Quantum information processing is a multi-disciplinary science involving physics, mathematics, computer science, and even quantum chemistry. It is centred around the idea of manipulating physical systems at the quantum level, either for simulation of physical systems, or numerical computation. Although it has been known for almost a decade that a quantum computer would enable the solution of problems deemed infeasible classically, constructing one has been beyond today's capabilities. In this work we explore one proposed implementation of a quantum computer: Nuclear Magnetic Resonance (NMR) spectroscopy. We also develop a numerical software tool, a pulse sequence compiler, for use in the implementation of quantum computer programs on an NMR quantum computer. Our pulse sequence compiler takes as input the specifications of the molecule used as a quantum register, the desired quantum gate, and experimental data on the actual effects of RF pulses on a sample of the molecule, and outputs an optimum set of pre and post 'virtual' gates that minimize the error induced.

Quantum information processing is a multi-disciplinary science involving physics, mathematics, computer science, and even quantum chemistry. It is centred around the idea of manipulating physical systems at the quantum level, either for simulation of physical systems, or numerical computation. Although it has been known for almost a decade that a quantum computer would enable the solution of problems deemed infeasible classically, constructing one has been beyond today's capabilities. In this work we explore one proposed implementation of a quantum computer: Nuclear Magnetic Resonance (NMR) spectroscopy. We also develop a numerical software tool, a pulse sequence compiler, for use in the implementation of quantum computer programs on an NMR quantum computer. Our pulse sequence compiler takes as input the specifications of the molecule used as a quantum register, the desired quantum gate, and experimental data on the actual effects of RF pulses on a sample of the molecule, and outputs an optimum set of pre and post 'virtual' gates that minimize the error induced.

The main topic of this thesis is linear optics and the implementation of quantum operations (measurements, quantum channels, and unitary rotations) on optical systems. In the opening chapter the basic notions needed to understand the rest of the thesis will be explained. These notions include defining a quantum state, measurement, quantum channel and the linear optics tool set. The work in this thesis takes both fundamental and practical approaches to studying linear optical networks. For instance in the first chapter a proof is provided that shows that any unitary on a single mode Fock state can be realised with linear optics. The proof is constructive, however the approach to realising the unitary is not suitable for experimental implementation because it requires complicated ancilla states. As in the KLM proposal the procedure works only stochastically however by allowing the size of the ancilla to grow the probability of failure can be made arbitrarly small. Furthermore we investigate the realisation of arbitrary channels in a specific encoding that we call a $d$-rail encoding. The only ancilla state that we allow is a vacuum ancilliary state and further restrictions were considered (e.g. photon counting). A proof is provided that using these resources only random unitaries can be applied deterministically using linear optics. An expression for the optimal probability of success for realising more general channels with these resources is also discussed. As a final topic we also investigate the realisation of a quantum non-demolition measurement onto the dual rail qubit space. The investigation is a blend of both fundamental and practical approaches. To begin we employ a modified KLM-like procedure and show that the scheme can be realised perfectly but stochastically. The probability that the proper measurement is made can be made arbitrarly close to one using a suitably large ancilla state. In addition we consider an existing scheme \cite{gisin10a} which uses practical sources (two single photon sources) to perform the measurement. The scheme does not realise the true measurement but instead has a free parameter in it which is the transmittiviy of a beamsplitter. The measurement will project onto a space that has a vacuum component. By adjusting the transmittivity of this beamsplitter the vacuum component can be made arbitrarly small but only at the expense of the probability of success of the procedure. In this thesis a modification that can be made to eliminate the vacuum component without changing the sources is introduced. The modification is surprisingly simple and only involves the addition of a single beamsplitter. In the proposal for the original amplifier it was used in simulations for DIQKD that included device imperfections. To show the improvement of our modification these DIQKD simulations are reproduced using the modified amplifier and its results are compared to the results of the original amplifier.

This thesis describes the back action of microwave-photon detection via a Josephson photomultiplier (JPM), a superconducting qubit coupled strongly to a high-quality mi- crowave cavity, and the applications of these devices. The back action operator depends qualitatively on the duration of the measurement interval, resembling the regular photon annihilation operator at short interaction times and approaching a variant of the photon subtraction operator at long times. The optimal operating conditions of the JPM differ from those considered optimal for processing and storing of quantum information, in that a short T2 of the JPM suppresses the cavity dephasing incurred during measurement. Un- derstanding this back action opens the possibility to perform multiple JPM measurements on the same state, hence performing efficient state tomography. In addition, this the- sis describes the creation of non-classical states of microwave radiation via single photon detection using JPMs. When operated in the low T2 regime, the back action of a JPM resembles the photon subtraction operator. Using the non-linearity of this back action, it is possible to create non-classical states of microwave radiation, including squeezed vacuum and odd Schro ̈dinger cat states, starting from a coherent state.

