dc.contributor.author | Rai, Ravi | |
dc.date.accessioned | 2021-12-06T14:35:25Z | |
dc.date.available | 2021-12-06T14:35:25Z | |
dc.date.issued | 2021-12-06T14:35:25Z | |
dc.identifier.uri | http://hdl.handle.net/10222/81044 | |
dc.description.abstract | In quantum computing, computational tasks are represented by quantum circuits. These circuits are composed of gates whose physical realization comes at a cost. Typically, gates from the so-called Clifford group are considered cheap, while non Clifford gates are considered expensive. Consequently, non-Clifford operations are often seen as a resource whose use should be minimized. In this thesis, following recent work by Beverland and others, we study lower bounds for the number of non-Clifford gates in quantum circuits. We focus on lower bounds that can be derived from monotones, which are real-valued functions of quantum states that are non-increasing under Clifford operations. We first provide a detailed presentation of two recently
introduced monotones: the stabilizer nullity and the dyadic monotone. We then discuss how these monotones can be used to give lower bounds for the non-Clifford resources for two important quantum operations: the multiply-controlled Pauli Z gate and the modular adder. | en_US |
dc.language.iso | en | en_US |
dc.subject | Quantum Computing | en_US |
dc.title | Lower Bounds for Quantum Circuits | en_US |
dc.date.defence | 2021-08-20 | |
dc.contributor.department | Department of Mathematics & Statistics - Math Division | en_US |
dc.contributor.degree | Master of Science | en_US |
dc.contributor.external-examiner | n/a | en_US |
dc.contributor.graduate-coordinator | Sara Faridi | en_US |
dc.contributor.thesis-reader | Peter Selinger | en_US |
dc.contributor.thesis-reader | Karl Dilcher | en_US |
dc.contributor.thesis-supervisor | Neil Julien Ross | en_US |
dc.contributor.ethics-approval | Not Applicable | en_US |
dc.contributor.manuscripts | Not Applicable | en_US |
dc.contributor.copyright-release | Not Applicable | en_US |