Higgott, Oscar;
(2024)
Practical and Efficient Quantum
Error Correction.
Doctoral thesis (Ph.D), UCL (University College London).
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Abstract
Building a scalable quantum computer requires the use of quantum error correction, which protects components and quantum operations from noise and imperfections that would otherwise corrupt the computation. However, quantum error correcting codes add significant redundancy, with a large number of physical qubits used to encode each logical qubit. Furthermore, the control software used to operate a quantum error correcting code, called the decoder, must be fast enough to keep up with the hardware and accurate enough to identify which errors occurred with high probability. In Part I of this thesis, we focus on methods for decoding topological quantum codes including the surface code, which currently forms the basis of many experimental efforts to build a quantum computer. We also introduce optimal local unitary circuits for encoding unknown states in surface codes. We present sparse blossom, a decoder which can process data fast enough to keep up with superconducting quantum computers in a regime of practical interest. We also introduce belief-matching, a computationally efficient decoder which has improved accuracy, and schedule-induced gauge fixing, a technique for decoding subsystem surface codes more effectively by improving the circuits used for their implementation. In Part II we construct quantum error correcting codes derived from tilings of negatively curved surfaces. These constructions exploit properties of hyperbolic geometry to improve the encoding efficiency. By reducing the size of operators that must be measured, we find efficient parallelised quantum circuits implementing our constructions, which we show outperform the surface code for practical physical error rates.
| Type: | Thesis (Doctoral) |
|---|---|
| Qualification: | Ph.D |
| Title: | Practical and Efficient Quantum Error Correction |
| Open access status: | An open access version is available from UCL Discovery |
| Language: | English |
| Additional information: | Copyright © The Author 2023. Original content in this thesis is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) Licence (https://creativecommons.org/licenses/by-nc/4.0/). Any third-party copyright material present remains the property of its respective owner(s) and is licensed under its existing terms. Access may initially be restricted at the author’s request. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Physics and Astronomy |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10186408 |
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