation, we examine phonon-induced decoherence and assess its impact on the rate of production, and indistinguishability, of single photons emitted from an optically driven quantum dot system. We find that, above a certain threshold of desired indistinguishability, it is possible to mitigate the deleterious effects of phonons by exploiting a three-level Raman process for photon production. We introduce a master equation technique for quantum jump situations that should have wide application in other situations. The final chapter focusses on toric error correcting codes. Toric codes form part of the class of surface codes that have attracted a lot of attention due to their ability to tolerate a high level of errors, using only local operations. We investigate the power of small scale toric codes and determine the minimum size of code necessary for a first experimental demonstration of toric coding power.

Quantum information processing (QIP) is an interdisciplinary field concerned with the development of computers and information processing systems that utilize quantum mechanical properties of nature to carry out their function. QIP systems have become vastly more practical since the turn of the century. Today, QIP applications span imaging, cryptographic security, computation, and simulation (quantum systems that mimic other quantum systems). Many important strategies improve quantum versions of classical information system hardware, such as single photon detectors and quantum repeaters. Another more abstract strategy engineers high-dimensional quantum state spaces, so that each successful event carries more information than traditional two-level systems allow. Photonic states in particular bring the added advantages of weak environmental coupling and data transmission near the speed of light, allowing for simpler control and lower system design complexity. In this dissertation, numerous novel, scalable designs for practical high-dimensional linear-optical QIP systems are presented. First, a correlated photon imaging scheme using orbital angular momentum (OAM) states to detect rotational symmetries in objects using measurements, as well as building images out of those interactions is reported. Then, a statistical detection method using chains of OAM superpositions distributed according to the Fibonacci sequence is established and expanded upon. It is shown that the approach gives rise to schemes for sorting, detecting, and generating the recursively defined high-dimensional states on which some quantum cryptographic protocols depend. Finally, an ongoing study based on a generalization of the standard optical multiport for applications in quantum computation and simulation is reported upon. The architecture allows photons to reverse momentum inside the device. This in turn enables realistic implementation of controllable linear-optical scattering vertices for carrying out quantum walks on arbitrary graph structures, a powerful tool for any quantum computer. It is shown that the novel architecture provides new, efficient capabilities for the optical quantum simulation of Hamiltonians and topologically protected states. Further, these simulations use exponentially fewer resources than feedforward techniques, scale linearly to higher-dimensional systems, and use only linear optics, thus offering a concrete experimentally achievable implementation of graphical models of discrete-time quantum systems.

Neste trabalho realizamos a implementação experimental de informação quântica (IQ) em um sistema de dois bits quânticos (q-bits) de spin 3/2 via ressonância quadrupolar nuclear (RQN). Foram implementadas portas lógicas quânticas que são necessárias para a criação e manipulação dos estados pseudo-puros (PPSs). Ademais, foi proposto um método de tomografia de estado quântico (TEQ) baseado na seleção de coerências de múltiplo quantum por ciclagem de fases. A TEQ foi empregada para avaliar os estados quânticos implementados experimentalmente. A amostra utilizada foi um monocristal de KClO3, o núcleo medido foi 35Cl, que possui spin 3/2. Neste sistema foi possível obter os quatro PPSs da base computacional. Sobre os PPSs foram aplicados portas lógicas quânticas CNOT e Hadamard, que produziram estados de sobreposição e estados emaranhados. Sobre os estados emaranhados foram analisados os conceitos de correlações clássicas e quânticas. A TEQ dos estados implementados experimentalmente mostrou altas fidelidades (maior de 90%). Também foi possível criar estados coerentes de spin aplicando rotações sobre os PPSs. Com base nos estados coerentes de spin foram gerados estados coerentes comprimidos mediante a aplicação de evoluções não lineares, presentes naturalmente em sistemas de RQN. Estes resultados promissores mostram que a RQN pode ser satisfatoriamente aplicada como uma ferramenta experimental em estudos de IQ. / In this work we describe the experimental implementation of quantum information processing (QIP) in a two spin qubits system by nuclear quadrupole resonance (NQR). We implemented quantum gates and their applications in the creation and manipulation of pseudo-pure state (PPS). Furthermore, we propose one method of Quantum State Tomography (QST) based on coherence pathways selected by RF phase cycling. QST is one of the tools used to evaluate QIP implementations, it allows to completely evaluate the quantum state of the spin system. We experimentally implemented NQR-QIP in a KClO3 single crystal and observing 35Cl, a spin 3/2 nucleus. It was possible to obtain all the four PPS associated with the computational basis and to apply the Controlled-not (CNOT) and Hadamard gates on them. The reading of the resulting states was performed by the proposed QST method, and resulted in experimental quantum state fidelities greater than 90%. It was also possible to create squeezed spin states. This states are generated by non linear interactions, which naturally arise in a NQR system. These are very promising results and they indicate that NQR can be successfully applied as an experimental tool for studying fundamental QIP theory.

