Josephson Flux Qubits in Charge-Phase Regime

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Josephson Flux Qubits in Charge-Phase Regime

• M. H. S. Amin

D-Wave Systems Inc., Vancouver, Canada
Thanks to
P. Echternach (JPL) M. Grajcar (IPHT/Comenius) E.
Ilichev (IPHT) M. Kenyon (JPL) A. Kleinsasser
(JPL)
A. Maassen van den Brink (D-Wave) G. Rose
(D-Wave) A. Shnirman (Kalsruhe) A. Smirnov
(D-Wave) A. Zagoskin (D-Wave)
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Charge Qubit vs Flux Qubit
r EC /EJ
Charge qubits r gtgt1
Flux qubits r ltlt1
3
Decoherence Time t
Charge qubit
NEC/Chalmers/JPL t 5 ns
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Problems with Flux Qubits
1. Single shot readout difficult
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Problems with Flux Qubits
1. Single shot readout difficult
2. Exponential dependence of D on qubit
parameters
3. Controllable coupling difficult
4. Large sensitivity to flux noise
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Why Charge-Phase Regime?

• The effects of both charge and flux noise
• can be minimized
• Readout can be easily switched on and off
• Two degrees of freedom (instead of one) are
• available for e.g. coupling and readout
• Smaller sensitivity to system parameters

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Quantronium Qubit
E
1?
EJ
0?
ng
1/2
0? 2-1/2 ( n? n1?) . . .
Qubit States
1? 2-1/2 ( n? - n1?) . . .
Uncertainty in Charge ? Localization of phase
Phase can be used for readout
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Quantronium Qubit

