Tight Bounds on the Synthesis of 3-bit Reversible Circuits: NFT Library

The reversible circuit synthesis problem can be reduced to permutation group. This allows Schreier-Sims Algorithm for the strong generating set-finding problem to be used to find tight bounds on the synthesis of 3-bit reversible circuits using the NFT library. The tight bounds include the maximum and minimum length of 3-bit reversible circuits, the maximum and minimum cost of 3-bit reversible circuits. The analysis shows better results than that found in the literature for the lower bound of the cost. The analysis also shows that there are 1960 universal reversible sub-libraries from the main NFT library.Comment: 18 pages. arXiv admin note: text overlap with arXiv:1101.438

Applications of coherent classical communication and the Schur transform to quantum information theory

Quantum mechanics has led not only to new physical theories, but also a new understanding of information and computation. Quantum information began by yielding new methods for achieving classical tasks such as factoring and key distribution but also suggests a completely new set of quantum problems, such as sending quantum information over quantum channels or efficiently performing particular basis changes on a quantum computer. This thesis contributes two new, purely quantum, tools to quantum information theory--coherent classical communication in the first half and an efficient quantum circuit for the Schur transform in the second half.Comment: 176 pages. Chapters 1 and 4 are a slightly older version of quant-ph/0512015. Chapter 2 is quant-ph/0205057 plus unpublished extensions (slightly outdated by quant-ph/0511219) and chapter 3 is quant-ph/0307091, quant-ph/0412126 and change. Chapters 5-8 are based on quant-ph/0407082, but go much furthe