This project is a comprehensive investigation into the application of the exchange interaction, particularly with the realization of the SWAP^1/n quantum operator, in quantum information processing. We study the generation, characterization and application of entanglement in such systems. Given the non-commutativity of neighbouring SWAP^1/n gates, the mathematical study of combinations of these gates is an interesting avenue of research that we have explored, though due to the exponential scaling of the complexity of the problem with the number of qubits in the system, numerical techniques, though good for few-qubit systems, are found to be inefficient for this research problem when we look at systems with higher number of qubits. Since the group of SWAP^1/n operators is found to be isomorphic to the symmetric group Sn, we employ group-theoretic methods to find the relevant invariant subspaces and associated vector-states. Some interesting patterns of states are found including onedimensional invariant subspaces spanned by W-states and the Hamming-weight preserving symmetry of the vectors spanning the various invariant subspaces. We also devise new ways of characterizing entanglement and approach the separability problem by looking at permutation symmetries of subsystems of quantum states. This idea is found to form a bridge with the entanglement characterization tool of Peres-Horodecki's Partial Positive Transpose (PPT), for mixed quantum states. We also look at quantum information taskoriented 'distance' measures of entanglement, besides devising a new entanglement witness in the 'engle'. In terms of applications, we define five different formalisms for quantum computing: the circuit-based model, the encoded qubit model, the cluster-state model, functional quantum computation and the qudit-based model. Later in the thesis, we explore the idea of quantum computing based on decoherence-free subspaces. We also investigate ways of applying the SWAP^1/n in entanglement swapping for quantum repeaters, quantum communication protocols and quantum memory.

Physical implementations of quantum computers will inevitably be subject to errors. However, provided that the error rate is below some threshold, it is theoretically possible to build fault tolerant quantum computers that are arbitrarily reliable. A particularly attractive fault tolerant proposal, due to its high threshold value, relies on Clifford group quantum computation and access to ancilla qubits. These ancilla qubits must be prepared in a particular state termed the 'magic' state. It is possible to distill faulty magic states into pure magic states, which is of significant interest for experimental work where perfect state preparation is generally not possible. This thesis describes a liquid state nuclear magnetic resonance based scheme for distilling magic states. Simulations are presented that indicate that such a distillation is feasible if a high level of experimental control is achieved. Preliminary experimental results are reported that outline the challenges that must be overcome to attain such precise control.

Quantum information processing has been the subject of countless discoveries since the early 1990's. It is believed to be the way of the future for computation: using quantum systems permits one to perform computation exponentially faster than on a regular classical computer. Unfortunately, quantum systems that not isolated do not behave well. They tend to lose their quantum nature due to the presence of the environment. If key information is known about the noise present in the system, methods such as quantum error correction have been developed in order to reduce the errors introduced by the environment during a given quantum computation. In order to harness the quantum world and implement the theoretical ideas of quantum information processing and quantum error correction, it is imperative to understand and quantify the noise present in the quantum processor and benchmark the quality of the control over the qubits. Usual techniques to estimate the noise or the control are based on quantum process tomography (QPT), which, unfortunately, demands an exponential amount of resources. This thesis presents work towards the characterization of noisy processes in an efficient manner. The protocols are developed from a purely abstract setting with no system-dependent variables. To circumvent the exponential nature of quantum process tomography, three different efficient protocols are proposed and experimentally verified. The first protocol uses the idea of quantum error correction to extract relevant parameters about a given noise model, namely the correlation between the dephasing of two qubits. Following that is a protocol using randomization and symmetrization to extract the probability that a given number of qubits are simultaneously corrupted in a quantum memory, regardless of the specifics of the error and which qubits are affected. Finally, a last protocol, still using randomization ideas, is developed to estimate the average fidelity per computational gates for single and multi qubit systems. Even though liquid state NMR is argued to be unsuitable for scalable quantum information processing, it remains the best test-bed system to experimentally implement, verify and develop protocols aimed at increasing the control over general quantum information processors. For this reason, all the protocols described in this thesis have been implemented in liquid state NMR, which then led to further development of control and analysis techniques.

Physical implementations of quantum computers will inevitably be subject to errors. However, provided that the error rate is below some threshold, it is theoretically possible to build fault tolerant quantum computers that are arbitrarily reliable. A particularly attractive fault tolerant proposal, due to its high threshold value, relies on Clifford group quantum computation and access to ancilla qubits. These ancilla qubits must be prepared in a particular state termed the 'magic' state. It is possible to distill faulty magic states into pure magic states, which is of significant interest for experimental work where perfect state preparation is generally not possible. This thesis describes a liquid state nuclear magnetic resonance based scheme for distilling magic states. Simulations are presented that indicate that such a distillation is feasible if a high level of experimental control is achieved. Preliminary experimental results are reported that outline the challenges that must be overcome to attain such precise control.

