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Conference on Lasers and Electro-Optics

Parallelizing gates with high-dimensional ancillas

Katherine L. Brown, Suvabrata De, Viv M. Kendon

Published Jan 1, 2012• 0 citations
Publisher

Abstract

A qubus quantum computer can perform a quantum Fourier transform with a linear number of operations. This implies continuous-variable ancilla-driven quantum computation is equivalent to the quantum circuit model plus unbounded fan-out.
DOI
10.1364/qels.2012.qtu2e.4

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Using the qubus for quantum computing

Katherine Louise Brown

In this thesis I explore using the qubus for quantum computing. The qubus is an architecture of quantum computing, where a continuous variable ancilla is used to generate operations between matter qubits. I concentrate on using the qubus for two purposes - quantum simulation, and generating cluster states. Quantum simulation is the idea of using a quantum computer to simulate a quantum system. I focus on conducting a simulation of the BCS Hamiltonian. I demonstrate how to perform the necessary two qubit operations in a controlled fashion using the qubus. In particular I demonstrate an O(N3) saving over an implementation on an NMR computer, and a factor of 2 saving over a naıve technique. I also discuss how to perform the quantum Fourier transform on the qubus quantum computer. I show that it is possible to perform the quantum Fourier transform using just, 24⌊N/2⌋ + 7N − 6, this is an O(N) saving over a naıve method. In the second part of the thesis, I move on, and consider generating cluster states using the qubus. A cluster state, is a universal resource for one-way or measurement-based computation. In one-way computation, the pre-generated, entangled resource is used to perform calculations, which only require local corrections and measurement. I demonstrate that the qubus can generate cluster states deterministically, and in a relatively short time. I discuss several techniques of cluster state generation, one of which is optimal, given the physical architecture we are using. This can generate an n × m cluster in only 3nm − 2n − 2m + 4 operations. The alternative techniques look at generating a cluster using layers or columns, allowing it to be built dynamically, while the cluster is used to perform calculations. I then move on, and discuss problems with error accumulation in the generation process.

•Apr 1, 2011•7 citations
Models of universal quantum computation where the required interactions between computational qubits are mediated by some ancillary system are highly relevant to experimental realisations of a quantum computer. We introduce two such models of quantum computation, the first of which employs a d-level (qudit) ancilla and the second of which is based on the coherent states of n spins. The computation is implemented with geometric phase gates, created via controlled displacement operators defined on a discrete lattice phase space, in the case of a qudit ancilla, and a Bloch sphere, in the case of a spin coherent state ancilla. Both of these models are shown to be different possible generalisations to finite dimensions of the field-mode quantum bus (qubus) computer. We then consider the computational complexity of the qubus architecture and show that although in certain circumstances the model can be used to reduce the number of operations required to implement quantum circuits, contrary to previous claims [New J. Phys. 13, 095007, 2011] this is not the case for the quantum Fourier transform (QFT). Furthermore, using the generalisation of the qubus model to a qudit bus, we show that this reduction in the circuit complexity depends on the dimensionality of the bus.
In this thesis I explore using the qubus for quantum computing. The qubus is an architecture of quantum computing, where a continuous variable ancilla is used to generate operations between matter qubits. I concentrate on using the qubus for two purposes - quantum simulation, and generating cluster states. Quantum simulation is the idea of using a quantum computer to simulate a quantum system. I focus on conducting a simulation of the BCS Hamiltonian. I demonstrate how to perform the necessary two qubit operations in a controlled fashion using the qubus. In particular I demonstrate an O(N3) saving over an implementation on an NMR computer, and a factor of 2 saving over a naıve technique. I also discuss how to perform the quantum Fourier transform on the qubus quantum computer. I show that it is possible to perform the quantum Fourier transform using just, 24⌊N/2⌋ + 7N − 6, this is an O(N) saving over a naıve method. In the second part of the thesis, I move on, and consider generating cluster states using the qubus. A cluster state, is a universal resource for one-way or measurement-based computation. In one-way computation, the pre-generated, entangled resource is used to perform calculations, which only require local corrections and measurement. I demonstrate that the qubus can generate cluster states deterministically, and in a relatively short time. I discuss several techniques of cluster state generation, one of which is optimal, given the physical architecture we are using. This can generate an n × m cluster in only 3nm − 2n − 2m + 4 operations. The alternative techniques look at generating a cluster using layers or columns, allowing it to be built dynamically, while the cluster is used to perform calculations. I then move on, and discuss problems with error accumulation in the generation process.