Superconducting qubits for analogue quantum simulation Gerhard - - PowerPoint PPT Presentation

Superconducting qubits for analogue quantum simulation

Gerhard Kirchmair

Workshop on Quantum Science and Quantum Technologies ICTP Trieste

September 13th 2017

Experiments in Innsbruck on cQED

Quantum Magnetomechanic Josephson Junction array resonators Quantum Simulation using cQED

Outline

• Introduction to Circuit QED

– Cavities – Qubits – Coupling

• Analog quantum simulation of spin models

– 3D Transmons as Spins – Simulating dipolar quantum magnetism – First experiments

cavity QED → circuit QED

• ptical photons

⇓ microwave photons atoms as two level systems ⇓ nonlinear quantum circuits

• ptical resonators

⇓ microwave resonators QIP, quantum optics, 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

~ 𝜇/2 𝐹 b a Observed Q’s > 106

Reagor et.al. Appl. Phys. Lett. 102, 192604 (2013)

Quantum Circuits

𝐷 → 𝑅 Φ ← 𝑀

𝐼 = 𝑅

2

2 𝐷 + Φ

2

2 𝑀 𝑅 = ℏ 2 𝑎0 𝑏 + 𝑏† Φ = 𝑗 ℏ 𝑎0 2 𝑏 − 𝑏† 𝐼 = ℏ𝜕0 𝑏†𝑏 + 1 2

Φ Energy 1 2

𝑎0 = 𝑀 𝐷 ⟶ 1 … 100 Ω 𝜕0 = 1 𝑀𝐷 ⟶ 4 … 10 𝐻𝐼𝑨 Around a resonance:

Classical drive Quantum Harmonic Oscillator

Qubits – 3D Transmon

Josephson Junction

Superconductor(Al) Superconductor (Al) Insulating barrier 1 nm 𝐼 = −𝐹

𝑘 cos

𝜒 𝐼 = −𝐹

𝑘 cos

𝜒 + 𝑅

2

2 𝐷

Superconducting Qubits - Transmon

C

Transmon

𝐼 = −𝐹

𝑘 cos

𝜒 + 𝑅

2

2 𝐷Σ ≈ Φ

2

2 𝑀𝑘0 + 𝑅

2

2 𝐷Σ − 2𝑓 ℏ

2

Φ

4

24 𝑀𝑘0

Φ Energy 1 2

𝜒 = 2𝑓 ℏ Φ 𝐼 = ℏ𝜕0 𝑐†𝑐 − 𝐹𝑑 2 𝑐†𝑐

2

Using the same replacement rules as for the Harmonic Oscillator

𝐼 = ℏ 𝜕0 2 𝜏𝑨

𝐹𝑑 = 300 𝑁𝐼𝑨 = 𝛽 𝜕0 = 5 − 10 𝐻𝐼𝑨

Koch et.al. Phys. Rev. A 76, 042319

Transmon coupled to a Resonators

𝐼𝑗𝑜𝑢 = ℏ𝑕(𝑏†𝜏− + 𝑏𝜏+) Lr Cr Cq Cc Ej 𝐹𝑐 𝐹𝑏 Jaynes Cummings Hamiltonian driving, readout, interactions 𝐼 = ℏ 𝜕𝑟 2 𝜏𝑨 + ℏ𝜕𝑠 𝑏†𝑏 𝑕 = 50 − 250 MHz

Transmon - Transmon coupling

𝐼𝑗𝑜𝑢 = ℏ𝐾(𝜏+𝜏− + 𝜏−𝜏+) Cq1 Ej1 𝐹𝑐 Cq2 Cc Ej2 𝐹𝑏 Direct capacitive qubit-qubit interaction 𝐾 = 50 − 250 MHz

3D Transmon coupled to a Resonator

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

𝐹𝑟𝑣𝑐𝑗𝑢 𝐹𝑑𝑏𝑤

Observed Q’s up to 5 M 𝑈

1 , 𝑈2 ≤ 100 𝜈𝑡

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. The approach: Engineer a well controlled system that can be used as a quantum simulator for the system of interest.

…spins …interactions

The basic idea & some systems of interest…

2D spin lattice Open quantum systems Spin chain physics

…spins …interactions

Finite Element modeling - HFSS

Eigenmodes

• f the system:
• Phys. Rev. B 92, 174507 (2015)

Qubit – Qubit interaction

𝐾 𝑠, 𝜄1, 𝜄2 = 𝐾0𝑒𝑛

2 cos(𝜄1 − 𝜄2) − 3 cos 𝜄1 cos 𝜄2

𝑠3 + 𝐾𝑑𝑏𝑤

Interaction tunability

𝑭

• Qubit - Qubit angle and position
• tailor interactions
• Qubit - Cavity angle
• tailor readout & driving
• measure correlations

Spin chain physics

Scaling the system

• Fine grained readout
• Competition between short range dipole

and long range photonic interaction

• Band engineering is possible
• Inbuilt Purcell protection
• Dissipative state engineering

Open quantum systems

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

Analogue Quantum Simulation with Superconducting qubits In Collaboration with M. Dalmonte & D. Marcos & P. Zoller

𝐼 =

𝑗,𝑘

𝐾 𝜄1, 𝜄2 𝑠

𝑗,𝑘 3

𝑇𝑗

+𝑇 𝑘 − + ℎ. 𝑑.

