Translating one-way quantum computation to the circuit model: methods and applications - Silva, Raphael Dias da (2013)
In this thesis I study the one-way quantum computation (1WQC) model and some applications of the different ways of translating 1WQC algorithms into the circuit model. In a series of recent results, different sets of conditions for implementing a computation deterministically in the one-way model have been proposed, each of them with their own properties. Some of those sets of conditions - generically known as flow conditions - try to explore the distinct parallel power of the 1WQC model, by increasing the number of operations that can be performed simultaneously. Here I contribute to this line of research by defining a new type of flow, which I call the signal-shifted flow (SSF), which has an interesting parallel structure that equals that of a depth-optimal flow.I also introduce a new framework for translating 1WQC algorithms into the circuit model. This translation preserves not only the computation performed but also some features of the 1WQC algorithm design. Within this framework I give two algorithms, each implementing a different translation procedure: the first gives compact (in space use) circuits for Regular Flow one-way computations, and the second does the same for SSF one-way computations. As an application of the SSF translation procedure, I combine it with other translation and optimization techniques to give an automated quantum circuit optimization procedure. This procedure is based on back-and-forth translation between the 1WQC and the circuit model, using 1WQC techniques to time-optimize computations in the circuit model. In the second part of this thesis, I use 1WQC tools to analyze quantum circuits interacting with closed timelike curves (CTCs). I do so by translating to the 1WQC model CTC-assisted circuits, and then showing that in some cases they can be shown to be equivalent to time-respecting circuits. The predictions obtained in those cases are exactly those of the quantum CTC model based on post-selected teleportation, proposed by Bennett, Schumacher and Svetlichny (BSS). This enabled us to show that the BSS model for quantum CTCs makes predictions which disagree with those of the highly influential CTC model proposed by David Deutsch.