Quantum computing has the potential to transform information technology by offering algorithms for certain tasks, such as quantum simulation, that are vastly more efficient than what is possible with any classical device. But experimentally implementing practical quantum information processing is a very difficult task. Here we study two important, and closely related, aspects of this challenge: architectures for quantum computing, and quantum error correction Exquisite quantum control has now been achieved in small ion traps, in nitrogen-vacancy centres and in superconducting qubit clusters, but the challenge remains of how to scale these systems to build practical quantum devices. In Part I of this thesis we analyse one approach to building a scalable quantum computer by networking together many simple processor cells, thus avoiding the need to create a single complex structure. The difficulty is that realistic quantum links are very error prone. Here we describe a method by which even these error-prone cells can perform quantum error correction. Groups of cells generate and purify shared resource states, which then enable stabilization of topologically encoded data. Given a realistically noisy network (10% error rate) we find that our protocol can succeed provided that all intra-cell error rates are below 0.8%. Furthermore, we show that with some adjustments, the protocols we employ can be made robust also against high levels of loss in the network interconnects. We go on to analyse the potential running speed of such a device. Using levels of fidelity that are either already achievable in experimental systems, or will be in the near-future, we find that employing a surface code approach in a highly noisy and lossy network architecture can result in kilohertz computer clock speeds. In Part II we consider the question of quantum error correction beyond the surface code. We consider several families of topological codes, and determine the minimum requirements to demonstrate proof-of-principle error suppression in each type of code. A particularly promising code is the gauge color code, which admits a universal transversal gate set. Furthermore, a recent result of Bombin shows the gauge color code supports an error-correction protocol that achieves tolerance to noisy measurements without the need for repeated measurements, so called single-shot error correction. Here, we demonstrate the promise of single-shot error correction by designing a decoder and investigating its performance. We simulate fault-tolerant error correction with the gauge color code, and estimate a sustainable error rate, i.e. the threshold for the long time limit, of ~0.31% for a phenomenological noise model using a simple decoding algorithm.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:684335 |
| Date | January 2015 |
| Creators | Nickerson, Naomi |
| Contributors | Benjamin, Simon |
| Publisher | Imperial College London |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://hdl.handle.net/10044/1/31475 |
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