2016/11/30 by C.-L. Ho, C. -L. Ho, Tetsuo Deguchi +1
Computer Science · Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic structures and combinatorial models #Braid #Braid group #Braid theory #Law #Lie group #Mathematics #Physics #Pure mathematics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Fourier transform #Quantum computer #Quantum gate #Quantum many-body systems #Quantum mechanics #Unitary representation #Unitary state #math-ph #math.MP #math.RT #quant-ph
paper · pdf · doi:10.1209/0295-5075/118/40001
published as EPL 118 (2017) 40001 · 9 pages, no figures. arXiv admin note: text overlap with arXiv:1011.6229
openalex created_date 2016/11/30 · openalex publication_date 2017/05/01 · arxiv created 2017/10/26 · arxiv updated 2017/10/30 · openalex updated_date 2026/08/05
Using a braid group representation based on the Temperley-Lieb algebra, we construct braid quantum gates that could generate entangled n -partite D -level qudit states. D different sets of D n × D n unitary representation of the braid group generators are presented. With these generators the desired braid quantum gates are obtained. We show that the generalized GHZ states, which are maximally entangled states, can be obtained directly from these braid quantum gates without resorting to further local unitary transformations. We also point out an interesting observation, namely for a general multi-qudit state there exists a unitary braid quantum gate based on the Temperley-Lieb algebra that connects it from one of its component basis states, if the coefficient of the component state is such that the square of its norm is no less than 1/4.