E
2p
persistent currents
j

i
F0
j
d
Magic point
E01
d/2p
ng
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Dual of Quantronium
Flux qubit
E
D
Energy Levels
1/2
Fe/ F0
Uncertainty in phase ? Localization of charge
What charge?
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Aharonov-Casher Effect
Aharonov-Bohm effect
e
F
Interference
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Aharonov-Casher Effect
F
Q
Interference
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Aharonov-Casher Effect
J.R. Friedman and D.A. Averin, PRL (2002).
t1
t1
Cg
F
Vg
t2
t2
? Two paths for flux to tunnel ? Interference
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Two Josephson Junction Qubit
Cg
Q
Vg
To charge/voltage detector
F
Coupling can be switched off during the operation
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Three Josephson Junction Qubit
h t2 /t1
t1
t2
T.P. Orlando et al. PRB 60, 15398 (1999)
? Small flux, small coupling to environment ?
Two islands available for coupling
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Energy Eigenstates
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Energy Eigenstates
Effective Hamiltonian
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Energy Eigenstates
Effective Hamiltonian
r EC /EJ
Eigenenergies
h t2 /t1
nA (VgACg/2e)
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Energy Eigenstates
Effective Hamiltonian
r EC /EJ
Eigenenergies
h t2 /t1
nA (VgACg/2e)
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Island Voltages
At f Fx/F0-1/2 0
Magic Point nA nB f 0 ? VA VB
0
No Coupling
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Island Voltages
At f Fx/F0-1/2 0
Magic Point nA nB f 0 ? VA VB
0
No Coupling
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Island Voltages
At f Fx/F0-1/2 0
Magic Point nA nB f 0 ? VA VB
0
No Coupling
Coupled regime ? VA Max ,
VB 0
Directional Coupling
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Some Numerics
Small sensitivity to system parameters at large
r ( EC /EJ)
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Readout Scheme
Switchable Readout
Sensitive charge (voltage) detector
Off Vg 0 during the operations On
Vg e/2Cg at the time of readout
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Two Qubit Coupling
Switchable Coupling
Qubits are coupled only if V(1)gB ? 0 and
V(2)gA ? 0.
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Multi-Qubit Coupling
Coupling via a bus island
Can couple every two qubits
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Multi-Qubit Coupling
Nearest neighbors coupling
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Suggested Parameters
EC / EJ 0.1, a 0.8, Cg 0.1 C D ?
5.6 GHz, h ? 0.13 Island Voltage
VA ? 3.7 mV Island Charge QA
? 0.2e QA large enough to be measured by rf-SET
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Comparison with Other Qubits
3JJ flux qubit
Charge-phase qubit
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Comparison with Other Qubits
3JJ flux qubit
Charge-phase qubit
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Comparison with Other Qubits
3JJ flux qubit
Charge-phase qubit
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Comparison with Other Qubits
Quantronium qubit Charge-phase
qubit
Same sensitivity to background charge noise
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Comparison with Other Qubits
Quantronium qubit Charge-phase
qubit
Same sensitivity to background charge noise
Anharmonicity A (E21- E10 )/ E10
Harmonic oscillator A 0
Ideal qubit A ?
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Comparison with Other Qubits
Quantronium qubit Charge-phase
qubit
Same sensitivity to background charge noise
A 0.2 A
1.7
10 times better anharmonicity
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Conclusion
-Operation in charge-phase regime is possible and
desirable for flux qubits -Single shot readout
possible with no effect on other
qubits -Controlled coupling to other qubits
easily achievable
Compared to the 3JJ qubit -Three orders of
magnitude less sensitive to flux fluctuations
-Smaller L, i.e. smaller coupling to the
magnetic environment -One order of magnitude
less sensitive to system parameters
Compared to the quantronium - Same
sensitivity to the background charge
fluctuations - 10 times larger
anharmonicity
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Conclusion
-Operation in charge-phase regime is possible and
desirable for flux qubits -Single shot readout
possible with no effect on other
qubits -Controlled coupling to other qubits
easily achievable
Compared to the 3JJ qubit -Three orders of
magnitude less sensitive to flux fluctuations
-Smaller L, i.e. smaller coupling to the
magnetic environment -One order of magnitude
less sensitive to system parameters
Compared to the quantronium - Same
sensitivity to the background charge
fluctuations - 10 times larger
anharmonicity
36
Conclusion
-Operation in charge-phase regime is possible and
desirable for flux qubits -Single shot readout
possible with no effect on other
qubits -Controlled coupling to other qubits
easily achievable
Compared to the 3JJ qubit -Three orders of
magnitude less sensitive to flux fluctuations
-Smaller L, i.e. smaller coupling to the
magnetic environment -One order of magnitude
less sensitive to system parameters
Compared to the quantronium - Same
sensitivity to the background charge
fluctuations - 10 times larger
anharmonicity
37
Conclusion
-Operation in charge-phase regime is possible and
desirable for flux qubits -Single shot readout
possible with no effect on other
qubits -Controlled coupling to other qubits
easily achievable
Compared to the 3JJ qubit -Three orders of
magnitude less sensitive to the flux
fluctuations -Smaller L, i.e. smaller
coupling to the magnetic environment -One
order of magnitude less sensitive to system
parameters
Compared to the quantronium - Same
sensitivity to the background charge
fluctuations - 10 times larger
anharmonicity
38
Conclusion
-Operation in charge-phase regime is possible and
desirable for flux qubits -Single shot readout
possible with no effect on other
qubits -Controlled coupling to other qubits
easily achievable
Compared to the 3JJ qubit -Three orders of
magnitude less sensitive to flux fluctuations
-Smaller L, i.e. smaller coupling to the
magnetic environment -One order of magnitude
less sensitive to system parameters
Compared to the quantronium - Same
sensitivity to the background charge
fluctuations - 10 times larger
anharmonicity
39
Conclusion
-Operation in charge-phase regime is possible and
desirable for flux qubits -Single shot readout
possible with no effect on other
qubits -Controlled coupling to other qubits
easily achievable
Compared to the 3JJ qubit -Three orders of
magnitude less sensitive to flux fluctuations
-Smaller L, i.e. smaller coupling to the
magnetic environment -One order of magnitude
less sensitive to system parameters
Compared to the quantronium - Same
sensitivity to the background charge
fluctuations - 10 times larger
anharmonicity