LEADER 04619nam 22007695 450 001 9910739449703321 005 20200630071723.0 010 $a1-4614-6336-X 024 7 $a10.1007/978-1-4614-6336-8 035 $a(CKB)3460000000120296 035 $a(EBL)1106166 035 $a(OCoLC)828794275 035 $a(SSID)ssj0000879603 035 $a(PQKBManifestationID)11482899 035 $a(PQKBTitleCode)TC0000879603 035 $a(PQKBWorkID)10852218 035 $a(PQKB)10194745 035 $a(DE-He213)978-1-4614-6336-8 035 $a(MiAaPQ)EBC6315124 035 $a(MiAaPQ)EBC1106166 035 $a(Au-PeEL)EBL1106166 035 $a(CaPaEBR)ebr10983233 035 $a(PPN)168305062 035 $a(EXLCZ)993460000000120296 100 $a20130217d2013 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aQuantum Walks and Search Algorithms /$fby Renato Portugal 205 $a1st ed. 2013. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d2013. 215 $a1 online resource (227 p.) 225 1 $aQuantum Science and Technology,$x2364-9054 300 $aDescription based upon print version of record. 311 $a1-4899-8802-5 311 $a1-4614-6335-1 320 $aIncludes bibliographic references (pages [215]-218) and index. 327 $aIntroduction -- The Postulates of Quantum Mechanics -- Introduction to Quantum Walks -- Grover's Algorithm and its Generalization -- Quantum Walks on Infinite Graphs -- Quantum Walks on Finite Graphs -- Limiting Distribution and Mixing Time -- Spatial Algorithms -- Hitting Time -- Appendix: Linear Algebra for Quantum Computation. 330 $aThis book addresses an interesting area of quantum computation called quantum walks, which play an important role in building quantum algorithms, in particular search algorithms. Quantum walks are the quantum analogue of classical random walks. It is known that quantum computers have great power for searching unsorted databases. This power extends to many kinds of searches, particularly to the problem of finding a specific location in a spatial layout, which can be modeled by a graph. The goal is to find a specific node knowing that the particle uses the edges to jump from one node to the next. This book is self-contained with main topics that include: Grover's algorithm, describing its geometrical interpretation and evolution by means of the spectral decomposition of the evolution operater Analytical solutions of quantum walks on important graphs like line, cycles, two-dimensional lattices, and hypercubes using Fourier transforms Quantum walks on generic graphs, describing methods to calculate the limiting distribution and mixing time Spatial search algorithms, with emphasis on the abstract search algorithm (the two-dimensional lattice is used as an example) Szedgedy's quantum-walk model and a natural definition of quantum hitting time (the complete graph is used as an example) The reader will benefit from the pedagogical aspects of the book, learning faster and with more ease than would be possible from the primary research literature. Exercises and references further deepen the reader's understanding, and guidelines for the use of computer programs to simulate the evolution of quantum walks are also provided. 410 0$aQuantum Science and Technology,$x2364-9054 606 $aQuantum theory 606 $aQuantum computers 606 $aComputers 606 $aSpintronics 606 $aQuantum Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19080 606 $aQuantum Computing$3https://scigraph.springernature.com/ontologies/product-market-codes/M14070 606 $aTheory of Computation$3https://scigraph.springernature.com/ontologies/product-market-codes/I16005 606 $aQuantum Information Technology, Spintronics$3https://scigraph.springernature.com/ontologies/product-market-codes/P31070 615 0$aQuantum theory. 615 0$aQuantum computers. 615 0$aComputers. 615 0$aSpintronics. 615 14$aQuantum Physics. 615 24$aQuantum Computing. 615 24$aTheory of Computation. 615 24$aQuantum Information Technology, Spintronics. 676 $a530.120151 700 $aPortugal$b Renato$4aut$4http://id.loc.gov/vocabulary/relators/aut$0984133 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910739449703321 996 $aQuantum Walks and Search Algorithms$92247683 997 $aUNINA