Quantum computing offers the potential for efficiently solving otherwise classically difficult problems, with applications in material and drug design, cryptography, theoretical physics, number theory and more. However, quantum systems are notoriously fragile; interaction with the surrounding environment and lack of precise control constitute noise, which makes construction of a reliable quantum computer extremely challenging. Threshold theorems show that by adding enough redundancy, reliable and arbitrarily long quantum computation is possible so long as the amount of noise is relatively low---below a ``threshold'' value. The amount of redundancy required is reasonable in the asymptotic sense, but in absolute terms the resource overhead of existing protocols is enormous when compared to current experimental capabilities. In this thesis we examine a variety of techniques for reducing the resources required for fault-tolerant quantum computation. First, we show how to simplify universal encoded computation by using only transversal gates and standard error correction procedures, circumventing existing no-go theorems. The cost of certain error correction procedures is dominated by preparation of special ancillary states. We show how to simplify ancilla preparation, reducing the cost of error correction by more than a factor of four. Using this optimized ancilla preparation, we then develop improved techniques for proving rigorous lower bounds on the noise threshold. The techniques are specifically intended for analysis of relatively large codes such as the 23-qubit Golay code, for which we compute a lower bound on the threshold error rate of 0.132 percent per gate for depolarizing noise. This bound is the best known for any scheme. Additional overhead can be incurred because quantum algorithms must be translated into sequences of gates that are actually available in the quantum computer. In particular, arbitrary single-qubit rotations must be decomposed into a discrete set of fault-tolerant gates. We find that by using a special class of non-deterministic circuits, the cost of decomposition can be reduced by as much as a factor of four over state-of-the-art techniques, which typically use deterministic circuits. Finally, we examine global optimization of fault-tolerant quantum circuits. Physical connectivity constraints require that qubits are moved close together before they can interact, but such movement can cause data to lay idle, wasting time and space. We adapt techniques from VLSI in order to minimize time and space usage for computations in the surface code, and we develop a software prototype to demonstrate the potential savings.

The main topic of this thesis is linear optics and the implementation of quantum operations (measurements, quantum channels, and unitary rotations) on optical systems. In the opening chapter the basic notions needed to understand the rest of the thesis will be explained. These notions include defining a quantum state, measurement, quantum channel and the linear optics tool set. The work in this thesis takes both fundamental and practical approaches to studying linear optical networks. For instance in the first chapter a proof is provided that shows that any unitary on a single mode Fock state can be realised with linear optics. The proof is constructive, however the approach to realising the unitary is not suitable for experimental implementation because it requires complicated ancilla states. As in the KLM proposal the procedure works only stochastically however by allowing the size of the ancilla to grow the probability of failure can be made arbitrarly small. Furthermore we investigate the realisation of arbitrary channels in a specific encoding that we call a $d$-rail encoding. The only ancilla state that we allow is a vacuum ancilliary state and further restrictions were considered (e.g. photon counting). A proof is provided that using these resources only random unitaries can be applied deterministically using linear optics. An expression for the optimal probability of success for realising more general channels with these resources is also discussed. As a final topic we also investigate the realisation of a quantum non-demolition measurement onto the dual rail qubit space. The investigation is a blend of both fundamental and practical approaches. To begin we employ a modified KLM-like procedure and show that the scheme can be realised perfectly but stochastically. The probability that the proper measurement is made can be made arbitrarly close to one using a suitably large ancilla state. In addition we consider an existing scheme \cite{gisin10a} which uses practical sources (two single photon sources) to perform the measurement. The scheme does not realise the true measurement but instead has a free parameter in it which is the transmittiviy of a beamsplitter. The measurement will project onto a space that has a vacuum component. By adjusting the transmittivity of this beamsplitter the vacuum component can be made arbitrarly small but only at the expense of the probability of success of the procedure. In this thesis a modification that can be made to eliminate the vacuum component without changing the sources is introduced. The modification is surprisingly simple and only involves the addition of a single beamsplitter. In the proposal for the original amplifier it was used in simulations for DIQKD that included device imperfections. To show the improvement of our modification these DIQKD simulations are reproduced using the modified amplifier and its results are compared to the results of the original amplifier.

This thesis describes the back action of microwave-photon detection via a Josephson photomultiplier (JPM), a superconducting qubit coupled strongly to a high-quality mi- crowave cavity, and the applications of these devices. The back action operator depends qualitatively on the duration of the measurement interval, resembling the regular photon annihilation operator at short interaction times and approaching a variant of the photon subtraction operator at long times. The optimal operating conditions of the JPM differ from those considered optimal for processing and storing of quantum information, in that a short T2 of the JPM suppresses the cavity dephasing incurred during measurement. Un- derstanding this back action opens the possibility to perform multiple JPM measurements on the same state, hence performing efficient state tomography. In addition, this the- sis describes the creation of non-classical states of microwave radiation via single photon detection using JPMs. When operated in the low T2 regime, the back action of a JPM resembles the photon subtraction operator. Using the non-linearity of this back action, it is possible to create non-classical states of microwave radiation, including squeezed vacuum and odd Schro ̈dinger cat states, starting from a coherent state.

