Superconducting for analogue quantum simulation

Gerhard Kirchmair

Workshop on Quantum Science and Quantum Technologies ICTP Trieste

September 13th 2017 Experiments in Innsbruck on cQED

Quantum Simulation using cQED Quantum Magnetomechanic

Josephson Junction array resonators Outline

• Introduction to Circuit QED – Cavities – Qubits – Coupling

• Analog quantum simulation of models – 3D as Spins – Simulating dipolar quantum magnetism – First experiments cavity QED → circuit QED

optical photons atoms as two level systems ⇓ optical resonators ⇓ microwave photons ⇓ nonlinear quantum circuits microwave resonators QIP, , quantum measurement…

Many groups around the world: Yale University, UC Santa Barbara, ETH Zurich, TU Delft, Princeton, University of Chicago, Chalmers, Saclay, KIT Karlsruhe … Cavities Waveguide microwave resonator

~ 휆/2

Observed Q’s > 106 b

퐸

a Reagor et.al. Appl. Phys. Lett. 102, 192604 (2013) Quantum Circuits Around a resonance: Energy

Φ ← 퐿 퐶 → 푄 2 1 Classical drive 0

2 2 Φ 푄 Φ 퐻 = + 2 퐶 2 퐿

ℏ ℏ 푍 푄 = 푎 + 푎† Φ = 푖 0 푎 − 푎† 2 푍0 2 퐿 푍0 = ⟶ 1 … 100 Ω 1 퐶 퐻 = ℏ휔 푎†푎 + 0 2 1 휔 = ⟶ 4 … 10 퐺퐻푧 Quantum Harmonic Oscillator 0 퐿퐶 Qubits – 3D Josephson Junction

Superconductor(Al)

1 nm Insulating barrier

Superconductor (Al)

퐻 = −퐸푗 cos 휑

2 푄 퐻 = −퐸 cos 휑 + 푗 2 퐶 Superconducting Qubits - Transmon Energy Transmon

C 2 1 0 Φ

2 2 2 2 4 푄 Φ 푄 2푒 Φ 2푒 퐻 = −퐸푗 cos 휑 + ≈ + − 휑 = Φ 2 퐶Σ 2 퐿푗0 2 퐶Σ ℏ 24 퐿푗0 ℏ Using the same replacement rules as for the Harmonic Oscillator

퐸 2 퐻 = ℏ휔 푏†푏 − 푐 푏†푏 0 2

휔0 휔0 = 5 − 10 퐺퐻푧 퐻 = ℏ 휎푧 Koch et.al. Phys. Rev. A 76, 042319 2 퐸푐 = 300 푀퐻푧 = 훼 Transmon coupled to a Resonators

Cc

C C Ej q r Lr 퐸푏 퐸푎

휔푞 퐻 = ℏ 휎 + ℏ휔 푎†푎 2 푧 푟

† − + 퐻푖푛푡 = ℏ𝑔(푎 휎 + 푎휎 ) 𝑔 = 50 − 250 MHz

Jaynes Cummings Hamiltonian

driving, readout, interactions Transmon - Transmon coupling

Cc

C C Ej1 q1 q2 Ej2 퐸푏 퐸푎

Direct capacitive -qubit interaction

+ − − + 퐻푖푛푡 = ℏ퐽(휎 휎 + 휎 휎 ) 퐽 = 50 − 250 MHz 3D Transmon coupled to a Resonator

Large mode volume compensated by large 퐸푞푢푏푖푡 “Dipolemoment” of the qubit

퐸푐푎푣 ~ mm

Observed Q’s up to 5 M 푇1 , 푇2 ≤ 100 휇푠 Superconducting qubits for analog quantum simulation of spin models Phys. Rev. B 92, 174507 (2015)

Viehmann et.al. Phys. Rev. Lett. 110, 030601 (2013) & NJP 15, 3 (2013) Quantum Simulation

The problem: Simulating interacting quantum many-body systems on a classical computer is very hard.

…spins …interactions

The approach: Engineer a well controlled system that can be used as a for the system of interest. The basic idea & some systems of interest…

Spin chain 2D spin lattice Open quantum systems

…spins …interactions Finite Element modeling - HFSS

Eigenmodes of the system:

Phys. Rev. B 92, 174507 (2015) Qubit – Qubit interaction

cos(휃 − 휃 ) − 3 cos 휃 cos 휃 퐽 푟, 휃 , 휃 = 퐽 푑2 1 2 1 2 + 퐽 1 2 0 푚 푟3 푐푎푣 Interaction tunability

푬

• Qubit - Qubit angle and position Spin chain physics • tailor interactions • Qubit - Cavity angle • tailor readout & driving • measure correlations Scaling the system

• Fine grained readout Open quantum systems • Competition between short range dipole and long range photonic interaction • Band engineering is possible • Inbuilt Purcell protection • Dissipative state engineering To do list – theory input

• How to best characterize these systems?

• What do we want to measure?

