Braiding Operators are Universal Quantum Gates Export

@article{citeulike:4233024, abstract = {This paper explores of the role of unitary braiding operators in quantum computing. We show that a single specific solution R (the Bell basis change matrix) of the Yang-Baxter Equation is a universal gate for quantum computing, in the presence of local unitary transformations. We show that this same R generates a new non-trivial invariant of braids, knots, and links. Other solutions of the Yang-Baxter Equation are also shown to be universal for quantum computation. The paper discusses these results in the context of comparing quantum and topological points of view. In particular, we discuss quantum computation of link invariants, the relationship between quantum entanglement and topological entanglement, teleportation, and the structure of braiding in a topological quantum field theory.}, archivePrefix = {arXiv}, author = {Kauffman, Louis H. and Lomonaco, Samuel J.}, citeulike-article-id = {4233024}, citeulike-linkout-0 = {http://arxiv.org/abs/quant-ph/0401090}, citeulike-linkout-1 = {http://arxiv.org/pdf/quant-ph/0401090}, eprint = {quant-ph/0401090}, keywords = {braids, quantum-computation}, month = {Aug}, posted-at = {2009-03-27 17:11:26}, priority = {4}, title = {Braiding Operators are Universal Quantum Gates}, url = {http://arxiv.org/abs/quant-ph/0401090}, year = {2004} }

TY - JOUR ID - citeulike:4233024 L3 - citeulike-article-id:4233024 N2 - This paper explores of the role of unitary braiding operators in quantum computing. We show that a single specific solution R (the Bell basis change matrix) of the Yang-Baxter Equation is a universal gate for quantum computing, in the presence of local unitary transformations. We show that this same R generates a new non-trivial invariant of braids, knots, and links. Other solutions of the Yang-Baxter Equation are also shown to be universal for quantum computation. The paper discusses these results in the context of comparing quantum and topological points of view. In particular, we discuss quantum computation of link invariants, the relationship between quantum entanglement and topological entanglement, teleportation, and the structure of braiding in a topological quantum field theory. TI - Braiding Operators are Universal Quantum Gates KW - braids KW - quantum-computation AU - Kauffman, Louis AU - Lomonaco, Samuel PY - 2004/Aug/12/ UR - http://arxiv.org/abs/quant-ph/0401090 ER -