Superconducting qubits for analogue quantum simulation

Gerhard Kirchmair

Workshop on Quantum Science and Quantum TechnologiesICTP Trieste

September 13th 2017

Experiments in Innsbruck on cQED

Quantum Magnetomechanic

Josephson Junction arrayresonators

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

optical photons⇓

microwave photons

atoms as two level systems⇓

nonlinear quantum circuitsoptical 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

~ 𝜆/2

𝐸

b

a

Observed Q’s > 106

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

Quantum Circuits

𝐶 → 𝑄 Φ ← 𝐿

𝐻 = 𝑄2

2 𝐶+ Φ

2

2 𝐿

𝑄 =ℏ

2 𝑍0𝑎 + 𝑎† Φ = 𝑖

ℏ 𝑍02

𝑎 − 𝑎†

𝐻 = ℏ𝜔0 𝑎†𝑎 +1

2

Φ

Energy

0

1

2

𝑍0 =𝐿

𝐶⟶ 1…100 Ω

𝜔0 =1

𝐿𝐶⟶ 4…10 𝐺𝐻𝑧

Around a resonance:

Classical drive

Quantum Harmonic Oscillator

Qubits – 3D Transmon

Josephson Junction

Superconductor(Al)

Superconductor (Al)

Insulating barrier1 nm

𝐻 = −𝐸𝑗 cos 𝜑

𝐻 = −𝐸𝑗 cos 𝜑 + 𝑄2

2 𝐶

Superconducting Qubits - Transmon

C

Transmon

𝐻 = −𝐸𝑗 cos 𝜑 + 𝑄2

2 𝐶Σ≈

Φ2

2 𝐿𝑗0+

𝑄2

2 𝐶Σ−

2𝑒

ℏ

2 Φ4

24 𝐿𝑗0

Φ

Energy

0

1

2

𝜑 =2𝑒

ℏΦ

𝐻 = ℏ𝜔0 𝑏†𝑏 −

𝐸𝑐2

𝑏†𝑏2

Using the same replacement rules as for the Harmonic Oscillator

𝐻 = ℏ𝜔0

2𝜎𝑧

𝐸𝑐 = 300 𝑀𝐻𝑧 = 𝛼

𝜔0 = 5 − 10 𝐺𝐻𝑧

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

Transmon coupled to a Resonators

𝐻𝑖𝑛𝑡 = ℏ𝑔(𝑎†𝜎− + 𝑎𝜎+)

LrCrCq

Cc

Ej

𝐸𝑏 𝐸𝑎

Jaynes Cummings Hamiltonian

driving, readout, interactions

𝐻 = ℏ𝜔𝑞2𝜎𝑧 + ℏ𝜔𝑟 𝑎

†𝑎

𝑔 = 50 − 250 MHz

Transmon - Transmon coupling

𝐻𝑖𝑛𝑡 = ℏ𝐽(𝜎+𝜎− + 𝜎−𝜎+)

Cq1Ej1

𝐸𝑏

Cq2

Cc

Ej2

𝐸𝑎

Direct capacitive qubit-qubit interaction

𝐽 = 50 − 250 MHz

3D Transmon coupled to a Resonator

~ mm

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

𝐸𝑞𝑢𝑏𝑖𝑡

𝐸𝑐𝑎𝑣

Observed Q’s up to 5 M 𝑇1 , 𝑇2 ≤ 100 𝜇𝑠

Superconducting qubits foranalog 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 systemsSpin chain physics

…spins …interactions

Finite Element modeling - HFSS

Eigenmodesof the system:

Phys. Rev. B 92, 174507 (2015)

