Transcript Demonstration of conditional gate operation using

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 = 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
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2.2 Experiment
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2.3 Results
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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
1.
2.
3.
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
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