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

2. the DQM lab team Thomas G. McConkey Doctoral Student John R. Rinehart Doctoral Student Carolyn “Cary” T. Earnest Doctoral Student Corey Rae H. McRae Doctoral Student Jérémy Béjanin Master’s Student Yousef Rohanizadegan Research Assistant Matteo Mariantoni Principal Investigator Daryoush Shiri Postdoctoral Fellow Collaborators: 1)Prof. Michael J. Hartmann Heriot Watt University 2)Prof. Frederick W. Strauch Williams College 3)Prof. Adrian Lupaşcu IQC 4)Prof. Christopher M. Wilson IQC 5)Prof. Zbig R. Wasilewski WIN 6)Dr. Austin G. Fowler UC Santa Barbara 7)Prof. David G. Cory IQC 8)Prof. Guo-Xing Miao IQC 9)Prof. Roger G. Melko UW 10)Sadegh Raeisi IQC 11)Yuval R. Sanders IQC

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

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

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

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

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

8. LC resonator superconducting quantum circuits

9. LC resonator superconducting quantum circuits ~ 7 GHz

10. dielectric material transmission-line resonator superconducting quantum circuits

11. coplanar waveguide resonator superconducting quantum circuits T 1 ~ 5  s T 2 ~ 2T 1 M. Mariantoni et al., Nature Phys. 7, 287 (2011)

12. Josephson junction → nonlinearity qubit superconducting quantum circuits

13. ~ 7 GHz ~ 6.8 GHz  an ~ 200 MHz superconducting quantum circuits qubit

14. superconducting quantum circuits qubit capacitor C inductor L junction T 1 ~ 500 ns T 2 ~ 150 ns M. Mariantoni et al., Nature Phys. 7, 287 (2011)

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

16. one-qubit pulses and one-qubit quantum errors P.W. Shor, Phys. Rev. A 52, 2493 (1995)

17. Q1Q1 Q2Q2 M1M1 M2M2 B Z2Z2 Z1Z1 create, write, re-create, zero, read entanglement

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

19. the CZ-  gate qubit qutrit

20. phase qubit qutrit the CZ-  gate

21. qutrit-resonator interaction the CZ-  gate

22. qutrit-resonator interaction the CZ-  gate

23. qutrit-resonator interaction the CZ-  gate

24. resonant semi-resonant qutrit-resonator interaction the CZ-  gate

25. resonant semi-resonant two-qubit CZ-  gate the CZ-  gate

26. resonant semi-resonant control target 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. DiCarlo et al., Nature (London) 460, 240-244 (2009) T. Yamamoto,…, M.M.,... et al., Phys. Rev. B 82, 184515 (2010) two-qubit CZ-  gate the CZ-  gate

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

28. resonant semi-resonant two-qubit CZ-  gate the CZ-  gate

29. resonant semi-resonant two-qubit CZ-  gate the CZ-  gate M. Mariantoni et al., Science 334, 61 (2011)

30. resonant semi-resonant M. Mariantoni et al., Science 334, 61 (2011) two-qubit CZ-  gate the CZ-  gate

31.  -meter: Generalized Ramsey (a) the CZ-  gate

32. i.compensate dynamic phase ii.varying z cmp  Ramsey fringe  -meter: Generalized Ramsey (a) the CZ-  gate

33.  -meter: Generalized Ramsey (b) the CZ-  gate

34.  -meter: Generalized Ramsey (a-b) the CZ-  gate

35.  -meter: Generalized Ramsey (a-b) the CZ-  gate

36.  = 0.01  =  /2  =   -meter: Generalized Ramsey (a-b) the CZ-  gate

37. process tomography the CZ-  gate fidelity ~70% fidelity ~60% qubit T 1 ~500 ns, T 2 ~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. data and syndrome qubit syndrome → measured data surface code

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

42. Z-stabilizer 1 23 4 stabilizers

43. Z-stabilizer 1 23 4  zeroing gate stabilizers

44. Z-stabilizer 1 23 4  projects stabilizers

45. X-stabilizer 1 23 4  projects stabilizers

46. one qubit  qubit state destroyed

47. stabilizers

50. quiescent state +1 stabilizers

51. +1 quiescent state +1 +1 +1 +1 +1 +1 +1 stabilizers

52. quiescent state +1 +1 +1 +1 time quantum error detection

53. time +1 +1 +1 +1  bit-flip error quantum error detection

54. +1 +1 +1 +1  bit-flip error  phase-flip error time protected memory +1 1)any error 2)boundaries 3)measurement errors  “minimum weight matching” → polynomial +1 quantum error detection

