Control and Measurement of Multiple Qubits in Circuit Quantum Electrodynamics Andreas Wallraff (ETH Zurich) www.qudev.ethz.ch M. Baur, D. Bozyigit, R. Bianchetti, C. Eichler, S. Filipp, J. Fink, T. Frey, C. Lang, P. Leek, G. Littich, G. Puebla-Hellmann, L. Steffen, A. van Loo (ETH Zurich) A. Blais (Sherbrooke Sherbrooke, Canada) J. Gambetta (Waterloo, Canada)
Controlling the Interaction of Light and Matter...... is challenging on the level of single (artificial) atoms and single photons dipole moment d (usually small in atoms ~ ea 0 ) single photon fields E 0 (small in 3D) photon/atom interaction (usually small) d and E 0 can be controlled in superconducting circuits: perform basic quantum optics experiments D. Walls, G. Milburn, Quantum Optics (Spinger-Verlag, Berlin, 1994)
Cavity Quantum Electrodynamics
Circuit Realization of Cavity QED with individual photons and qubits...... in superconducting circuits: A. Blais, et al., PRA 69, 062320 (2004) A. Wallraff et al., Nature (London) 431, 162 (2004)
elements: the cavity: a superconducting 1D transmission line resonator with large vacuum field E 0 and long photon life time 1/ the artificial atom: a superconducting qubit with large dipole A. Blais et al., PRA 69, 062320 (2004)
Resonant Vacuum Rabi Mode Splitting first demonstration in a solid: A. Wallraff et al., Nature (London) 431, 162 (2004) this data: J. Fink et al., Nature (London) 454, 315 (2008) R. J. Schoelkopf, S. M. Girvin, Nature (London) 451, 664 (2008)
5 Years of Quantum Electrodynamics with Circuits Vacuum Rabi Mode Splitting A. Wallraff et al., Nature 431, 162 (2004) Coherent Flux-Qubit / SQUID Coupling I. Chiorescu et al., Nature 431, 159 (2004) Quantum AC-Stark Shift D. Schuster et al., Nature 445, 515 (2007) Lamb Shift A. Fragner et al., Science 322, 1357 (2008) Fock and Arbitrary Photon States M. Hofheinz et al., Nature 454, 30(2008) 310 M. Hofheinz et al., Nature 459, 546 (2009) Root n Nonlinearity J. Fink et al., Nature 454, 315 (2008) Two Photon Nonlinearities F. Deppe et al., Nat. Phys. 4, 686 (2008) Super Splitting and Root n Nonlinearity L. Bishop et al., Nat. Phys. 5, 105 (2009) Single Photon Source A. Houck et al.,, Nature 449,328 (2007) Single Qubit MASER O. Astafiev et al., Nature 449, 588 (2007) Cooling and Amplification M. Grajcar et al., Nat. Phys. 4, 612 (2008) Quantum Bus M. Sillanpaa et al., Nature 449, 438 (2007) H. Majer et al., Nature 449, 443 (2007) L. DiCarlo et al., Nature 460, 240-244 (2009)
Cavity QED with Multiple Photons Atoms coupling n photons to single atom li N t t i l h t. Rev. Lett. 103, 083601 (2009)
Multi-Atom Cavity QED
Multi-Qubit Circuit QED Schematic
Three Qubit Circuit QED Setup
Three Qubit Circuit QED Sample
N = 1, 2, 3 Qubit Cavity Anti Crossing, Phys. Rev. Lett. 103, 083601 (2009)
the spectrum: the states: states equally shared between photon and qubit
the spectrum: the states: bright states: superposition of a photon and a Bell state dark state
the spectrum: the states: one photon plus three qubit entagled W-state two dark states
the spectrum: scaling of collective coupling with J. Fink et al., Phys. Rev. Lett. 103, 083601 (2009)
This work: excitation spectrum of 4 coupled quantum systems measured Tavis-Cummings model tested in the discrete limit a step towards multi-qubit QIPC in circuit QED The future: investigate collective excitations with small but fixed number of qubits Dicke states superradiance generate complex entangled states using collective interactions
quantum bus g g g Leek et al., Phys. Rev. B 79, 180511(R) (2009) controlling photon life times on the quantum bus P. Leek, M. Baur et al., Quantum Device Lab (2009) measuring entanglement t by joint read-out with a single detector t Filipp et al., Phys. Rev. Lett. 102, 200402 (2009)
Circuit QED for Quantum Information Processing benefits of architecture: isolation of qubits from environment maintains i addressability quantum non-demolition qubit read out conversion of quantum information between qubits and photons long-range photon mediated qubit/qubit interactions
Out of Single Qubit L. Steffen et al., Quantum Device Lab, ETH Zurich (2008)
