School of Physics - Theses
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ItemMatrix product states in quantum information processing( 2015)We employ the newly developed Matrix Product State (MPS) formalism to simulate two problems in the context of quantum information processing. One is the Boson sampling problem, the other is the ground state energy density of an n-qubit Hamiltonian. We find that the MPS representation of the Boson sampling problem is inefficient due to large entan- glement as the number of photons increases. In the context of adiabatic quantum computing (AQC), MPS is used to find the first four moments of an n-qubit Hamiltonian to approximate the ground state energy density of the Hamiltonian. We show an advantage of using the first-four-moment method over the conventional adiabatic procedure. Future work around AQC using MPS is discussed.
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ItemRealistic read-out and control for Si:P based quantum computers( 2008)This thesis identifies problems with the current operation proposals for Si:P based solid-state quantum computing architectures and outlines realistic alternatives as an effective fix. The focus is qubit read-out and robust two-qubit control of the exchange interaction in the presence of both systematic and environmental errors. We develop a theoretical model of the doubly occupied D- read-out state found in Si:P based nuclear spin architectures. We test our theory by using it to determine the binding energy of the D- state, comparing to known results. Our model can be used in detailed calculations of the adiabatic read-out protocol proposed for these devices. Regarding this protocol, preliminary calculations suggest the small binding energy of the doubly occupied read-out state will result in a state dwell-time less than that required for measurement using a single electron transistor (SET). We propose and analyse an alternative approach to single-spin read-out using optically induced spin to charge transduction, showing that the top gate biases required for qubit selection are significantly less than those demanded by the adiabatic scheme, thereby increasing the D+D- lifetime. Implications for singlet-triplet discrimination for electron spin qubits are also discussed.
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ItemControllable few state quantum systems for information processing( 2006-10)This thesis investigates several different aspects of the physics of few state quantum systems and their use in information processing applications. The main focus is performing high precision computations or experiments using imperfect quantum systems. Specifically looking at methods to calibrate a quantum system once it has been manufactured or performing useful tasks, using a quantum system with only limited spatial or temporal coherence. A novel method for characterising an unknown two-state Hamiltonian is presented which is based on the measurement of coherent oscillations. The method is subsequently extended to include the effects of decoherence and enable the estimation of uncertainties. Using the uncertainty estimates, the achievable precision for a given number of measurements is computed. This method is tested experimentally using the nitrogen-vacancy defect in diamond as an example of a two-state quantum system of interest for quantum information processing. The method of characterisation is extended to higher dimensional systems and this is illustrated using the Heisenberg interaction between spins as an example. The use of buried donors in silicon is investigated as an architecture for realising quantum-dot cellular automata as an example of quantum systems used for classical information processing. The interaction strengths and time scales are calculated and both coherent and incoherent evolution are assessed as possible switching mechanisms. The effects of decoherence on the operation of a single cell and the scaling behaviour of a line of cells is investigated. The use of type-II quantum computers for simulating classical systems is studied as an application of small scale quantum computing. An algorithm is developed for simulating the classical Ising model using Metropolis Monte-Carlo where random number generation is incorporated using quantum superposition. This suggests that several new algorithms could be developed for a type-II quantum computer based on probabilistic cellular automata.
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ItemTowards large-scale quantum computation( 2005-05)This thesis deals with a series of quantum computer implementation issues from the Kane 31P in 28Si architecture to Shor’s integer factoring algorithm and beyond. The discussion begins with simulations of the adiabatic Kane CNOT and readout gates, followed by linear nearest neighbor implementations of 5-qubit quantum error correction with and without fast measurement. A linear nearest neighbor circuit implementing Shor’s algorithm is presented, then modified to remove the need for exponentially small rotation gates. Finally, a method of constructing optimal approximations of arbitrary single-qubit fault-tolerant gates is described and applied to the specific case of the remaining rotation gates required by Shor’s algorithm.
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ItemTopological quantum error correction and quantum algorithm simulations( 2011)Quantum computers are machines that manipulate quantum information stored in the form of qubits, the quantum analogue to the classical bit. Unlike the bit, quantum mechanics allows a qubit to be in a linear superposition of both its basis states. Given the same number of bits and qubits, the latter stores exponentially more information. Quantum algorithms exploit these superposition states, allowing quantum computers to solve problems such as prime number factorisation and searches faster than classical computers. Realising a large-scale quantum computer is difficult because quantum information is highly susceptible to noise. Error correction may be employed to suppress the noise, so that the results of large quantum algorithms are valid. The overhead incurred from introducing error correction is neutralised if all elementary quantum operations are constructed with an error rate below some threshold error rate. Below threshold, arbitrary length quantum computation is possible. We investigate two topological quantum error correcting codes, the planar code and the 2D colour code. We find the threshold for the 2D colour code to be 0.1%, and improve the planar code threshold from 0.75% to 1.1%. Existing protocols for the transmission of quantum states are hindered by maximum communication distances and low communication rates. We adapt the planar code for use in quantum communication, and show that this allows the fault-tolerant transmission of quantum information over arbitrary distances at a rate limited only by local quantum gate speed. Error correction is an expensive investment and thus one seeks to employ as little as possible without compromising the integrity of the results. It is therefore important to study the robustness of algorithms to noise. We show that using the matrix product state representation allows one to simulate far larger instances of the quantum factoring algorithm than under the traditional amplitude formalism representation. We simulate systems with as many as 42 qubits on a single processor with 32GB RAM, comparable to amplitude formalism simulations performed on far larger computers.