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
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) 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(GHz) Exponential suppression of charge noise: charge of suppression Exponential Data: Data: SchoelkopfLab 2007 (unpublished) GateCharge itworks!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, 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