Qubit Coherence: Tomography of Ramsey Experiment
qubit A qubit B Two near identical superconducting qubits ~ 8 mm Local control of coupling bus magnetic flux allows independent selection of qubit transition frequencies qubit A Local drive lines allow selective excitation of individual qubits ~ selective qubit drive line
/Resonator Sideband Transitions 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>
standard resonator configuration coupled at in and output: all modes: nominally identical Q identical photon life time P. Leek et al., Quantum Device Lab (2007-2009)
Engineering Mode Dependent Photon Life Times center coupled resonator configuration: odd modes are decoupled: high Q long photon life time coherent manipulation P. Leek et al., Quantum Device Lab (2007-2009)
Engineering Mode Dependent Photon Life Times center coupled resonator configuration: even modes are strongly coupled: low Q short photon life time dispersive qubit measurement P. Leek et al., Quantum Device Lab (2007-2009)
Realization P. Leek et al., Quantum Device Lab (2007-2009)
fundamental: odd mode decoupled high Q long life time storage mode 1 st harmonic: even mode coupled low Q short life time measurement mode 2 nd harmonic: odd decoupled high Q long life time storage mode P. Leek et al., Quantum Device Lab (2007-2009)
low Q mode (T 1 1 ~ 39 ns) high Q mode (T 2 1 ~1600ns) M. Baur, P. Leek et al., Quantum Device Lab (2009)
Fock-State (n=1) : create Fock state with blue sideband pulse return qubit to g> wait bring qubit to e> annihilate Fock state with blue sideband pulse measure qubit state : high Q photon T 1, ~ 1.45 s M. Baur, P. Leek et al., Quantum Device Lab (2009)
pulse sequence: high Q photon T * ~ 19 s 1.9 T 2, M. Baur, P. Leek et al., Quantum Device Lab (2009)
Side Band Rabi Oscillations with Fock-States n = 0, 1, 2 p p states with BSB Ω 1 scaling of Rabi frequency Ω n nω 1 2Ω1 imperfections due to preparation 3Ω1 MB M. Baur, P. PLeek et al., Quantum Device Lab (2009) prospects: p towards ion-trap style 2-qubit gates (sideband CNOT gate): Cirac/Zoller, Sorensen/Molmer, Chuang,...
Two-Mode Bell-State Generation and Measurement
Two-Mode Bell-State Generation and Measurement storage measurement P. Leek, M. Baur et al., Quantum Device Lab (2009)
Photons: Weihs et al., PRL 81 (1998); supercond. qubits: Steffen et al., Science 313 (2006).
Correlation Measurement with Individual Readout table of single shot values (±1): k σ k z 1 1 +1 2-1 K -1
Correlation Measurement with Individual Readout table of single shot values (±1): k σ k z 1 1 σ k z 1 +1 +1 2-1 -1 K -1 +1
Correlation Measurement with Individual Readout table of single shot values (±1): k σ k z 1 1 σ k z σ k z σ k z 1 +1 +1 (+1).(+1) = +1 2-1 -1 (-1).(-1) = +1 K -1 +1 (-1).(+1)=-1
Correlation Measurement with Individual Readout rotation of qubit: h σ x 1i, h 1 σ z i and h σ x σ z i are measured
Correlation Measurement with Individual Readout orh σ x 1i, h 1 σ y i and h σ x σ y i, a.s.o. -> all combinations of {σ x, σ y, σ z } give full information about the state
Correlation Measurement with Joint Readout Circuit QED-Setup: only single detection device plus single qubit operations
Homodyne Measurement of Cavity Frequency Shift Amplitude difference (δq) depends on state of both qubits: qubit-qubit correlations can be determined from transmission measurement & Schoelkopf, PRA 69, 062320 (2004)
experimental state fidelity: F = 86% concurrence: Pure F 0.541 = 100% entanglement of formation : 0.371 overlap with calculation l F = 99%
experimental state fidelity: F = 86% Pure concurrence: F = 100% 0.518 entanglement of formation : 0.374 overlap with calculation l F = 99% P. Leek et al., Phys. Rev. B 79, 180511(R) (2009) S. Filipp et al., Phys. Rev. Lett. 102, 200402 (2009)
N atom cavity QED... test of Tavis-Cummings model... generation of all 4 Bell states using sidebands... towards a universal gate... realization of two qubit tomography correlations w/o single-shot measurement using joint dispersive read-out
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