DWave Systems Inc.

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D-Wave Systems Inc. THE QUANTUM COMPUTING
COMPANYTM
A.M. Zagoskin (D-Wave Systems and UBC)
Tunable coupling of superconducting qubits
A. Blais (Yale University) A. Maassen van den
Brink (D-Wave Systems) A.Yu. Smirnov (D-Wave
Systems)
Quantum Mechanics on the Large Scale, Banff,
April 12-17, 2003
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D-Wave Systems Inc.
Direct coupling of superconducting qubits
Capacitive coupling - charge qubits
Capacitive coupling- CBJJ qubits
Blais, Maassen van den Brink, and Zagoskin, PRL
90 (2003) 127901
Johnson et al., PRB 67 (2003) 020509(R)
Pashkin et al., Nature 421 (2003) 823
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D-Wave Systems Inc.
Direct coupling of superconducting qubits
Inductive coupling - 3JJ qubits
Makhlin, Schön, and Shnirman, Rev.Mod.Phys. 73
(2001) 357
Ilichev et al. (2003)
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D-Wave Systems Inc.
Direct coupling of superconducting qubits
Inductive coupling - 3JJ qubits
Paauw et al. (2002)
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D-Wave Systems Inc.
Direct coupling of superconducting qubits
Inductive coupling - 3JJ qubits
Akisato, quant-ph_0303128 (2002)
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Coupling through a resonant tank circuit
b
a
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Coupling through virtual states
Coupled charge qubits
Coupled phase qubits
Makhlin, Schön, and Shnirman, Rev.Mod.Phys. 73
(2001) 357
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D-Wave Systems Inc.
Qubit-qubit entanglement in cavity QED
Rauschenbeutel et al., Science 288 (2000) 2024
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Superconducting tanks and qubits
Ilichev et al., cond-mat/0303433 (2003)
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D-Wave Systems Inc.
Superconducting tanks and qubits
Ilichev et al., cond-mat/0303433 (2003)
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Tunable inductance
Assuming ??1, we obtain
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Mediated coupling
Blais, Maassen van den Brink, and Zagoskin, PRL
90 (2003) 127901
Plastina and Falci, cond-mat/0206586 (2002)
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Tuning a large Josephson junction
Moderate response to bias current.
Weak sensitivity to bias noise. Fine tuning.
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Coupled CBJJs
Qubit
Blais, Maassen van den Brink, and Zagoskin, PRL
90 (2003) 127901
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CBJJ qubit coupled to a tunable bus
Josephson frequency
Coupling parameter
In the 0q1bgt, 1q0bgt-subspace
(in resonance)
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Coherent qubit-bus oscillations
If Cj6 pF, Cc25 fF, Ic21 ?A, Ibias20.8
?A, there are three levels in each well
(interlevel spacing 1 GHz), and coherent
oscillations have period Th/?40 ns.
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Two-qubit operations
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Two-qubit operaions
Ib
Ib,2
Ib,decouple
Ib,1
Ib,1
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D-Wave Systems Inc.
Decoupling of CBJJ qubit from the bus
Decoupling is achieved if decrease the bus
current to Ibias20.43 ?A. The degenerate
eigenstates are 0.9990q1bgt0.0071q0bgto(10-3
) 0.0070q1bgt0.9991q0bgto(10-3)
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Additional noise in CBJJ qubit-bus system
Noise source bias current fluctuations
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Additional noise in CBJJ qubit-bus system
In resonance,
For T 25 mK, R 560 k?, CJ 6 pF, Cc 25 fF,
Ic20 ?A T1,2 1 ms
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D-Wave Systems Inc.
Quality of coupled CBJJ qubits
Blais, Maassen van den Brink, and Zagoskin, PRL
90 (2003) 127901
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D-Wave Systems Inc.
Quality of coupled CBJJ qubits
Blais, Maassen van den Brink, and Zagoskin, PRL
90 (2003) 127901
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D-Wave Systems Inc.
Coupled quantroniums
Blais, Maassen van den Brink, and Zagoskin, PRL
90 (2003) 127901
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Phase qubits coupled through a resonator
Ic CJ
Ib
IT
CT
LT
M2
M1
I1
I2
Smirnov and Zagoskin, cond-mat/0207214 (2002)
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Phase qubits coupled through a resonator
If both qubits are in a degeneracy point and near
resonance
Jaynes-Cummings Hamiltonian
Smirnov and Zagoskin/cond-mat/0207214 (2002)
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Qubit tank
1 2
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Qubit tank
For a 3JJ phase qubit with Iq450 nA, L25 pH,
fT1 GHz the frequency of the corresponding
coherent oscillations is f00.1 GHz.
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State pump
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State pump
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D-Wave Systems Inc.
State pump
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D-Wave Systems Inc.
State pump
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D-Wave Systems Inc.
State pump
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D-Wave Systems Inc.
State pump
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D-Wave Systems Inc.
State pump
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D-Wave Systems Inc.
State pump
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D-Wave Systems Inc.
State pump
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D-Wave Systems Inc.
State pump
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Equal qubits, equal couplings
1 3,4 2
No classical entanglement!
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(Teleportation)1/2
For n0 there are only three constituent states
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(Teleportation)1/2
Starting from the state
?in0gt?(a11gtb01gt) ? 02gt, after time
t1/2 2-1/2 ??/? we reach the state
?out0gt? 01gt?( -a12gtb02gt)
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(Teleportation)1/2
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(Teleportation)1/2
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D-Wave Systems Inc.
(Teleportation)1/2
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D-Wave Systems Inc.
(Teleportation)1/2
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D-Wave Systems Inc.
(Teleportation)1/2
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D-Wave Systems Inc.
(Teleportation)1/2
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D-Wave Systems Inc.
(Teleportation)1/2
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D-Wave Systems Inc.
Photon-splitting and qubit-qubit entanglement
If instead start from the state
?in1gt?01gt?02gt,
and after tB 2-3/2 ??/? the Bell state of two
qubits is formed
For the above choice of parameters and Q1000
the decay time in the tank 1 ??s, while tB 1
ns
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Phase-charge duality
The previous results apply to capacitively
coupled charge qubits.
Plastina and Falci, cond-mat/0206586 (2002)
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Phase-charge vocabulary
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Tunable capacitance
Effective capacitance can also be tuned
C2
C1
C
EJ
Vg
Averin and Bruder, cond-mat/0304166 (2003)
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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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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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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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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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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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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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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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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.