Quantum computers offer great potential for significant speedup in executing certain algorithms compared to their classical counterparts. One of the most promising physical systems in which implementing such a device seems viable are trapped atomic ions. All of the fundamental operations needed for quantum information processing have already been experimentally demonstrated in trapped ion systems. Today, the remaining two obstacles are to improve the fidelities of these operations up to the point where quantum error correction techniques can be successfully applied, as well as to scale up the present systems to a higher number of quantum bits (qubits). This thesis addresses both issues. On the one hand, it decribes the experimental implementation of a high-fidelity two-qubit quantum logic gate, which is the most technically demanding fundamental operation to realise in practice. On the other hand, the presented work is carried out in a microfabricated surface ion trap - an architecture that holds the promise of scalability. The gate is applied directly to hyperfine "atomic clock" qubits in ⁴³Ca⁺ ions using the near-field microwave magnetic field gradient produced by an integrated trap electrode. To protect the gate against fluctuating energy shifts of the qubit states, as well as to avoid the need to null the microwave field at the position of the ions, a dynamically decoupled Mølmer-Sørensen scheme is employed. After accounting for state preparation and measurement errors, the achieved gate fidelity is 99.7(1)%. In previous work, the same apparatus has been used to demonstrate coherence times of T^*₂ ≈ 50 s and all single-qubit operations with fidelity > 99.95%. To gain access to the "atomic clock" qubit transition in ⁴³Ca⁺, a static magnetic field of 146G is applied. The resulting energy level Zeeman-structure is spread over many times the linewidth of the atomic transition used for Doppler cooling. This thesis presents a simple and robust method for Doppler cooling and obtaining high fluorescence from this qubit in spite of the complicated level structure. A temperature of 0.3mK, slightly below the Doppler limit, is reached.

The goal of this work is to understand the application of the evolutionary programming approach to the problem of quantum circuit design. This problem is motivated by the following observations: <ul> <li>In order to keep up with the seemingly insatiable demand for computing power our computing devices will continue to shrink, all the way down to the atomic scale, at which point they become quantum mechanical systems. In fact, this event, known as Moore?s Horizon, is likely to occur in less than 25 years. </li> <li> The recent discovery of several quantum algorithms which can solve some interesting problems more efficiently than any known classical algorithm. </li> <li> While we are not yet certain that quantum computers will ever be practical to build, there do now exist the first few astonishing experimental devices capable of briefly manipulating small quantities of quantum information. The programming of these devices is already a nontrivial problem, and as these devices and their algorithms become more complicated this problem will quickly become a significant challenge. </li> </ul> The Evolutionary Programming (EP) approach to problem solving seeks to mimic the processes of evolutionary biology which have resulted in the awesome complexity of living systems, almost all of which are well beyond our current analysis and engineering capabilities. This approach is motivated by the highly successful application of Koza?s Genetic Programming (GP) approach to a variety of circuit design problems, and specifically the preliminary reports byWilliams and Gray and also Rubinstein who applied GP to quantum circuit design. Accompanying this work is software for evolutionary quantum circuit design which incorporates several advances over previous approaches, including: <ul> <li>A formal language for describing parallel quantum circuits out of an arbitary elementary gate set, including gates with one or more parameters. </li> <li> A fitness assessment procedure that measures both average case fidelity with a respect for global phase equivalences, and implementation cost. </li> <li> A Memetic Programming (MP) based reproductive strategy that uses a combination of global genetic and local memetic searches to effectively search through diverse circuit topologies and optimize the parameterized gates they contain. </li> </ul> Several benchmark experiments are performed on small problems which support the conclusion that Evolutionary Programming is a viable approach to quantum circuit design and that further experiments utilizing more computational resources and more problem insight can be expected to yield many new and interesting quantum circuits.

We explore quantum-resistant key establishment and hybrid encryption. We nd that while the discrete logarithm problem is e ciently solved by a quantum computer using Shor's algorithm, some instances are insecure even using classical computers. The discrete logarithm problem based on a symmetric group Sn is e - ciently solved in polynomial time. We design a PUF-based 4-round group key establishment protocol, adjusting the model to include a physical channel capable of PUF transmission, and modify adversarial capabilities with respect to the PUFs. The result is a novel group key establishment protocol which avoids computational hardness assumptions and achieves key secrecy. We contribute a hybrid encryption scheme by combining a key encapsulation mechanism (KEM) with a symmetric key encryption scheme by using two hash functions. We require only one-way security in the quantum random oracle model (QROM) of the KEM and one-time security of the symmetric encryption scheme in the QROM. We show that this hybrid scheme is IND-CCA secure in the QROM. We rely on a powerful theorem by Unruh that provides an upper bound on indistinguishability between the output of a random oracle and a random string, when the oracle can be accessed in quantum superposition. Our result contributes to the available IND-CCA secure encryption schemes in a setting where quantum computers are under adversarial control. Finally, we develop a framework and describe biometric visual cryptographic schemes generically under our framework. We formalize several security notions and de nitions including sheet indistinguishability, perfect indistinguishability, index recovery, perfect index privacy, and perfect resistance against false authentication. We also propose new and generic strategies for attacking e-BVC schemes such as new distinguishing attack, new index recovery, and new authentication attack. Our quantitative analysis veri es the practical impact of our framework and o ers concrete upper bounds on the security of e-BVC. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2018. / FAU Electronic Theses and Dissertations Collection