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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ItemDonor activation and isotopic enrichment of silicon via ion implantation for quantum computing( 2020)Quantum computers are set to revolutionise technology by harnessing the immense promise of quantum mechanics, the law governing nature on the atomic scale, to enable a dramatically increased efficiency for certain algorithms over their classical counterparts. By storing and manipulating information on quantum bits (qubits), which can exist in a superposition of 0 and 1 at the same time and can be entangled with each other, instead of classical bits, which are strictly 0 or 1, certain problems that are intractable with classical computation can be solved. To realise a qubit, a quantum system that exists in two or more states, such as a spin in a magnetic field, is required. Group V donors in silicon (Si) are promising qubit candidates that can store quantum information in both the spin of the donor nucleus and the donor electron that it binds by the Coulomb potential. Si offers an ideal platform due to its isotopic composition of predominantly spin-zero nuclei (over 92% is 28Si with nuclear spin I=0), that can provide a noise-free host lattice, and the wealth of knowledge accumulated in the microelectronics industry. The most versatile method for introducing donors in Si is ion implantation, a foundational technique of the information technology industry that has already demonstrated the production of long-lived phosphorus (P) donor qubits. This method is explored in this thesis. The bismuth (Bi) donor offers some useful properties for quantum devices, such as an increased quantum memory, clock transitions and the potential to couple to superconducting flux qubits. To fabricate a quantum device that employs Bi, it is necessary to implant and activate a Bi donor in Si. Here, the optimum implantation and thermal annealing strategy is determined to maximise the operational yield of near-surface Bi donor qubits by repairing the Si crystal damage and electrically activating the donor, evidenced by the measurement of Bi donor electron spin resonance. A further critical issue in donor qubit fabrication is the depletion of the nuclear spin-1/2 29Si isotope to extend coherence times, which would be beneficial to be performed routinely. Accordingly, a method of isotopically enriching a surface layer of natural Si via sputtering during the high fluence implantation of 28Si- ions was developed. This technique increases the accessibility of producing spin-free 28Si material by requiring only a conventional ion implanter and naturally abundant sources. The successful recrystallisation of this 28Si layer and the demonstration of increased coherence times for implanted P donors make this a promising technique for integrating into the fabrication of implanted donor qubits. Finally, the measurement of the full extent of the 29Si depletion on the coherence time requires a low concentration of donors implanted into this ~100 nm thick surface layer of 28Si. Therefore,a high sensitivity technique capable of probing a small number of spins is essential. This challenge is addressed by the design and implementation of a low-temperature electrically detected magnetic resonance (EDMR) system, capable of measuring spin transitions of donor electrons in Si with a sensitivity at least 5 orders of magnitude greater than for conventional electron spin resonance systems. In future, this will allow for the coherence times of donors implanted into our enriched 28Si layers to be determined from the linewidth of EDMR signals. This thesis lays the foundations for exploiting Bi donor clock transitions in qubit devices and addresses the challenge of providing an isotopically enriched 28Si matrix for donor qubits that is shown to extend qubit coherence times and thus makes progress towards the scalable fabrication of a donor spin quantum computer.
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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.