The Transmon Qubit - Sam Bader

The Transmon Qubit Sam Bader December 14, 2013. Contents 1 Introduction 2. 2 Qubit Architecture 4. Cooper Pair Box .. 4. Classical Hamiltonian .. 4. Quantized Hamiltonian .. 5. Capacitively-shunted CPB .. 7. The ratio EJ /Ec .. 7. 3 Circuit QED 9. Vocabulary of Cavity QED .. 9. Jaynes-Cummings Hamiltonian .. 10. Effects of the coupling: resonant and dispersive limits .. 10. Purcell Effect .. 11. Translating into Circuit QED .. 12. Why Circuit QED is easier than Cavity QED .. 12. Circuit QED Hamiltonian .. 13. 4 Control and Readout Protocol 15. Measurement .. 15. Single Qubit gates .. 16. Modeling drives .. 16. Applying gates .. 16. Multi- Qubit gates and entanglement .. 17. 5 Conclusion 19. A Derivation of Classical Hamiltonians for Qubit Systems 20. Cooper Pair Box .. 20. Transmon with transmission line .. 21. B Quantum Circuits 23. Charge basis .. 23. Phase basis .. 24. C Perturbation Theory for the Transmon 25. Periodic Potentials .. 25. Transforming away the offset charge .. 26.

The rst term of the Hamiltonian represents the capacitive/charging energy and the second term is the Josephson inductive energy. Note that the charging term depends on the excess charge minus an

Tags:

  Josephson, Transmon

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