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1. COUPLING SUPERCONDUCTING QUBITS
VIA A CAVITY BUS
MAJER ET.AL. NATURE (2007)
OVIDIU COTLET AND LÁSZLÓ SZŐCS
5/12/2012 Majer et al. Nature (2007) 1

2. DiVincenzo’s Criteria for
Quantum Computing
1. Scalability and well-defined qubits
2. Initialization of qubits
3. Small decoherence
4. 1 and 2 qubit gates
5. Measurement
arXiv:cond-mat/9612126
5/12/2012 Majer et al. Nature (2007) 2

3. Motivation
o Previous studies have shown that two
nearby qubits can be coupled with local
interactions
o Highly desirable to perform gate
operations between two distant qubits
– How to accomplish?
– Use a quantum bus (cavity photons) to
transfer information Strong coupling limit

o Why use photons?
5/12/2012 Majer et al. Nature (2007) 3

4. Experiment Goals
o Demonstrate a coherent, nonlocal
coupling between two qubits in a
transmission line cavity
o Cavity mediates the qubit-qubit interaction
via photons
Blais et al. Rhy. Rev. A (2007)
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5. THEORY
o Begin with the Jaynes Cummings (JC)
Hamiltonian
o Eigenstates and eigenenergies readily obtained
o Vacuum Rabi splitting can be observed by
moving to a rotating frame and solving the
equations of motion
5/12/2012 Majer et al. Nature (2007) 5

6. THEORY
o The solution is
, which produces 2 peaks at
o This allows for a measurement of the
coupling constant
5/12/2012 Majer et al. Nature (2007) 6

7. Theory
o Consider the strongly dispersive limit,
o Using the canonical Schrieffer-Wolf
Transformation, eliminate interaction term
to 1st order
5/12/2012 Majer et al. Nature (2007) 7

8. THEORY
o That was for 1 qubit. How about 2?
o Natural generalization:
o Can easily show that
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9. THEORY
o Salient features:
– No TLS-cavity interaction (no energy is
exchanged)
– Cavity frequency shifted by qubit state
– Qubit-qubit interaction can be effectively
turned off by making the qubits strongly
detuned from one another:
5/12/2012 Majer et al. Nature (2007) 9

10. THEORY
o A.C. Stark Shift: rearrange the Hamiltonian
o By applying a strongly detuned drive, we can
adjust the number of photons in the
cavity, thereby adjusting the qubit transition
frequency.
5/12/2012 Majer et al. Nature (2007) 10

11. Experiment Setup
5/12/2012 Majer et al. Nature (2007) 11

12. Strong Qubit-Cavity Coupling
o Demonstrate that each-qubit can be
strongly coupled to the cavity
o Use vacuum Rabi splitting to determine
the coupling constants
o Ensures that we can go into strongly
dispersive limit and that qubit-qubit
coupling is big
5/12/2012 Majer et al. Nature (2007) 12

13. Strongly Dispersive Limit
o Cavity shields qubits from the
environment.
o Can further isolate qubit by strongly
detuning it from the cavity
5/12/2012 Majer et al. Nature (2007) 13

14. Qubit-Qubit Interaction
o Qubits interact by exchanging their
excitations through virtual photons in the
cavity:
5/12/2012 Majer et al. Nature (2007) 14

15. Single Qubit Control
o Demonstrate fast control of each qubit
individually in order to satisfy the 1st part
of criteria 4
o Detune the qubits from one another:
o Apply a pulse at , then apply a
measurement pulse at to monitor
transmission
o From transmission, infer :
5/12/2012 Majer et al. Nature (2007) 15

16. Single Qubit Control
o Response consistent with that of single qubit Rabi
oscillation  coupling does not affect single qubit
operation
o Determine decoherence time to be 78 and 120
ns, which is larger than the coherent manipulation
time
5/12/2012 Majer et al. Nature (2007) 16

17. Multiplex Measurement
o Use π pulses to put your qubits into desired states:
o Use probing field resonant with cavity and compare
theoretical (via master equation) with actual value
5/12/2012 Majer et al. Nature (2007) 17

18. Coherent State Transfer Between
Qubits
o Can transfer the state of one qubit to the
other by turning qubit-qubit coupling on
and off
o Use off-resonant Stark drive to quickly push
qubits into resonance
5/12/2012 Majer et al. Nature (2007) 18

19. Coherent State Transfer
1. Initially qubits are 80 MHz detuned, and are
allowed to relax to
2. Apply π pulse to create or
3. Apply Stark pulse to bring qubits into
resonance for some variable time
Because not eigenstates of
system, we’ll see oscillation
5/12/2012 Majer et al. Nature (2007) 19

20. Coherent State Transfer
o Quarter period of
oscillation between
qubits is
o This is the second
part of
DiVincenzo’s
criterion 4
5/12/2012 Majer et al. Nature (2007) 20

21. Coherent State Transfer
o Observed qubit-qubit
oscillation frequency
agrees very well with
value of J measured
from CW spectroscopy
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22. Summary
o Demonstrated non-local coupling of qubits
o Qubit-qubit interaction is due to the
exchange of virtual photons, protecting
against cavity induced losses
o Qubits may be manipulated individually
and a universal 2 qubit gate can be
performed
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23. Summary
1. ✓
Scalability and well-defined qubits
2. Initialization of qubits ✓
3. Small decoherence ✓
4. 1 and 2 qubit gates ✓
5. Measurement ✓
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24. Thank you for your time and attention.
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