Optimal control of coupled Josephson qubits

A. Spörl, T. Schulte-Herbrüggen, S. J. Glaser, V. Bergholm, M. J. Storcz, J. Ferber, and F. K. Wilhelm
Phys. Rev. A 75, 012302 – Published 2 January 2007

Abstract

In two and three coupled Josephson charge qubits, we exemplify how to take pulses for realizing quantum gates from fidelity-limited pioneering stages to the decoherence limit of near time optimal high-fidelity controls. Thus, a CNOT gate can be obtained with a fidelity >1109 for the two qubits. Even when including higher charge states, the leakage is below 1%, although the pulses are nonadiabatic. The controls are five times faster than the pioneering experiment [Nature (London) 425, 941 (2003)] for otherwise identical parameters—i.e., a progress towards the error-correction threshold by a factor of 100. We outline schemes to generate these shaped pulses by Cauer synthesis, or more generally by few LCR circuits. The approach generalizes to larger systems: e.g., directly realizing a TOFFOLI gate in three linearly coupled charge qubits is shown to be 13 times faster than decomposing it into a circuit of nine CNOT gates of the above experimental work. In view of the next generation of fast pulse shapers, the combination of methods is designed to find wide application in quantum control of pseudospin and macroscopic quantum systems.

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  • Received 28 September 2006

DOI:https://doi.org/10.1103/PhysRevA.75.012302

©2007 American Physical Society

Authors & Affiliations

A. Spörl, T. Schulte-Herbrüggen*, and S. J. Glaser

  • Department of Chemistry, Technische Universität München, Lichtenbergstrasse 4, 85747 Garching, Germany

V. Bergholm

  • Materials Physics Laboratory, POB 2200 (Technical Physics) FIN-02015 HUT, Helsinki University of Technology, Espoo, Finland

M. J. Storcz, J. Ferber, and F. K. Wilhelm

  • Physics Department, ASC, and CeNS, Ludwig-Maximilians-Universität, Theresienstr. 37, 80333 Munich, Germany

  • *Electronic address: tosh@ch.tum.de
  • Present address: Institute for Quantum Computing, University of Waterloo, 200 University Ave, Waterloo N2L3G1, Canada; Electronic address: fwilhelm@iqc.ca

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Vol. 75, Iss. 1 — January 2007

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