• How do we verify/validate our measurements

• How does it work in the open system case? Simulating dipolar quantum magnetism Model to simulate

XY model on a ladder: Superfluid and Dimer phase

Analogue Quantum Simulation with Superconducting qubits

퐽 휃1, 휃2 + − 푧 퐻 = 3 푆푖 푆푗 + ℎ. 푐. + ℎ푗푆푖 푖,푗 푟푖,푗 푖 In Collaboration with M. Dalmonte & D. Marcos & P. Zoller Static properties of the model Order parameter and Disorder influence on the Bond Correlation Bond Correlation

CP

SF DP

퐿−1 훼 훼 훼 푗 훼 훼 푧 푧 퐷 = 퐷푗 퐷푗 = −1 푆푗 푆푗+1 훼 = 푥, 푧 퐵 = 퐷퐿/2 푗=1

Bond order parameter shows formation of triplets for J2/J1=0.5 Adiabatic state preparation

System size: L = 6, 2J2 = J1 =2p 100 MHz,

Including disorder dh/J1=0.25 Experimental progress Experimental progress - Qubits  Single qubit control, frequency tunable

T1≈ 40 µ푠, T2 ≤ 25 µ푠 Experimental progress - Qubits  Multiple qubits and interactions

+ − − + 퐻푖푛푡 = ℏ퐽(휎 휎 + 휎 휎 ) 6.85

6.81 퐽 ≈ 70 MHz 2 J

Frequency Frequency (GHz) 6.77

B-field (a.u.) Qubit measurements & state preparation • During the simulation:

휔푖 = 휔푗 ∀ 푖, 푗

• We want to measure: 푚 푚 휎푖 ⨂휎푗

• We want to be able to bring excitations into the system

 fast flux tunability necessary Tuning fields with a Magnetic Hose

SC steel

Long-distance Transfer and Routing of Static Magnetic Fields Phys. Rev. Let. 112, 253901(2014) Experimental progress - Magnetic Hose

푇1 ≥ 15 µ푠 Purcell limited

푇2 < 15 µ푠 depends on flux bias Experimental progress - Magnetic Hose 50ns

flux pulse p pulse readout t Not perfectly compensated

Trise < 50 ns Experimental progress – Waveguides

 High Q Stripline resonators for waveguides

AIP Advances 7, 085118 (2017) Experimental progress - Waveguides . Waveguides with resonators and qubits

Qubits Resonators Conclusion • Circuit QED

Cc

Cq L Ej Cr r

• 3D Transmons behave like dipoles

• Simulate models on 1D and 2D lattices

• Work in progress Quantum Circuits Group Innsbruck – April 2017

Stefan Michael Aleksei Oleschko Schmidt Sharafiev Phani R. Christian David Muppalla Oscar Schneider Zöpfl Gargiulo

Quantum Circuits Around a resonance:

Φ ← 퐿 퐶 → 푄 x

2 2 2 2 2 푄 Φ 푝 푚휔 푥 Lagrangian 퐻 = +  퐻 = + 2 퐶 2 퐿 2 푚 2

energy in magnetic field  potential energy energy in electric field  kinetic energy Resonators and Cavities Coplanar Waveguide Resonators

out 퐸

Microwaves in Ground Plane Why interfaces matter… dirt happens

E d Nb - + + -

a-Al2O3

“participation ratio” = fraction of energy stored in material

even a thin (few nanometer) surface layer will store ≈ 1/1000 of the energy

If surface loss tangent is poor ( tand ≈ 10-2) would limit Q ≈ 105 as shown in: Increase spacing Gao et al. 2008 (Caltech) decreases energy on surfaces O’Connell et al. 2008 (UCSB) Wang et al. 2009 (UCSB) increases Q tech. solution: Bruno et al. 2015 (Delft) Circuit model explanation

J < 0

J > 0 Josephson Junction

Superconductor(Al) Ψ퐴 1 nm Insulating barrier

Ψ퐵 Superconductor (Al)

2푒 퐼 휑 = 퐼 sin 휑 휑 = 푉(푡) Josephson relations: 푐 ℏ

Regular inductance Josephson Junction

ℏ 1 푉퐿 = 퐿퐼  푉푗푗 = 퐼 2푒 퐼푐 cos 휑 2 Φ 휑2 휑4 퐸 =  퐸 = −퐸 cos 휑 ≈ 퐸 −퐸 + ⋯ 2 퐿 푗 푗 2 푗 12 2푒 Φ 휑 = Φ = 2휋 ℏ Φ0 Josephson Junction

Superconductor(Al)

1 nm Insulating barrier

Superconductor (Al)

Junction fabrication: • thin film deposition • Shadow bridge technique

500nm

6 Transmon 4 10 Sweet Spot 3D Transmon 3D Fluxonium 10 (Yale, ETH) (Saclay, Yale) (Yale, IBM, Delft) (Yale)

105 103

) ns Charge Echo (NEC) Improved

3D Transmon # Operationen # (Yale, IBM, Nakamura Fluxonium Kohärenz Zeit ( Zeit Kohärenz Delft) (NEC) (Yale) 100 1

10 0.1

Jahr