Demonstration of conditional gate operation using superconducting

charge qubitsT. 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 = 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

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 EJ = 0

•Charge as a good quantum number•Degeneracy points => no energy needed to tunnel to the box

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

1.4 Energy band with EJ <> 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][1]

3: Data analysis

3.1 Truth table

• Implementation of CNOT operation succeeded !

=> compare data with simulation data

3.2 Data discussionTarget 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 componentmaybe 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 list1. 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

[2]