demonstration of conditional gate operation using superconducting charge qubits t. yamamoto, yu. a....
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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
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2.2 Experiment
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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]
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