Top Banner

Click here to load reader

Presentazone15

Aug 28, 2014

ReportDownload

Technology

 

  • Entanglement Dynamics Marta Agati Quantum Computa- tion Quantum Computing and Quantum Mechanics Superconducting Qubits Charge Qubit Noise in Josephson Qubits Methods Entanglement Dynamics Transvers Coupling, Asymmetric Fluctuator Transvers Coupling, Comparison with Symmetric Fluctuator Comparison with Longitudinal Coupling Conclusions Quantum Computation Superconducting Qubits Noise in Josephson Qubits Entanglement Dynamics Conclusions Entanglement Dynamics of Two Superconducting Qubits Subject to Random Telegraph Noise Marta Agati Universit degl Studi di Catania Dipartimento di Fisica e Astronomia Corso di Laurea in Fisica Matis CNR-IMM UOS Catania Centro Siciliano Fisica Nucleare e Struttura della Materia (CSFNSM) QUINN QUantum INformation and Nanonsystems group Relatore Prof.ssa Elisabetta Paladino Correlatore Prof. Giuseppe Falci Dott. Antonio DArrigo July 16, 2013 Marta Agati Entanglement Dynamics
  • Entanglement Dynamics Marta Agati Quantum Computa- tion Quantum Computing and Quantum Mechanics Superconducting Qubits Charge Qubit Noise in Josephson Qubits Methods Entanglement Dynamics Transvers Coupling, Asymmetric Fluctuator Transvers Coupling, Comparison with Symmetric Fluctuator Comparison with Longitudinal Coupling Conclusions Quantum Computation Superconducting Qubits Noise in Josephson Qubits Entanglement Dynamics Conclusions Contents 1 Quantum Computation Quantum Computing and Quantum Mechanics 2 Superconducting Qubits Charge Qubit 3 Noise in Josephson Qubits Methods 4 Entanglement Dynamics Transvers Coupling, Asymmetric Fluctuator Transvers Coupling, Comparison with Symmetric Fluctuator Comparison with Longitudinal Coupling 5 Conclusions Marta Agati Entanglement Dynamics
  • Entanglement Dynamics Marta Agati Quantum Computa- tion Quantum Computing and Quantum Mechanics Superconducting Qubits Charge Qubit Noise in Josephson Qubits Methods Entanglement Dynamics Transvers Coupling, Asymmetric Fluctuator Transvers Coupling, Comparison with Symmetric Fluctuator Comparison with Longitudinal Coupling Conclusions Quantum Computation Superconducting Qubits Noise in Josephson Qubits Entanglement Dynamics Conclusions Quantum Computing and Quantum Mechanics Introduction to Quantum Computation Michael A. Nielsen, Isaac L. Chuang; Quantum Computation and Quantum Information, Cambridge University Press, 2010 Marta Agati Entanglement Dynamics
  • Entanglement Dynamics Marta Agati Quantum Computa- tion Quantum Computing and Quantum Mechanics Superconducting Qubits Charge Qubit Noise in Josephson Qubits Methods Entanglement Dynamics Transvers Coupling, Asymmetric Fluctuator Transvers Coupling, Comparison with Symmetric Fluctuator Comparison with Longitudinal Coupling Conclusions Quantum Computation Superconducting Qubits Noise in Josephson Qubits Entanglement Dynamics Conclusions Quantum Computing and Quantum Mechanics Contents 1 Quantum Computation Quantum Computing and Quantum Mechanics 2 Superconducting Qubits Charge Qubit 3 Noise in Josephson Qubits Methods 4 Entanglement Dynamics Transvers Coupling, Asymmetric Fluctuator Transvers Coupling, Comparison with Symmetric Fluctuator Comparison with Longitudinal Coupling 5 Conclusions Marta Agati Entanglement Dynamics
  • Entanglement Dynamics Marta Agati Quantum Computa- tion Quantum Computing and Quantum Mechanics Superconducting Qubits Charge Qubit Noise in Josephson Qubits Methods Entanglement Dynamics Transvers Coupling, Asymmetric Fluctuator Transvers Coupling, Comparison with Symmetric Fluctuator Comparison with Longitudinal Coupling Conclusions Quantum Computation Superconducting Qubits Noise in Josephson Qubits Entanglement Dynamics Conclusions Quantum Computing and Quantum Mechanics Unit of Quantum Information Quantum bit or Qubit Quantum bit or Qubit = 0|0 + 1|1 Superposition Principle Multiple-Qubit state Two qubits = 00|00 + 01|01 + 10|10 + 11|11 Product State S = |01 +|11 2 = |0 +|1 2 |1 Entangled State (Bell State) E = |00 +|11 2 Michael A. Nielsen, Isaac L. Chuang; Quantum Computation and Quantum Information, Cambridge University Press, 2010 Marta Agati Entanglement Dynamics
  • Entanglement Dynamics Marta Agati Quantum Computa- tion Quantum Computing and Quantum Mechanics Superconducting Qubits Charge Qubit Noise in Josephson Qubits Methods Entanglement Dynamics Transvers Coupling, Asymmetric Fluctuator Transvers Coupling, Comparison with Symmetric Fluctuator Comparison with Longitudinal Coupling Conclusions Quantum Computation Superconducting Qubits Noise in Josephson Qubits Entanglement Dynamics Conclusions Quantum Computing and Quantum Mechanics Unit of Quantum Information Quantum bit or Qubit Quantum bit or Qubit = 0|0 + 1|1 Superposition Principle Multiple-Qubit state Two qubits = 00|00 + 01|01 + 10|10 + 11|11 Product State S = |01 +|11 2 = |0 +|1 2 |1 Entangled State (Bell State) E = |00 +|11 2 Michael A. Nielsen, Isaac L. Chuang; Quantum Computation and Quantum Information, Cambridge University Press, 2010 Marta Agati Entanglement Dynamics
