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Departments of and ,

Quantum computation and with circuit QED

Jens Koch

filling in for Steven M. Girvin Quick outline

Superconducting

overview and challenges

from the CPB to the

Circuit QED

basic concept

:

coupling of qubits over long distance

( with circuits)

Outlook Departments of Physics and Applied Physics, Yale University Circuit QED at Yale

EXPERIMENT THEORY

PIs: Rob Schoelkopf, 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) (ETH Zurich) R. Huang (Taipei) K. Moon (Yonsei)

Sometimes… noise is NOT the signal! [… sorry, Mr. Landauer]

• Noise can lead to relaxation ( ) bad for ! dephasing ( )

• Persistent problem with superconducting qubits: short

Reduce noise itself Reduce sensitivity to noise

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 , 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) Frequency (GHz) Exponential suppression of charge noise: charge of suppression Exponential Data: Data: SchoelkopfLab 2007 (unpublished) GateCharge itworks! GateCharge 15 15 MHz 8 MHz 1 MHz 100 100 MHz 30 MHz E 25 J 14 10 17 20 /Ec γ , κ κ > g = vacuum Rabi freq. Rabi vacuum = quantumfeedback = cavity decay rate cavity = decay

= “transverse”= rate decay

κ γ κ κκ γ γγ 2g open quantumsystems strongcoupling:

quantuminformation processing

electrodynamics couplingatom discrete / modeof EM field • • centralparadigm of for study Cavity Cavity circuit& quantum

coherentcontrol, conditional quantumevolution, decoherence

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, 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) 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, 449 , 443 (2007)

two (several) qubits in resonator multiplexed control and readout

coupling via virtual 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 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 one and two-qubit gates multiplexed control and readout via the cavity quantum optics with circuits