Superconducting Qubits Lecture 4 - ETH Z · 2009. 11. 9. · 2-Qubit Chip • Two near identical...
Transcript of Superconducting Qubits Lecture 4 - ETH Z · 2009. 11. 9. · 2-Qubit Chip • Two near identical...
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Superconducting QubitsLecture 4
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Non-Resonant Coupling for Qubit Readout
A. Blais, R.-S. Huang, A. Wallraff, S. M. Girvin, and R. J. Schoelkopf, PRA 69, 062320 (2004)
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Measurement Technique
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Dispersive Shift of Resonance Frequency
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Qubit Spectroscopy with Dispersive Read-Out
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CW Spectroscopy of Cooper Pair Box
D. I. Schuster et al., Phys. Rev. Lett. 94, 123062 (2005)
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Line Shape
Abragam, Oxford University Press (1961)
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Excited State Population
D. I. Schuster, A. Wallraff, A. Blais, L. Frunzio, R.-S. Huang, J. Majer, S. Girvin, and R. J. Schoelkopf, Phys. Rev. Lett. 94, 123062 (2005)
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Line Width
D. I. Schuster, A. Wallraff, A. Blais, L. Frunzio, R.-S. Huang, J. Majer, S. Girvin, and R. J. Schoelkopf, Phys. Rev. Lett. 94, 123062 (2005)
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Coherent Control and Readout in a Cavity
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Coherent Control of a Qubit in a Cavity
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Qubit Control and Readout
Wallraff, Schuster, Blais, ... Girvin, and Schoelkopf, Phys. Rev. Lett. 95, 060501 (2005)
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Varying the Control Pulse Length
Wallraff, Schuster, Blais, ... Girvin, Schoelkopf, PRL 95, 060501 (2005)
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High Visibility Rabi Oscillations
A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, J. Majer, S. M. Girvin, and R. J. Schoelkopf,
Phys. Rev. Lett. 95, 060501 (2005)
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Rabi Frequency
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L. Steffen et al., Quantum Device Lab, ETH Zurich (2008)
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Measurements of Coherence Time
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Coherence Time Measurement: Ramsey Fringes
A. Wallraff et al., Phys. Rev. Lett. 95, 060501 (2005)
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L. Steffen et al., Quantum Device Lab, ETH Zurich (2008)
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Sources of Decoherence
magnetic-field noise?
trapped vortices?
charge fl ct ations?
paramagnetic/nuclear spins?
charge fluctuations?environment circuit modes?
phonons? quasiparticletunneling?
photons?
tunneling?
G. Ithier et al., Phys. Rev. B 72, 134519 (2005)
charge/Josephson-energy fluctuations?
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• remove sources of decoherence• improve materials
• use dynamic methods to counteract specific sources of decoherence• spin echo• geometric manipulations
• reduce sensitivity of quantum systems to specific sources of decoherence• make use of symmetries in design and operation
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Lars Steffen et al. (2009)P. J. Leek, J. Fink et al., Science 318, 1889 (2007)
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Tomography of a Spin Echo
L. Steffen et al., Quantum Device Lab, ETH Zurich (2008)
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Coupling Superconducting Qubits andGenerating Entanglementusing Sideband Transitions
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2-Qubit Chip
• Two near identical superconducting qubits
qubit Bqubit A
~ 8 mm • Local control of magnetic flux allows independent selection of
coupling busp
qubit transition frequencies
• Local drive lines allowLocal drive lines allow selective excitation of individual qubitsqubit A
~selective qubit drive line
et al., Phys. Rev. B 79, 180511(R) (2009)
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2-Qubit Circuit with Selective Control
joint dispersive read-out
Local magnetic fields created using small
Selective qubit excitation using locally capacitively
using small inductively
coupled coilsusing locally capacitively
coupled drive linesP. Leek et al., Phys. Rev. B 79, 180511(R) (2009)
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Sideband Transitions in Circuit QED
‣ dispersive coupling allows joint excitations to be driven
‣ sideband transitions forbidden to first order: use two photon transition
Wallraff et al., PRL 99, 050501 (2007)
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/Resonator Sideband Transitions
simultaneous excitation of qubit and resonator: |g,0> |e,1>simultaneous excitation of qubit and resonator: |g,0> |e,1>
entangle a qubit with a photon on the bus: |g,0> |g,0> + |e,1>
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Bell State Preparation
Transfer
Qubit A π pulse qubit A
Transferentanglement to qubits to createΨ Bell stateΨ Bell state
Cavity
Entangle qubit B with cavity using blue sideband B
Qubit B
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Bell State Preparation π pulse qubit A to convert to
Transfer
Qubit A π pulse qubit A
Φ Bell state
Transferentanglement to qubit A to createΨ Bell stateΨ Bell state
CavityCharacterise the Entangle qubit B with cavity using blue sideband B
final state usingquantum state
tomography with
Qubit B joint msrmnt
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Joint Two Qubit Readout
Amplitude difference (δQ) depends on state of both qubits:
qubit-qubit correlations can be determined from transmission measurement
Filipp et al., Phys. Rev. Lett. 102, 200402 (2009)Majer et al., Nature (London) 445, 443 (2007)
Blais, Huang, Wallraff, Girvin & Schoelkopf, PRA 69, 062320 (2004)
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Pure
experimentalstate fidelity:
F = 86%Pure
F = 100%concurrence:
0.541entanglement of formation :of formation :
0.371
overlap with l l ticalculation
F = 99%
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Pure
experimentalstate fidelity:
F = 86%PureF = 100%concurrence:
0.518entanglement of formation :
0.374
overlap with l l ticalculation
F = 99%
P. Leek et al., Phys. Rev. B 79, 180511(R) (2009)S. Filipp et al., Phys. Rev. Lett. 102, 200402 (2009)
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DiVincenzo Criteria fulfilled for Superconducting Qubits
for Implementing a Quantum Computer in the standard (circuit approach) to quantum information processing (QIP):
#1. A scalable physical system with well-characterized qubits.#2. The ability to initialize the state of the qubits.#3. Long (relative) decoherence times, much longer than the gate-operation time.
#4. A universal set of quantum gates.
#5. A qubit-specific measurement capability.
plus two criteria requiring the possibility to transmit information:
#6. The ability to interconvert stationary and mobile (or flying) qubits.#7. The ability to faithfully transmit flying qubits between specified locations.