55. +1 +1 +1 +1 +1 +1 +1 +1 error chains and logical qubits error on first qubit

56. +1 +1 +1 +1 +1 +1 +1 +1 error chains and logical qubits error on first qubit

57. +1 +1 +1 +1 +1 +1 +1 +1 error chains and logical qubits error on second qubit

58. +1 +1 +1 +1 +1 +1 +1 error chains and logical qubits error on second qubit

59. +1 +1 +1 +1 +1 +1 +1 error chains and logical qubits error on third qubit

60. +1 +1 +1 +1 +1 +1 +1 +1 error chains and logical qubits error on third qubit

61. +1 +1 +1 +1 +1 +1 +1 +1 error chains and logical qubits error on fourth qubit

62. +1 quiescent state +1 +1 +1 +1 +1 +1 +1 error chains and logical qubits

63. +1 +1 +1 +1 +1 +1 +1 +1 error chains and logical qubits error on last qubit

64. +1 +1 +1 +1 +1 +1 +1 +1 error chains and logical qubits error on third qubit

65. +1 +1 +1 +1 +1 +1 +1 +1 error chains and logical qubits back to original quiescent state

66. fault tolerance – surface codes physical → logical qubit = error rate 10 -14 A.G. Fowler et al., Phys. Rev. A 86, 032324 (2012)

67. fault tolerance – surface codes physical qubits → logical qubit = error rate 10 -14 1)nearest neighbor interactions 2)CNOT physical gates fast ~ 100 ns with F ≥ 99 % 3)readout fast ~ 100 ns with F ≥ 90 % 4)interface with classical electronics 5)overhead proof-of-concept → 3/5 physical qubits quantum memory → 10  10 = 10 2 physical qubits Shor → 10 3 to 10 4 physical qubits 

68. A. Megrant et al., App. Phys. Lett. 100, 113510 (2012) fault tolerance – surface codes 1) CNOT physical gates R. Barends et al., Phys. Rev. Lett. 111, 080502 (2013) Xmon Xmon lifetime T 1 ~ 50  s T gate ~ 50 ns = 0.05  s → F  exp(- T gate / T 1 ) = exp(- 0.05  s / 50  s) ~ 99.9 % R. Barends et al., App. Phys. Lett. 99, 113507 (2011)

69. fault tolerance – surface codes physical qubits → logical qubit = error rate 10 -14 1)nearest neighbor interactions 2)CNOT physical gates fast ~ 100 ns with F ≥ 99 % 3)readout fast ~ 100 ns with F ≥ 90 % 4)interface with classical electronics 5)overhead proof-of-concept → 3/5 physical qubits quantum memory → 10  10 = 10 2 physical qubits Shor → 10 3 to 10 4 physical qubits  

70. fault tolerance – surface codes 2) readout R. Vijay et al., Nature (London) 490, 77 (2012) readout time  r ~ 100 ns F > 90 %

71. fault tolerance – surface codes physical qubits → logical qubit = error rate 10 -14 1)nearest neighbor interactions 2)CNOT physical gates fast ~ 100 ns with F ≥ 99 % 3)readout fast ~ 100 ns with F ≥ 90 % 4)interface with classical electronics 5)overhead proof-of-concept → 3/5 physical qubits quantum memory → 10  10 = 10 2 physical qubits Shor → 10 3 to 10 4 physical qubits    

72. surface code proof-of-concept → 3/5 physical qubits → 3-4 years quantum memory → 10 2 physical qubits → 8-9 years Shor to factor a 2000 bit number in 24 h with 1 nuclear power plant → 300  10 6 physical qubits oon the best classical super-cluster: many times the age of the universe and virtually infinite power perspective

73. resonator-qubit 2D lattice A,|g ⟩ unit cell B B Z R R R … … … … Q,|  ⟩

74. A,|g ⟩ B … … … …  higher isolation → OFF coupling B Q,|  ⟩ resonator-qubit 2D lattice

75. B B Q,|  ⟩ A,|g ⟩ R R R … … …  higher isolation → OFF coupling  encoding → multiple measurement resonator-qubit 2D lattice

76. Z … … …  higher isolation → OFF coupling  encoding → multiple measurement  zero Q,|  ⟩ leakage to third state resonator-qubit 2D lattice

77. see also D.P. DiVincenzo, Phys. Scr., T 137, 014020 (2009) A,|g ⟩ B B Z R R R … … …  higher isolation → OFF coupling  encoding → multiple measurement  zero and/or store Q,|  ⟩ resonator-qubit 2D lattice