Qubit – Qubit interaction

𝐽 𝑟, 𝜃1, 𝜃2 = 𝐽0𝑑𝑚2cos(𝜃1 − 𝜃2) − 3 cos 𝜃1 cos 𝜃2

𝑟3+ 𝐽𝑐𝑎𝑣

Interaction tunability

𝑬

• 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

𝐻 =

𝑖,𝑗

𝐽 𝜃1, 𝜃2

𝑟𝑖,𝑗3 𝑆𝑖

+𝑆𝑗− + ℎ. 𝑐. +

𝑖

ℎ𝑗𝑆𝑖𝑧

XY model on a ladder: Superfluid and Dimer phase

Static properties of the modelOrder parameter and

Bond Correlation

Disorder influence on the Bond Correlation

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

𝐷𝛼 =

𝑗=1

𝐿−1

𝐷𝑗𝛼 𝐷𝑗

𝛼 = −1 𝑗𝑆𝑗𝛼𝑆𝑗+1

𝛼 𝛼 = 𝑥, 𝑧 𝐵𝑧 = 𝐷𝐿/2𝑧

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 µ𝑠, T2 ≤ 25 µ𝑠

Experimental progress - Qubits

Multiple qubits and interactions

𝐻𝑖𝑛𝑡 = ℏ𝐽(𝜎+𝜎− + 𝜎−𝜎+)

6.81

6.85

6.77Freq

uen

cy (

GH

z)

B-field (a.u.)

2 J𝐽 ≈ 70 MHz

Qubit measurements & state preparation

• During the simulation:

𝜔𝑖 = 𝜔𝑗 ∀ 𝑖, 𝑗

• We want to measure:𝜎𝑖𝑚⨂𝜎𝑗

𝑚

• 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 FieldsPhys. Rev. Let. 112, 253901(2014)

SC steel

Experimental progress - Magnetic Hose

𝑇1 ≥ 15 µ𝑠

Purcell limited

𝑇2 < 15 µ𝑠

depends on flux bias

Experimental progress - Magnetic Hose

readoutflux 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

LrCrCq

Cc

Ej

OscarGargiulo

Phani R.Muppalla

ChristianSchneider

DavidZöpfl

StefanOleschko

MichaelSchmidt

AlekseiSharafiev

Quantum Circuits Group Innsbruck – April 2017

Quantum Circuits

𝐶 → 𝑄 Φ ← 𝐿

𝐻 = 𝑄2

2 𝐶+ Φ

2

2 𝐿

Around a resonance:

𝐻 = 𝑝 2

2 𝑚+𝑚𝜔2 𝑥 2

2

x

energy in magnetic field potential energy

energy in electric field kinetic energy

Lagrangian

Resonators and CavitiesCoplanar Waveguide Resonators

𝐸

Ground PlaneMicrowaves in

out

Why interfaces matter… dirt happens

Increase spacing decreases energy on surfacesincreases 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 barrier1 nm

Josephson relations: 𝐼 𝜑 = 𝐼𝑐 sin𝜑 𝜑 =2𝑒

ℏ𝑉(𝑡)

𝐸 = −𝐸𝑗 cos 𝜑 ≈ 𝐸𝑗𝜑2

2−𝐸𝑗

𝜑4

12+⋯

𝜑 =2𝑒

ℏΦ = 2𝜋

Φ

Φ0

𝐸 =Φ 2

2 𝐿

Ψ𝐴

Ψ𝐵

𝑉𝑗𝑗 =ℏ

2𝑒

1

𝐼𝑐 cos𝜑 𝐼𝑉𝐿 = 𝐿 𝐼

Regular inductance Josephson Junction

Josephson Junction

Superconductor(Al)

Superconductor (Al)

Insulating barrier1 nm

500nm

Junction fabrication:• thin film deposition• Shadow bridge technique

Charge Qubit Coherence

# O

pe

rati

on

en

0.1

104

103

1

Koh

ären

z Ze

it (

ns)

10

106

105

100

Nakamura (NEC)

Charge Echo(NEC)

Sweet Spot(Saclay, Yale)

Transmon(Yale, ETH)

3D Transmon(Yale, IBM, Delft)

Improved3D Transmon

(Yale, IBM,Delft)Fluxonium

(Yale)

Jahr

3D Fluxonium(Yale)