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

Leonardo DiCarlo Leonardo DiCarlo Superconducting quantum circuits: Superconducting quantum circuits: Circuit QED 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 Resonator modes (usually we focus on fundamental) are set by l the total resonator length I the end terminations (short or open circuit) the phase velocity (slower than speed of light in vacuum by factor 2-3) Transmon qubit l Short-circuited end Open-circuited end µ 100 m Transmission-line resonator The coupling between qubit and resonator is typically capacitive

Qubit-resonator interaction w q I qubit resonator Transmon qubit w 2 g r µ 100 m Houck et al., Nature (2007) Transmission-line resonator Qubit flux bias (arbitrary units) ( ) ˆ = s + s 2 g ˆ † ˆ H ! g a a Jaynes-Cummings interaction + - int r r

Dispersive regime n = - 2 D 2 2 g / w n = 1 q + D 2 g 2 / Photon resonator qubit n = 2 / 1 - D g ladder n = w 0 2 / + D g 2 g r w w q r D = w - w n = q r 0 1 0 Qubit flux bias (arbitrary units) c = 2 D 2 2 g / Dispersive regime: D = w - w >> g q r 1 0 ˆ = - ! cs † ˆ Z H a a int r r w r w + D w - D 2 2 g / g / r r

Dispersive qubit-qubit interactions right qubit right qubit left qubit left qubit Cavity-qubit resonant interaction Vacuum Rabi splitting 2 g cavity 2g V R Flux bias on right transmon (a.u.) DiCarlo et al. , Nature (2009)

Dispersive qubit-qubit interactions right qubit right qubit left qubit ( ) ´ D 2 g g / Dispersive qubit-qubit natural slow-down swap interaction speed factor ~1/10 left qubit D 2 2 g / D cavity V R Flux bias on right transmon (a.u.) DiCarlo et al. , Nature (2009)

First-generation two-qubit quantum processor Flux line Transmon Single resonator Transmon Flux line 1 mm One resonator for both qubit-qubit coupling and for readout DiCarlo et al. , Nature (2009)

Second-generation two-qubit processor Bus resonator Readout Readout resonator resonator Feedline 1 mm Different resonators for qubit-qubit coupling and for readout of each qubit Groen et al ., Phys. Rev. Lett. (2013)

Second-generation four-qubit processor Readout Readout resonator resonator Bus resonator Feedline Feedline Readout Readout resonator resonator 1 mm Different resonators for qubit-qubit coupling and for readout of each qubit Saira et al ., Phys. Rev. Lett. (2014)

Second-generation five-qubit processor Challenge: identify the readout resonators and bus resonators 1 mm Different resonators for qubit-qubit coupling and for readout of each qubit Riste et al ., Nature Communications (2015)

Connections to external circuitry