+

𝑗

ℎ𝑘𝑇𝑗

𝑨

XY model on a ladder: Superfluid and Dimer phase

Static properties of the model

Order parameter and Bond Correlation Disorder influence on the Bond Correlation Bond order parameter shows formation of triplets for J2/J1=0.5

𝐸𝛽 =

𝑘=1 𝑀−1

𝐸

𝑘 𝛽

𝐸

𝑘 𝛽 = −1 𝑘𝑇 𝑘 𝛽𝑇 𝑘+1 𝛽

𝛽 = 𝑦, 𝑨 𝐶𝑨 = 𝐸𝑀/2

𝑨

SF DP CP

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 µ𝑡, T2 ≤ 25 µ𝑡

Experimental progress - Qubits

 Multiple qubits and interactions

𝐼𝑗𝑜𝑢 = ℏ𝐾(𝜏+𝜏− + 𝜏−𝜏+)

6.81 6.85 6.77 Frequency (GHz) B-field (a.u.)

2 J 𝐾 ≈ 70 MHz

Qubit measurements & state preparation

• During the simulation:

𝜕𝑗 = 𝜕𝑘 ∀ 𝑗, 𝑘

• We want to measure:

𝜏𝑗

𝑛⨂𝜏 𝑘 𝑛

• We want to be able to bring excitations into the

system  fast flux tunability necessary

Tuning fields with a Magnetic Hose

Long-distance Transfer and Routing of Static Magnetic Fields

• Phys. Rev. Let. 112, 253901(2014)

SC steel

Experimental progress - Magnetic Hose

𝑈1 ≥ 15 µ𝑡 Purcell limited 𝑈2 < 15 µ𝑡 depends on flux bias

Experimental progress - Magnetic Hose

readout flux pulse

50ns

p pulse

t

Trise < 50 ns Not perfectly compensated

Experimental progress – Waveguides

 High Q Stripline resonators for waveguides

AIP Advances 7, 085118 (2017)

Experimental progress - Waveguides

• Waveguides with resonators and qubits

Qubits Resonators

• 3D Transmons behave like dipoles

Conclusion

• Circuit QED
• Simulate models on 1D and 2D lattices
• Work in progress

Lr Cr Cq Cc Ej

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

Quantum Circuits Group Innsbruck – April 2017

Quantum Circuits

𝐷 → 𝑅 Φ ← 𝑀

𝐼 = 𝑅

2

2 𝐷 + Φ

2

2 𝑀 Around a resonance: 𝐼 = 𝑞 2 2 𝑛 + 𝑛𝜕2 𝑦 2 2

x

energy in magnetic field  potential energy energy in electric field  kinetic energy 

Lagrangian

Resonators and Cavities

Coplanar Waveguide Resonators 𝐹 Ground Plane Microwaves in

• ut

Why interfaces matter… dirt happens

Increase spacing decreases energy on surfaces increases Q

Gao et al. 2008 (Caltech) O’Connell et al. 2008 (UCSB) Wang et al. 2009 (UCSB)

• tech. solution:

+ +

• E

d a-Al2O3 Nb

“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:

Bruno et al. 2015 (Delft)

Circuit model explanation

J < 0 J > 0

Josephson Junction

Superconductor(Al) Superconductor (Al) Insulating barrier 1 nm Josephson relations: 𝐽 𝜒 = 𝐽𝑑 sin 𝜒 𝜒 = 2𝑓 ℏ 𝑊(𝑢) 𝐹 = −𝐹

𝑘 cos 𝜒 ≈ 𝐹 𝑘

𝜒2 2 −𝐹

𝑘

𝜒4 12 + ⋯ 𝜒 = 2𝑓 ℏ Φ = 2𝜌 Φ Φ0 𝐹 = Φ 2 2 𝑀

Ψ

𝐵

Ψ𝐶

𝑊

𝑘𝑘 = ℏ

2𝑓 1 𝐽𝑑 cos 𝜒 𝐽 𝑊

𝑀 = 𝑀

𝐽

 

Regular inductance Josephson Junction

Josephson Junction

Superconductor(Al) Superconductor (Al) Insulating barrier 1 nm

500nm

Junction fabrication:

• thin film deposition
• Shadow bridge technique

Charge Qubit Coherence

# Operationen 0.1 104 103 1 Kohärenz Zeit (ns) 10 106 105 100

Nakamura (NEC) Charge Echo (NEC) Sweet Spot (Saclay, Yale) Transmon (Yale, ETH) 3D Transmon (Yale, IBM, Delft) Improved 3D Transmon (Yale, IBM, Delft) Fluxonium (Yale)

Jahr

3D Fluxonium (Yale)