Quantum information processing has been the subject of countless discoveries since the early 1990's. It is believed to be the way of the future for computation: using quantum systems permits one to perform computation exponentially faster than on a regular classical computer. Unfortunately, quantum systems that not isolated do not behave well. They tend to lose their quantum nature due to the presence of the environment. If key information is known about the noise present in the system, methods such as quantum error correction have been developed in order to reduce the errors introduced by the environment during a given quantum computation. In order to harness the quantum world and implement the theoretical ideas of quantum information processing and quantum error correction, it is imperative to understand and quantify the noise present in the quantum processor and benchmark the quality of the control over the qubits. Usual techniques to estimate the noise or the control are based on quantum process tomography (QPT), which, unfortunately, demands an exponential amount of resources. This thesis presents work towards the characterization of noisy processes in an efficient manner. The protocols are developed from a purely abstract setting with no system-dependent variables. To circumvent the exponential nature of quantum process tomography, three different efficient protocols are proposed and experimentally verified. The first protocol uses the idea of quantum error correction to extract relevant parameters about a given noise model, namely the correlation between the dephasing of two qubits. Following that is a protocol using randomization and symmetrization to extract the probability that a given number of qubits are simultaneously corrupted in a quantum memory, regardless of the specifics of the error and which qubits are affected. Finally, a last protocol, still using randomization ideas, is developed to estimate the average fidelity per computational gates for single and multi qubit systems. Even though liquid state NMR is argued to be unsuitable for scalable quantum information processing, it remains the best test-bed system to experimentally implement, verify and develop protocols aimed at increasing the control over general quantum information processors. For this reason, all the protocols described in this thesis have been implemented in liquid state NMR, which then led to further development of control and analysis techniques.

The ability to resolve molecules individually has many potential applications. These include understanding the local environments of single molecules including details of their interactions with surroundings. The ability to individually address and manipulate the spin states is also required for spin based quantum information processing. Although optical detection techniques, such as optically detected electron spin resonance (ESR) seem very powerful in these contexts, multiple molecules in the focal volume of a diffraction limited confocal microscope spot cannot in general be resolved individually. Here we propose to solve this problem using optically detected ESR imaging based on the use of high field gradients. In the present research, subwavelength single molecule imaging is demonstrated by using the optically detected ESR technique and the optically detected electron spin echo envelope modulation (ESEEM) technique. Ultra fast Rabi nutation experiments are also performed to demonstrate the feasibility of fast spin manipulations at a low microwave power. Micrometer sized gradient coils, together with micrometer sized co-planar microstrip transmission lines, are designed and fabricated by optical lithography in order to produce the necessary high magnetic field gradients. These fabricated devices are used to demonstrate this subwavelength imaging technique by imaging single electron spins of the nitrogen-vacancy (NV) defect in diamond. In this demonstration, multiple NV defects, unresolved in a single focal volume of a diffraction limited microscope are successfully resolved by the optically detected ESR techniques. Specifically, two neighboring NV defects separated by about 170nm are resolved. Ultra Fast electron spin nutation with an oscillation period of 1.33ns is also achieved by the high microwave magnetic field induced by the current flowing through the fabricated co-planar microstrip lines. These optically detected ESR and ESEEM techniques combined with the micrometer sized gradient coil may find many applications, including single molecule imaging and quantum information processing.

Photonic quantum information processing has emerged as a powerful platform for realising quantum-enhanced technologies. In order to be scalable, many of these technologies depend on the availability of a suitable quantum memory for the coherent storage and on-demand retrieval of photonic quantum states. In this thesis, I investigate broadband light storage in a room-temperature Raman memory, implemented both in free space and, for the first time, inside a low-finesse optical cavity designed for low-noise operation. The ability of the Raman memory to preserve phase coherence was tested by storing coherent polarisation states in two spatially separate atomic ensembles. Polarisation storage with a fidelity of up to 97 ± 1% was demonstrated by performing full process tomography on the system. The Raman memory was then interfaced for the first time with a spontaneous parametric downconversion (SPDC) source of heralded, GHz-bandwidth single photons. The memory performance was characterised by measuring the second-order autocorrelation of the retrieved fields. While the SPDC input photon statistics showed a clear influence on the statistics of the retrieved field, four-wave mixing (FWM) noise, stimulated by spontaneous Raman scattering, prevented the preservation of non-classical photon statistics during read-out. Suppressing this source of noise represents the last remaining challenge for realising a broadband single-photon Raman memory suitable for quantum information applications. To this end, I demonstrate a novel cavity implementation of the Raman memory which reduces the FWM contribution relative to the signal field by re-distributing the density of states into which the noise photons can be scattered. Cavity-enhanced memory operation was investigated using weak coherent input states, showing a significant improvement of the signal-to-noise ratio compared to the free-space memory implementation. This proof-of-principle demonstration suggests that cavity Raman memories may offer a practical route towards low-noise, high-bandwidth quantum storage at room temperature.