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Quantum Computation and Quantum Optics with Circuit QED

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Quantum Computation and Quantum Optics with Circuit QED Departments of Physics and Applied Physics, Yale University Quantum computation and quantum optics with circuit QED Jens Koch filling in for Steven M. Girvin Quick outline Superconducting qubits overview and challenges from the CPB to the transmon Circuit QED basic concept quantum bus: coupling of qubits over long distance ( quantum optics with circuits) Outlook Departments of Physics and Applied Physics, Yale University Circuit QED at Yale EXPERIMENT THEORY PIs: Rob Schoelkopf, Michel Devoret PI: Steve Girvin Jay Gambetta Jens Koch Andrew Houck David Schuster Terri Yu Lev Bishop Johannes Majer Luigi Frunzio David Price Daniel Ruben Jerry Chow Joseph Schreier Blake Johnson Emily Chan Alexandre Blais (Sherbrooke) Jared Schwede Joe Chen (Cornell) Cliff Cheung (Harvard) Aashish Clerk (McGill) Andreas Wallraff (ETH Zurich) R. Huang (Taipei) K. Moon (Yonsei) Sometimes… noise is NOT the signal! [… sorry, Mr. Landauer] • Noise can lead to energy relaxation ( ) bad for qubit! dephasing ( ) • Persistent problem with superconducting qubits: short Reduce noise itself Reduce sensitivity to noise materials science approach design improved quantum circuits eliminate two-level fluctuators find smart ways to beat the noise! J. Martinis et al., PRL 95, 210503 (2005) Paradigmatic example: sweet spot for the Cooper Pair Box Quantronics Group (Saclay) D. Vion et al., Science 296 , 886 (2002). CPB as a charge qubit, sweet spot Charge limit: big small perturbation sweet spot only sensitive nd energy to 2 order fluctuations in gate charge! Vion et al., (gate charge) Science 296 , 886 (2002) Make the sweet spot sweeter: increase E J/E C charge dispersion anharmonicity Steve can see it with his naked eye! Anharmonicity Flatter charge dispersion, decreases… become insensitive to charge noise ! …only Island volume ~1000 times bigger algebraically …exponentially! than conventional CPB island Quantum rotor picture for the CPB Schrödinger eq. for the CPB circuit (phase basis) quantum rotor (charged, in constant has exact solution magnetic field ) (Mathieu functions, Mathieu characteristic values) Exponential suppression of charge noise: it works! Data: Schoelkopf Lab 2007 (unpublished) EJ/Ec 1 MHz 25 8 MHz 20 15 MHz 17 14 30 MHz 10 Frequency (GHz) Frequency 100 MHz Gate Charge Gate Charge Cavity & circuit quantum electrodynamics • coupling atom / discrete mode of EM field • central paradigm for study of open quantum systems coherent control, quantum information processing conditional quantum evolution, quantum feedback decoherence 2g = vacuum Rabi freq. κκκ = cavity decay rate γγγ = “transverse” decay rate strong coupling: g > κ , γ Coupling transmon - resonator qubit coupling to resonator: resonator mode coupling becomes even bigger! Generalized Jaynes-Cummings Hamiltonian Dispersive limit: dynamical Stark shift Hamiltonian QND readout, coherent control Strong coupling to cavity CPB 2g = 12MHz • Transition dipole matrix element gets larger • Measure vacuum Rabi avoided crossings to see large coupling Transmon: 2g ~ 350 MHz (coupling even stronger!) Data: Schoelkopf Lab 2007 (unpublished) Coherence in 2 nd generation transmon T Measurement 1 Schoelkopf Lab 2007 µ At flux sweet spot: T1 = 2.8 s still not limited by 1/f noise! Ramsey experiment dephasing time µ T2 = 1.75 s no echo, not at flux sweet spot Consistent T 1 times for seven qubits Cavity as a Quantum Bus: circuit QED with two qubits Schoelkopf Lab – J. Majer, …, M.H. Devoret, S.M. Girvin, R.J. Schoelkopf, Nature 449 , 443 (2007) two (several) qubits in resonator multiplexed control and readout coupling via virtual photons resonator as “quantum bus” similar work: M.A. Sillanpää, J.I. Park, R.W. Simmonds, Nature 449 , 438 (2007) 1 and 2-qubit gates with the quantum bus Control and measurement of individual qubits Coherent 2-qubit oscillations Design for six qubits coupled on a single bus, with individual flux control Q1 Q2 Q3 In Out Q4 Q5 Q6 Sample box with 6 flux lines: qubit addressing, 8 x 20 GHz connections 2 flux lines: input/output for measurement and control Schoelkopf lab Summary • Need to improve coherence in superconducting qubits reduce overall noise (materials science) reduce sensitivity to noise (sweet spots, new quantum circuits) transmon • Transmon: optimized CPB by increasing become exponentially insensitive to charge noise! retain sufficient anharmonicity (loss only algebraic) µ µ confirmed in recent experiments (T 1~3 s, T 2~2 s) • circuit QED with transmons one and two-qubit gates multiplexed control and readout via the cavity quantum optics with circuits.
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