acase@tulane.edu / In this dissertation we test our ability to implement linear entangling operations between small numbers of photons for application in quantum communication and computation. We begin by presenting a fast and highly parallelizable numerical algorithm for simulating linear optical circuits on classical hardware. Then, we apply this algorithm to three independent topics in quantum information: First, in Chapter 2, we determine the information capacity of an optical quantum channel and show that a linear encoding is generally sufficient to achieve this capacity. In Chapter 3 we introduce a computational encoding basis wherein qubits are stored in single-photon blocks and then test our ability to apply entangling operations between blocks. Finally, in Chapter 4, we use our algorithm to make progress in the long-standing problem of designing a near-perfect optical Bell state analyzer. We find a clear trend in state distinguishability as we incorporate unentangled pairs of ancilla photons. We also prove that if a measurement outcome in which all photons are bunched into only two output modes is possible, then perfect state discrimination is impossible. We then present a set of conditions that prevent this outcome. / 1 / Jake A Smith

The experiments described in this thesis form an investigation into the path towards establishing the requirements of quantum computing in a linear optical system. Our qubits are polarisation encoded photons for which the basic operations of quantum computing, single qubit rotations, are a well understood problem. The difficulty lies in the interaction of photons. To achieve these we use measurement induced non-linearities. The first experiment in this thesis describes the thorough characterisation of a controlled-sign gate based on such non-linearities. The photons are provided as pairs generated through parametric down-conversion, and as such share correlations unlikely to carry over into large scale implementations of the future. En route to such larger circuits, a characterisation of the actions of the controlled-sign gate is conducted, when the input qubits have been generated independently from each other, revealing a large drop in process fidelity. To explore the cause of this degradation of the gate performance a thorough and highly accurate model of the gate is derived including the realistic description of faulty circuitry, photon loss and multi-photon emission by the source. By simulating the effects of the various noise sources individually, the heretofore largely ignored multi-photon emission is identified as the prime cause of the degraded gate performance, causing a drop in fidelity nearly three times as large as any other error source. I further draw the first comparison between the performance of an experimental gate to the error probabilities per gate derived as thresholds for fault-tolerant quantum computing. In the absence of a single vigourous threshold value, I compare the gate performance to the models that yielded the highest threshold to date as an upper bound and to the threshold of the Gremlin-model, which allows for the most general errors. Unsurprisingly this comparison reveals that the implemented gate is clearly insufficient, however just remedying the multi-photon emission error will allow this architecture to move to within striking distance of the boundary for fault-tolerant quantum computing. The utilised methodology can be applied to any gate in any architecture and can, combined with a suitable model of the noise sources, become an important guide for developments required to achieve fault tolerant quantum computing. The final experiment on the path towards linear optical quantum computing is the demonstration of a pair of basic versions of Shor's algorithm which display the essential entanglement for the algorithm. The results again highlight the need for extensive measurements to reveal the fundamental quality of the implemented algorithm, which is not accessible with limited indicative measurements. In the second part of the thesis, I describe two experiments on other forms of entanglement by extending the actions of a Fock-State filter, a filter that is capable of attenuating single photon states stronger than multi-photon states, to produce entangled states. Furthermore this device can be used in conjunction with standard wave-plates to extend the range of operations possible on the bi-photonic qutrit space, showing that this setup suffices to produce any desired qutrit state, thereby giving access to new measurement capabilities and in the process creating and proving the first entanglement between a qubit and a qutrit.

