Leonardo DiCarlo Leonardo DiCarlo Superconducting quantum circuits: - - PowerPoint PPT Presentation

Leonardo DiCarlo

Superconducting quantum circuits: Circuit QED

Leonardo DiCarlo

Superconducting quantum circuits: Circuit QED

Circuit QED: Cavity QED with wires

Josephson-junction qubits Transmission-line resonators

• mediate interaction between qubits
• allow qubit readout

Blais et al., Phys. Rev. A (2004)

Qubit-resonator interaction

100 m µ

I

Transmission-line resonator Transmon qubit

The coupling between qubit and resonator is typically capacitive Resonator modes (usually we focus on fundamental) are set by

the total resonator length the end terminations (short or open circuit) the phase velocity (slower than speed of light in vacuum by factor 2-3)

l l

Short-circuited end Open-circuited end

Qubit-resonator interaction

resonator qubit

r

w

q

w

Qubit flux bias (arbitrary units)

2g

100 m µ

I

Transmission-line resonator Transmon qubit

( )

† int r r

ˆ ˆ ˆ H g a a s s

+

• =

+ !

Jaynes-Cummings interaction

2g

Houck et al., Nature (2007)

Dispersive regime

resonator qubit

2g

Qubit flux bias (arbitrary units)

1 n = 2 n = 1 n =

n =

r

w

q

w n =

g

• D

g + D

2 / g

• D

2 / g + D r

w

r

w

q

w

2

2 2 / g c = D

2 r

/ g w - D

2 r

/ g w + D

Dispersive regime:

q r

g w w D =

• >>

q r

w w D =

• †

int r r

ˆ ˆZ H a a cs = -!

Photon ladder

1 1

left qubit right qubit

Dispersive qubit-qubit interactions

cavity left qubit right qubit Cavity-qubit resonant interaction Vacuum Rabi splitting

R

V

Flux bias on right transmon (a.u.)

2g

2g

DiCarlo et al., Nature (2009)

Dispersive qubit-qubit interactions

Dispersive qubit-qubit swap interaction cavity left qubit right qubit

R

V

Flux bias on right transmon (a.u.)

2

2 / g D D

( )

2 / g g ´ D

slow-down factor ~1/10 natural speed

left qubit right qubit DiCarlo et al., Nature (2009)

First-generation two-qubit quantum processor

1 mm One resonator for both qubit-qubit coupling and for readout Flux line Flux line Single resonator Transmon Transmon

DiCarlo et al., Nature (2009)

Groen et al., Phys. Rev. Lett. (2013)

Second-generation two-qubit processor

Different resonators for qubit-qubit coupling and for readout of each qubit Bus resonator

Readout resonator Readout resonator

Feedline 1 mm

Saira et al., Phys. Rev. Lett. (2014)

Second-generation four-qubit processor

Different resonators for qubit-qubit coupling and for readout of each qubit Bus resonator

Readout resonator Readout resonator Readout resonator Readout resonator

1 mm

Feedline Feedline

Second-generation five-qubit processor

Different resonators for qubit-qubit coupling and for readout of each qubit

Riste et al., Nature Communications (2015)

Challenge: identify the readout resonators and bus resonators

1 mm

Connections to external circuitry