2012/09/19 by Jacob Farinholt, Farinholt, Jacob
Chemistry · Mathematics · Physics and Astronomy · #Advanced NMR Techniques and Applications #Algebraic and Geometric Analysis #FOS: Physical sciences #Finite Group Theory Research #Mathematical Physics (math-ph) #Quantum Physics (quant-ph) #math-ph #math.MP #quant-ph
paper · pdf · doi:10.48550/arxiv.1209.4327
This paper has been withdrawn by the author due to the discovery of several crucial errors upon review. A new manuscript with more general results is forthcoming
openalex publication_date 2012/09/19 · arxiv created 2012/12/05 · arxiv updated 2012/12/07 · openalex created_date 2022/08/28 · openalex updated_date 2026/07/28
NOTE: PAPER WITHDRAWN (See Comments) The Clifford and Local Clifford groups for d > 2 dimensional systems have been topics of recent interest due to their applications in graph states, quantum codes, and possible applications in fast quantum algorithms. This paper studies these groups more abstractly, by first characterizing the Pauli Automorphism and Local Automorphism groups, and then using these results to determine characteristics of the Clifford and Local Clifford groups. Not only does such an approach reveal new information about the Clifford and Local Clifford groups, but it also shows how many previously derived results arise naturally as simple corollaries. Lastly, we give a systematic method of building an arbitrary Local Clifford operator from a small number of previously known gates, as well as a method to physically implement such an operator.