The experiments described in this thesis form an investigation into the path towards establishing the requirements of quantum computing in a linear optical system. Our qubits are polarisation encoded photons for which the basic operations of quantum computing, single qubit rotations, are a well understood problem. The difficulty lies in the interaction of photons. To achieve these we use measurement induced non-linearities. The first experiment in this thesis describes the thorough characterisation of a controlled-sign gate based on such non-linearities. The photons are provided as pairs generated through parametric down-conversion, and as such share correlations unlikely to carry over into large scale implementations of the future. En route to such larger circuits, a characterisation of the actions of the controlled-sign gate is conducted, when the input qubits have been generated independently from each other, revealing a large drop in process fidelity. To explore the cause of this degradation of the gate performance a thorough and highly accurate model of the gate is derived including the realistic description of faulty circuitry, photon loss and multi-photon emission by the source. By simulating the effects of the various noise sources individually, the heretofore largely ignored multi-photon emission is identified as the prime cause of the degraded gate performance, causing a drop in fidelity nearly three times as large as any other error source. I further draw the first comparison between the performance of an experimental gate to the error probabilities per gate derived as thresholds for fault-tolerant quantum computing. In the absence of a single vigourous threshold value, I compare the gate performance to the models that yielded the highest threshold to date as an upper bound and to the threshold of the Gremlin-model, which allows for the most general errors. Unsurprisingly this comparison reveals that the implemented gate is clearly insufficient, however just remedying the multi-photon emission error will allow this architecture to move to within striking distance of the boundary for fault-tolerant quantum computing. The utilised methodology can be applied to any gate in any architecture and can, combined with a suitable model of the noise sources, become an important guide for developments required to achieve fault tolerant quantum computing. The final experiment on the path towards linear optical quantum computing is the demonstration of a pair of basic versions of Shor's algorithm which display the essential entanglement for the algorithm. The results again highlight the need for extensive measurements to reveal the fundamental quality of the implemented algorithm, which is not accessible with limited indicative measurements. In the second part of the thesis, I describe two experiments on other forms of entanglement by extending the actions of a Fock-State filter, a filter that is capable of attenuating single photon states stronger than multi-photon states, to produce entangled states. Furthermore this device can be used in conjunction with standard wave-plates to extend the range of operations possible on the bi-photonic qutrit space, showing that this setup suffices to produce any desired qutrit state, thereby giving access to new measurement capabilities and in the process creating and proving the first entanglement between a qubit and a qutrit.

The experiments described in this thesis form an investigation into the path towards establishing the requirements of quantum computing in a linear optical system. Our qubits are polarisation encoded photons for which the basic operations of quantum computing, single qubit rotations, are a well understood problem. The difficulty lies in the interaction of photons. To achieve these we use measurement induced non-linearities. The first experiment in this thesis describes the thorough characterisation of a controlled-sign gate based on such non-linearities. The photons are provided as pairs generated through parametric down-conversion, and as such share correlations unlikely to carry over into large scale implementations of the future. En route to such larger circuits, a characterisation of the actions of the controlled-sign gate is conducted, when the input qubits have been generated independently from each other, revealing a large drop in process fidelity. To explore the cause of this degradation of the gate performance a thorough and highly accurate model of the gate is derived including the realistic description of faulty circuitry, photon loss and multi-photon emission by the source. By simulating the effects of the various noise sources individually, the heretofore largely ignored multi-photon emission is identified as the prime cause of the degraded gate performance, causing a drop in fidelity nearly three times as large as any other error source. I further draw the first comparison between the performance of an experimental gate to the error probabilities per gate derived as thresholds for fault-tolerant quantum computing. In the absence of a single vigourous threshold value, I compare the gate performance to the models that yielded the highest threshold to date as an upper bound and to the threshold of the Gremlin-model, which allows for the most general errors. Unsurprisingly this comparison reveals that the implemented gate is clearly insufficient, however just remedying the multi-photon emission error will allow this architecture to move to within striking distance of the boundary for fault-tolerant quantum computing. The utilised methodology can be applied to any gate in any architecture and can, combined with a suitable model of the noise sources, become an important guide for developments required to achieve fault tolerant quantum computing. The final experiment on the path towards linear optical quantum computing is the demonstration of a pair of basic versions of Shor's algorithm which display the essential entanglement for the algorithm. The results again highlight the need for extensive measurements to reveal the fundamental quality of the implemented algorithm, which is not accessible with limited indicative measurements. In the second part of the thesis, I describe two experiments on other forms of entanglement by extending the actions of a Fock-State filter, a filter that is capable of attenuating single photon states stronger than multi-photon states, to produce entangled states. Furthermore this device can be used in conjunction with standard wave-plates to extend the range of operations possible on the bi-photonic qutrit space, showing that this setup suffices to produce any desired qutrit state, thereby giving access to new measurement capabilities and in the process creating and proving the first entanglement between a qubit and a qutrit.

