T yamamoto yu a pashkin o astafiev y nakamura j s tsai
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T. Yamamoto, Yu. A. Pashkin, O. Astafiev, Y. Nakamura & J. S. Tsai. Demonstration of conditional gate operation using superconducting charge qubits. Presented by Martin Stattin and Vincent Peikert. Index. 1 Introduction: The one qubit system 1.1 Josephson Junction 1.2 Hamiltonian

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T. Yamamoto, Yu. A. Pashkin, O. Astafiev, Y. Nakamura & J. S. Tsai

Demonstration of conditional gate operation using superconducting charge qubits

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 = 0

Change 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 discussion

Numerical calculation of the density

matrix's time evolution

  • Target qubit:

  • good agreement with the

  • experiment (but a little offset)

  • 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

  • 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

  • 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

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


[2]


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