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D-Wave Systems Inc. THE QUANTUM COMPUTING COMPANY TM A.M. Zagoskin (D-Wave Systems and UBC) Tunable coupling of superconducting qubits Quantum Mechanics.

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Presentation on theme: "D-Wave Systems Inc. THE QUANTUM COMPUTING COMPANY TM A.M. Zagoskin (D-Wave Systems and UBC) Tunable coupling of superconducting qubits Quantum Mechanics."— Presentation transcript:

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2 D-Wave Systems Inc. THE QUANTUM COMPUTING COMPANY TM A.M. Zagoskin (D-Wave Systems and UBC) Tunable coupling of superconducting qubits Quantum Mechanics on the Large Scale, Banff, April 12-17, 2003 A. Blais (Yale University) A. Maassen van den Brink (D-Wave Systems) A.Yu. Smirnov (D-Wave Systems)

3 D-Wave Systems Inc. Direct coupling of superconducting qubits Capacitive coupling - charge qubits Capacitive coupling- CBJJ qubits Pashkin et al., Nature 421 (2003) 823 Blais, Maassen van den Brink, and Zagoskin, PRL 90 (2003) 127901 Johnson et al., PRB 67 (2003) 020509(R)

4 D-Wave Systems Inc. Direct coupling of superconducting qubits Il’ichev et al. (2003) Inductive coupling - 3JJ qubits Makhlin, Schön, and Shnirman, Rev.Mod.Phys. 73 (2001) 357

5 D-Wave Systems Inc. Direct coupling of superconducting qubits Paauw et al. (2002) Inductive+ coupling - 3JJ qubits

6 D-Wave Systems Inc. Direct coupling of superconducting qubits Inductive+ coupling - 3JJ qubits Akisato, quant-ph_0303128 (2002)

7 D-Wave Systems Inc. Coupling through a resonant tank circuit a b

8 D-Wave Systems Inc. Coupling through virtual states Coupled charge qubits Coupled phase qubits Makhlin, Schön, and Shnirman, Rev.Mod.Phys. 73 (2001) 357

9 D-Wave Systems Inc. Qubit-qubit entanglement in cavity QED Rauschenbeutel et al., Science 288 (2000) 2024

10 D-Wave Systems Inc. Superconducting tanks and qubits Ilichev et al., cond-mat/0303433 (2003)

11 D-Wave Systems Inc. Superconducting tanks and qubits Ilichev et al., cond-mat/0303433 (2003)

12 D-Wave Systems Inc. Tunable inductance Assuming  1, we obtain

13 D-Wave Systems Inc. Mediated coupling Blais, Maassen van den Brink, and Zagoskin, PRL 90 (2003) 127901 Plastina and Falci, cond-mat/0206586 (2002)

14 D-Wave Systems Inc. Tuning a large Josephson junction Weak sensitivity to bias noise. Fine tuning. Moderate response to bias current.

15 D-Wave Systems Inc. Coupled CBJJs Blais, Maassen van den Brink, and Zagoskin, PRL 90 (2003) 127901 Qubit

16 D-Wave Systems Inc. CBJJ qubit coupled to a tunable bus In the {|0 q 1 b >, |1 q 0 b >}-subspace Coupling parameter (in resonance) Josephson frequency

17 D-Wave Systems Inc. Coherent qubit-bus oscillations If C j =6 pF, C c =25 fF, I c =21  A, I bias =20.8  A, there are three levels in each well (interlevel spacing ~1 GHz), and coherent oscillations have period T=h/  ~40 ns.

18 D-Wave Systems Inc. Two-qubit operations:

19 D-Wave Systems Inc. Two-qubit operaions: IbIb I b,2 I b,1 I b,decouple

20 D-Wave Systems Inc. Decoupling of CBJJ qubit from the bus Decoupling is achieved if decrease the bus current to I bias =20.43  A. The “degenerate” eigenstates are 0.999|0 q 1 b >+0.007|1 q 0 b >+o(10 -3 ) 0.007|0 q 1 b >+0.999|1 q 0 b >+o(10 -3 )

21 D-Wave Systems Inc. Additional noise in CBJJ qubit-bus system Noise source: bias current fluctuations:

22 D-Wave Systems Inc. Additional noise in CBJJ qubit-bus system In resonance, For T = 25 mK, R = 560 k , C J = 6 pF, C c = 25 fF, I c =20  A T 1,2 ~ 1 ms

23 D-Wave Systems Inc. Quality of coupled CBJJ qubits Blais, Maassen van den Brink, and Zagoskin, PRL 90 (2003) 127901

24 D-Wave Systems Inc. Quality of coupled CBJJ qubits Blais, Maassen van den Brink, and Zagoskin, PRL 90 (2003) 127901

25 D-Wave Systems Inc. Coupled “quantroniums” Blais, Maassen van den Brink, and Zagoskin, PRL 90 (2003) 127901

26 D-Wave Systems Inc. Phase qubits coupled through a resonator Smirnov and Zagoskin, cond-mat/0207214 (2002) CTCT ITIT LTLT IbIb I c C J M1M1 M2M2 I1I1 I2I2

27 D-Wave Systems Inc. Phase qubits coupled through a resonator Smirnov and Zagoskin/cond-mat/0207214 (2002) If both qubits are in a degeneracy point and near resonance: Jaynes-Cummings Hamiltonian

28 D-Wave Systems Inc. Qubit + tank 1212

29 D-Wave Systems Inc. Qubit + tank For a 3JJ phase qubit with I q ~450 nA, L~25 pH, f T ~1 GHz the frequency of the corresponding coherent oscillations is f 0 ~0.1 GHz.

