2016/10/26 by Phillip R. Dukes, Dukes, Phillip R.
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Physics (quant-ph) #Quantum and electron transport phenomena #Quantum-Dot Cellular Automata
paper · pdf · doi:10.48550/arxiv.1610.08421
openalex publication_date 2016/10/26 · openalex created_date 2022/09/01 · openalex updated_date 2026/07/28
A distinguishability operator is defined for the continuous-time quantum walk\n(CTQW) of a bipartite quantum walker on two simply connected graphs,\nWGi,Gj = UGi\(t\) \⊗ UGj\(t'\) -\nUGj\(t'\) \⊗ UGi\(t\), where\nUGi\(t\) is the unitary CTQW operator for a labeled graph Gi\nover a time interval t. The null space of WGi,Gj defines the vector\nspace of initial bipartite states whose time development is either constant or\nonly dependent on t + t' and is invariant to which quantum walker subsystem\ngoes with each graph. The set of null spaces corresponding with a set of\nWGi,Gj have interesting relations as subspaces, intersections between\nsubspaces, and subspaces of intersections. These relations are depicted as\nEuler diagrams for labeled graphs of three and four vertices.\n