One of the current hot topics in physics is quantum information, which, broadly speaking, is concerned with exploring the information-processing and storing tasks that can be performed in quantum mechanical systems. Besides driving forward our experimental control and understanding of quantum systems, the field is also in the early stages of developing revolutionary new technology of far reaching implication. As part of these endeavors, this thesis presents some results in experimental quantum information. Specifically, we develop several new tools for performing quantum information processing in optical quantum systems, and use them to explore a number of applications and novel physical phenomena. A central theme, and one of the most sought after applications of quantum information, is the pursuit of a programmable quantum computer. This thesis is divided into 3 parts. In Part I we develop some new optical quantum logic gates, which are tools for manipulating quantum information and the fundamental building blocks of a quantum computer. We also develop a new technique for simplifying the construction of quantum logic circuits, by exploiting multi-level quantum systems, that has the potential for application in any physical encoding of quantum information. In Part II we use these tools to perform some of the first demonstrations of quantum algorithms. Each of these could, in principle, efficiently solve an important problem that is thought to be fundamentally intractable using conventional `classical' techniques. Firstly we implement a simplified version of the quantum algorithm for factoring numbers, and demonstrate the core processes, coherent control, and resultant entangled states required for a full-scale implementation. Secondly we implement an algorithm for calculating the energy of many-body quantum systems. Specifically, we calculate the energy spectrum of the Hydrogen molecule, in a minimal basis. Finally we demonstrate an algorithm for a novel model of quantum computing that uses mixed states. Here we perform the first characterisation of intrinsically non-classical correlations between fully separable quantum systems, captured by the 'discord'---a measure of quantum correlations in mixed states that goes beyond entanglement. Part III presents a technique that extends experimental control over biphotons---the novel quantum information carriers formed by the polarisation of two photons in the same spatial and temporal mode. We also generate and explore new forms of entanglement: producing the first instance of qubit-qutrit entanglement, by entangling the polarisation of a photon and a biphoton, and developing a technique that enables full control over the level of `W-class' of multi-partite entanglement between the polarisation of three photons.

M.Sc. / In this thesis we study the techniques used to calculate the Hamilton operators related to linear optical quantum computing. We also discuss the basic building blocks of linear optical quantum computing (LOQC) by looking at the logic gates and the physical instruments of which they are made.

The development of integrated quantum photonics is integral to many areas of quantum information science, in particular linear optical quantum computing. In this context, a diversity of physical systems is being explored and thus versatility and adaptability are important prerequisites for any candidate platform. Silicon oxynitride is a promising material because its refractive index can be varied over a wide range. This dissertation describes the development of silicon oxynitride waveguides for applications in the field of integrated quantum photonics. The project consisted of three stages: design, characterisation, and application. First, the parameter space was studied through simulations. The structures were optimised to achieve low-loss devices with a small footprint at a wavelength of 900 nm. Buried channel waveguides with a cross-section of 1.6 ?m x 1.6 ?m and a core (cladding) refractive index of 1.545 (1.505) were chosen. Second, following their fabrication with plasma-enhanced chemical vapour deposition, electron beam lithography, and reactive ion etching, the waveguides were characterised. The refractive index was shown to be tunable from the silica to the silicon nitride regime. Optimised tapers significantly improved the coupling efficiency. The minimum bend radius was measured to be less than 2 mm. Propagation losses as low as 1.45 dB cm-1 were achieved. Directional couplers with coupling ratios ranging from 0 to 1 were realised. Third, building blocks for linear optical quantum computing were demonstrated. Reconfigurable quantum circuits consisting of Mach-Zehnder interferometers with near perfect visibilities were fabricated along with a four-port switch. The potential of quantum speedup was illustrated by carrying out the Deutsch-Jozsa algorithm with a fidelity of 100 % using on-demand single photons from a quantum dot. This dissertation presents the first implementation of tunable Mach-Zehnder interferometers, which act on single photons, based on silicon oxynitride waveguides. Furthermore, for the first time silicon oxynitride photonic quantum circuits were operated with on-demand single photons. Accordingly, this work has created a platform for the development of integrated quantum photonics.