30 D-Wave Systems Inc. State pump

31 D-Wave Systems Inc. State pump

32 D-Wave Systems Inc. State pump

33 D-Wave Systems Inc. State pump

34 D-Wave Systems Inc. State pump

35 D-Wave Systems Inc. State pump

36 D-Wave Systems Inc. State pump

37 D-Wave Systems Inc. State pump

38 D-Wave Systems Inc. State pump

39 D-Wave Systems Inc. State pump

40 D-Wave Systems Inc. Equal qubits, equal couplings No “classical” entanglement! 1 3,4 2

41 D-Wave Systems Inc. (Teleportation) 1/2 For n=0 there are only three constituent states:

42 D-Wave Systems Inc. (Teleportation) 1/2 Starting from the state  in =|0>  (a|1 1 >+b|0 1 >)  | 0 2 >, after time t 1/2 = 2 -1/2   / we reach the state  out =|0>  | 0 1 >  ( -a|1 2 >+b|0 2 >)

43 D-Wave Systems Inc. (Teleportation) 1/2

44 D-Wave Systems Inc. (Teleportation) 1/2

45 D-Wave Systems Inc. (Teleportation) 1/2

46 D-Wave Systems Inc. (Teleportation) 1/2

47 D-Wave Systems Inc. (Teleportation) 1/2

48 D-Wave Systems Inc. (Teleportation) 1/2

49 D-Wave Systems Inc. (Teleportation) 1/2

50 D-Wave Systems Inc. Photon-splitting and qubit-qubit entanglement If instead start from the state  ’ in =|1>  |0 1 >  |0 2 >, and after t B = 2 -3/2   / the Bell state of two qubits is formed: For the above choice of parameters and Q=1000 the decay time in the tank ~ 1  s, while t B ~ 1 ns

51 D-Wave Systems Inc. Phase-charge duality Plastina and Falci, cond-mat/0206586 (2002) The previous results apply to capacitively coupled charge qubits.

52 D-Wave Systems Inc. Phase-charge vocabulary

53 D-Wave Systems Inc. Tunable capacitance Averin and Bruder, cond-mat/0304166 (2003) VgVg C1C1 C2C2 EJEJ C Effective capacitance can also be tuned

54 D-Wave Systems Inc. Conclusions Mediated coupling of qubits through tunable superconducting tank circuits allows: Two-qubit operations; Teleportation of qubit state; Effective coupling/uncoupling of non-tunable qubits; Coupling of qubits of different types; Tank protects qubits from the external noise; Independent optimization of qubit and tank parameters; Can be realized with available experimental techniques.

55 D-Wave Systems Inc. Conclusions Mediated coupling of qubits through tunable superconducting tank circuits allows: Two-qubit operations; Teleportation of qubit state; Effective coupling/uncoupling of non-tunable qubits; Coupling of qubits of different types; Tank protects qubits from the external noise; Independent optimization of qubit and tank parameters; Can be realized with available experimental techniques.

56 D-Wave Systems Inc. Conclusions Mediated coupling of qubits through tunable superconducting tank circuits allows: Two-qubit operations; Teleportation of qubit state; Effective coupling/uncoupling of non-tunable qubits; Coupling of qubits of different types; Tank protects qubits from the external noise; Independent optimization of qubit and tank parameters; Can be realized with available experimental techniques.

57 D-Wave Systems Inc. Conclusions Mediated coupling of qubits through tunable superconducting tank circuits allows: Two-qubit operations; Teleportation of qubit state; Effective coupling/uncoupling of non-tunable qubits; Coupling of qubits of different types; Tank protects qubits from the external noise; Independent optimization of qubit and tank parameters; Can be realized with available experimental techniques.

58 D-Wave Systems Inc. Conclusions Mediated coupling of qubits through tunable superconducting tank circuits allows: Two-qubit operations; Teleportation of qubit state; Effective coupling/uncoupling of non-tunable qubits; Coupling of qubits of different types; Tank protects qubits from the external noise; Independent optimization of qubit and tank parameters; Can be realized with available experimental techniques.

59 D-Wave Systems Inc. Conclusions Mediated coupling of qubits through tunable superconducting tank circuits allows: Two-qubit operations; Teleportation of qubit state; Effective coupling/uncoupling of non-tunable qubits; Coupling of qubits of different types; Tank protects qubits from the external noise; Independent optimization of qubit and tank parameters; Can be realized with available experimental techniques.

60 D-Wave Systems Inc. Conclusions Mediated coupling of qubits through tunable superconducting tank circuits allows: Two-qubit operations; Teleportation of qubit state; Effective coupling/uncoupling of non-tunable qubits; Coupling of qubits of different types; Tank protects qubits from the external noise; Independent optimization of qubit and tank parameters; Can be realized with available experimental techniques.

61 D-Wave Systems Inc. Conclusions Mediated coupling of qubits through tunable superconducting tank circuits allows: Two-qubit operations; Teleportation of qubit state; Effective coupling/uncoupling of non-tunable qubits; Coupling of qubits of different types; Tank protects qubits from the external noise; Independent optimization of qubit and tank parameters; Can be realized with available experimental techniques.

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