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1. Title goes here Building a superconducting quantum computer with the surface code Matteo Mariantoni Fall INTRIQ meeting, November 5th & 6th 2013

2. the DQM lab team • Collaborators: • Prof. Michael J. Hartmann • Heriot Watt University • Prof. Frederick W. Strauch • Williams College • Prof. Adrian Lupaşcu • IQC • Prof. Christopher M. Wilson • IQC • Prof. Zbig R. Wasilewski • WIN • Dr. Austin G. Fowler • UC Santa Barbara • Prof. David G. Cory • IQC • Prof. Guo-Xing Miao • IQC • Prof. Roger G. Melko • UW • SadeghRaeisi • IQC • Yuval R. Sanders • IQC Matteo Mariantoni Principal Investigator DaryoushShiri Postdoctoral Fellow Thomas G. McConkey Doctoral Student John R. Rinehart Doctoral Student Carolyn “Cary” T. Earnest Doctoral Student JérémyBéjanin Master’s Student Corey Rae H. McRae DoctoralStudent Yousef Rohanizadegan Research Assistant

3. lab virtual walkthrough DR photo credit BlueFors Cryogenics Oy the lab is being setup in these very days; it will be up and running by February 2014

4. lab realwalkthrough the lab is being setup in these very days; it will be up and running by February 2014

5. on the edge nano/micro meter space nano/micro meter space milli kelvin temperature frequency time giga hertz photo credit – M. Mariantoni and E. Lucero University of California Santa Barbara

6. on the edge milli kelvin temperature photo credit – BlueFors Cryogenics Oy

7. on the edge frequency time giga hertz photo credit – M. Mariantoni and E. Lucero

8. superconducting quantum circuits • LCresonator

9. superconducting quantum circuits • LCresonator ~ 7 GHz

10. superconducting quantum circuits • transmission-line resonator dielectric material

11. superconducting quantum circuits • coplanarwaveguide resonator T1 ~ 5 ms T2~ 2T1 M. Mariantoniet al., Nature Phys. 7, 287 (2011)

12. superconducting quantum circuits • qubit Josephson junction → nonlinearity

13. superconducting quantum circuits • qubit dan ~ 200 MHz ~ 6.8 GHz ~ 7 GHz

14. superconducting quantum circuits • qubit junction capacitor C inductor L T1 ~ 500 ns T2 ~ 150 ns M. Mariantoniet al., Nature Phys. 7, 287 (2011)

15. superconducting quantum circuits • resonator+qubit+control X,Y (p, p/2); Z junction resonator capacitor C inductor L + qubit g(Cb) ~ 100 MHz  10 ns A. Blais, R.-S. Huang, A. Wallraff, S.M. Girvin, and R.J. Schoelkopf, Phys. Rev. A 69, 062320 (2004); A. Wallraffet al., Nature (London) 431, 162 (2004) M. Mariantoniet al., Nature Phys. 7, 287 (2011)

16. one-qubitpulses and one-qubitquantum errors • pulses • ()  energizes the qubitfrom to • ()  prepares the qubitin state • ()  shifts the qubitby a certain phase, • errors • bit-flip ()  brings the qubit from to • phase-flip ()  shifts the qubitfrom to • any error P.W. Shor, Phys. Rev. A 52, 2493 (1995)

17. create, write, re-create, zero, read entanglement M1 B Q1 Z2 Z1 Q2 M2

18. M. Mariantoni et al., Science 334,61 (2011) i

19. the CZ-p gate • qutrit qubit

20. the CZ-p gate • qutrit phase qubit qutrit

21. the CZ-p gate • qutrit-resonator interaction

22. the CZ-p gate • qutrit-resonator interaction

23. the CZ-p gate • qutrit-resonator interaction

24. the CZ-p gate • qutrit-resonator interaction semi-resonant resonant

25. the CZ-p gate • two-qubitCZ-fgate semi-resonant resonant

26. the CZ-p gate • two-qubitCZ-fgate semi-resonant control resonant THEORY: F. W. Strauch et al., Phys. Rev. Lett. 91, 167005 (2003) G. Haack,…, M.M.,... et al., Phys. Rev. B 82, 024514 (2010) EXPERIMENT: L. DiCarloet al., Nature (London) 460, 240-244 (2009) T. Yamamoto ,…, M.M.,... et al., Phys. Rev. B 82, 184515 (2010) target

27. the CZ-p gate • CZ-p gate truth table semi-resonant control resonant target

28. the CZ-p gate • two-qubitCZ-fgate semi-resonant resonant

29. the CZ-p gate • two-qubitCZ-fgate semi-resonant resonant M. Mariantoni et al., Science 334,61 (2011)

30. the CZ-p gate • two-qubitCZ-fgate semi-resonant resonant M. Mariantoni et al., Science 334,61 (2011)

31. the CZ-p gate • f-meter: Generalized Ramsey (a)

32. the CZ-p gate • f-meter: Generalized Ramsey (a) compensate dynamic phase varying zcmp Ramsey fringe

33. the CZ-p gate • f-meter: Generalized Ramsey (b)

34. the CZ-p gate • f-meter: Generalized Ramsey (a-b)

35. the CZ-p gate • f-meter: Generalized Ramsey (a-b)

36. the CZ-p gate • f-meter: Generalized Ramsey (a-b) f = 0.01 f = p/2 f = p

37. the CZ-p gate • process tomography fidelity ~70% fidelity ~60% qubit T1~500 ns, T2~150 ns

38. superconducting surface code A.G. Fowler, M. Mariantoni, J.M. Martinis, and A.N. Cleland, Phys. Rev. A 86, 032324 (2012) ~ 50 pages of details

39. 2D lattice with nearest neighbor interactions A.G. Fowler, M. Mariantoni, J.M. Martinis, and A.N. Cleland, Phys. Rev. A 86, 032324 (2012) ~ 50 pages of details

40. surface code • data and syndrome qubit syndrome → measured data

41. surface code • face and vertex A.Yu. Kitaev, Annals of Physics 303, 2 (2003)

42. stabilizers • Z-stabilizer 1 2 3 4

43. stabilizers • Z-stabilizer • zeroing gate 1 2 3 4

44. stabilizers • Z-stabilizer • projects 1 2 3 4

45. stabilizers • X-stabilizer • projects 1 2 3 4

46. stabilizers one qubit detected by repeatedly measuring the qubit with combined and measurements  qubitstate destroyed

47. stabilizers pair of qubits, and , detected by repeatedly measuring the pair of qubits with and measurements

48. stabilizers pair of qubits, and , detected by repeatedly measuring the pair of qubits with and measurements

49. stabilizers error detection event BUT cannot be distinguished from an error!

50. stabilizers • quiescent state -1 +1