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

Index 1 Introduction: The one qubit system 1.1 Josephson Junction 1.2 Hamiltonian 1.3 Energy bands with EJ = 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

1: Introduction The one qubit system

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

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

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

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

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)

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

2: Experiment

2.1 Experiment setup [1][2]

2.2 Experiment [1]

2.3 Results [1]

3: Data analysis

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

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

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

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 , oct 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 , jul Lectures on quantum information systems WS 2006/2007, Wallraff, ETHZ

[2]