  • Entanglement Dynamics Marta Agati Quantum Computa- tion Quantum Computing and Quantum Mechanics Superconducting Qubits Charge Qubit Noise in Josephson Qubits Methods Entanglement Dynamics Transvers Coupling, Asymmetric Fluctuator Transvers Coupling, Comparison with Symmetric Fluctuator Comparison with Longitudinal Coupling Conclusions Quantum Computation Superconducting Qubits Noise in Josephson Qubits Entanglement Dynamics Conclusions Quantum Computing and Quantum Mechanics Unit of Quantum Information Quantum bit or Qubit Quantum bit or Qubit = 0|0 + 1|1 Superposition Principle Multiple-Qubit state Two qubits = 00|00 + 01|01 + 10|10 + 11|11 Product State S = |01 +|11 2 = |0 +|1 2 |1 Entangled State (Bell State) E = |00 +|11 2 Michael A. Nielsen, Isaac L. Chuang; Quantum Computation and Quantum Information, Cambridge University Press, 2010 Marta Agati Entanglement Dynamics
  • Entanglement Dynamics Marta Agati Quantum Computa- tion Quantum Computing and Quantum Mechanics Superconducting Qubits Charge Qubit Noise in Josephson Qubits Methods Entanglement Dynamics Transvers Coupling, Asymmetric Fluctuator Transvers Coupling, Comparison with Symmetric Fluctuator Comparison with Longitudinal Coupling Conclusions Quantum Computation Superconducting Qubits Noise in Josephson Qubits Entanglement Dynamics Conclusions Quantum Computing and Quantum Mechanics Entanglement Quantiers Two-Qubit Density Matrix = = (y y ) (y y ) Wootters Concurrence C(t) = 2Max 0, 1 2 3 4 i , i = {1, . . . , 4}, eigenvalues of the matrix arranged in decreasing order. Maximally Entangled States C=1 Product States C=0 Invariance for Local Unitary Transformations. W. K. Wotters, Entanglement of Formation of an Arbitrary State of two Qubits, Phys. Rev. Lett., 80, 10,( 1998) Marta Agati Entanglement Dynamics
  • Entanglement Dynamics Marta Agati Quantum Computa- tion Quantum Computing and Quantum Mechanics Superconducting Qubits Charge Qubit Noise in Josephson Qubits Methods Entanglement Dynamics Transvers Coupling, Asymmetric Fluctuator Transvers Coupling, Comparison with Symmetric Fluctuator Comparison with Longitudinal Coupling Conclusions Quantum Computation Superconducting Qubits Noise in Josephson Qubits Entanglement Dynamics Conclusions Quantum Computing and Quantum Mechanics Entanglement Quantiers Two-Qubit Density Matrix = = (y y ) (y y ) Wootters Concurrence C(t) = 2Max 0, 1 2 3 4 i , i = {1, . . . , 4}, eigenvalues of the matrix arranged in decreasing order. Maximally Entangled States C=1 Product States C=0 Invariance for Local Unitary Transformations. W. K. Wotters, Entanglement of Formation of an Arbitrary State of two Qubits, Phys. Rev. Lett., 80, 10,( 1998) Marta Agati Entanglement Dynamics
  • Entanglement Dynamics Marta Agati Quantum Computa- tion Quantum Computing and Quantum Mechanics Superconducting Qubits Charge Qubit Noise in Josephson Qubits Methods Entanglement Dynamics Transvers Coupling, Asymmetric Fluctuator Transvers Coupling, Comparison with Symmetric Fluctuator Comparison with Longitudinal Coupling Conclusions Quantum Computation Superconducting Qubits Noise in Josephson Qubits Entanglement Dynamics Conclusions Quantum Computing and Quantum Mechanics Quantum Gates Universary set of Quantum Gates Any multiple qubits logic gate may be composed of single qubit gates and at least one entanglement-generating two-qubit gate. CNot Gate (|0 + |1 ) |0 2 |00 + |11 2 Motivation for our study on the sensitivity of the entanglement to external inuences (environment) Michael A. Nielsen, Isaac L. Chuang; Quantum Computation and Quantum Information, Cambridge University Press, 2010 Marta Agati Entanglement Dynamics
  • Entanglement Dynamics Marta Agati Quantum Computa- tion Quantum Computing and Quantum Mechanics Superconducting Qubits Charge Qubit Noise in Josephson Qubits Methods Entanglement Dynamics Transvers Coupling, Asymmetric Fluctuator Transvers Coupling, Comparison with Symmetric Fluctuator Comparison with Longitudinal Coupling Conclusions Quantum Computation Superconducting Qubits Noise in Josephson Qubits Entanglement Dynamics Conclusions Quantum Computing and Quantum Mechanics Quantum Gates Universary set of Quantum Gates Any multiple qubits logic gate may be composed of single qubit gates and at lea