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Demonstration of conditional gate operation using superconducting charge qubits T. Yamamoto, Yu. A. Pashkin, O. Astafiev, Y. Nakamura & J. S. Tsai Presented by Martin Stattin and Vincent Peikert

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Index 1 Introduction: The one qubit system 1.1 Josephson Junction 1.2 Hamiltonian 1.3 Energy bands with EJ = 0 1.4 Energy bands with EJ <> 0 2 Experiment 2.1 Experiment setup 2.2 Experiment 2.3 Results 3 Data analysis 3.1 Truth table 3.2 Data disscussion 3.3 Improvements

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1: Introduction The one qubit system

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1.1 Josephson Junction Behaves like a circuit with capacitance and inhomogenous inductor Josephson energy responsible for coherent tunneling Superconducting elements Gate electrode in our case also superconducting => very precise charge tuning

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1.2 Hamiltonian Parabolar shape of the electric energy Josephson energy as a coupling between charge states => Charge is no good quantum number anymore !

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1.3 Energy band with E J = 0 Charge as a good quantum number Degeneracy points => no energy needed to tunnel to the box

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1.3 Energy bands with E J = 0 Change the quantum number from charge to energy !

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1.4 Energy band with E J <> 0 Charge is no good quantum number degeneracy points splitted up Possible to reach the degeneracy point by applying a special pulse ! => rabi oscillation (~ to E)

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1.5 Magnetic flux => The Josephson energy is a function of the magnetic flux !

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2: Experiment

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2.1 Experiment setup [1][2]

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2.2 Experiment [1]

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2.3 Results [1]

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3: Data analysis

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3.1 Truth table Implementation of CNOT operation succeeded ! => compare data with simulation data

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3.2 Data discussion Target qubit: good agreement with the experiment (but a little offset) Numerical calculation of the density matrix's time evolution Control qubit: Discrepency due to the unknown currend channel in the readout scheme Pulse induced currend should not exceed 2.4 pA but it does => currend has an extra component maybe from higher order Cooper-pair tunnerling

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3.3 Possible improvements Increasing Em Decrease the raise/fall time of the pulse by 25 % => red lines

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Source list 1.T. Yamamoto, Yu. A. Pashkin, O. Astafiev, Y. Nakamura & J. S. Tsai, Demonstration of conditional gate operation using superconducting charge qubits, Nature, Vol 425, pp 941-944, oct 2003 2.Yu. A. Pashkin, T. Yamamoto, O. Astafiev, Y. Nakamura, D. Averin & J. S. Tsai, Coupling two charge qubits, NEC Res. and Develop., Vol 44, no 3, pp 273-277, jul 2003 3.Lectures on quantum information systems WS 2006/2007, Wallraff, ETHZ

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UNIVERSITY OF NOTRE DAME Xiangning Luo EE 698A Department of Electrical Engineering, University of Notre Dame Superconducting Devices for Quantum Computation.

UNIVERSITY OF NOTRE DAME Xiangning Luo EE 698A Department of Electrical Engineering, University of Notre Dame Superconducting Devices for Quantum Computation.

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