superconducting qubits for analogue quantum...
TRANSCRIPT
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Superconducting qubits for analogue quantum simulation
Gerhard Kirchmair
Workshop on Quantum Science and Quantum TechnologiesICTP Trieste
September 13th 2017
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Experiments in Innsbruck on cQED
Quantum Magnetomechanic
Josephson Junction arrayresonators
Quantum Simulation using cQED
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Outline
• Introduction to Circuit QED
– Cavities
– Qubits
– Coupling
• Analog quantum simulation of spin models
– 3D Transmons as Spins
– Simulating dipolar quantum magnetism
– First experiments
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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 …
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Cavities
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Waveguide microwave resonator
~ 𝜆/2
𝐸
b
a
Observed Q’s > 106
Reagor et.al. Appl. Phys. Lett. 102, 192604 (2013)
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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
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Qubits – 3D Transmon
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Josephson Junction
Superconductor(Al)
Superconductor (Al)
Insulating barrier1 nm
𝐻 = −𝐸𝑗 cos 𝜑
𝐻 = −𝐸𝑗 cos 𝜑 + 𝑄2
2 𝐶
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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
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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
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Transmon - Transmon coupling
𝐻𝑖𝑛𝑡 = ℏ𝐽(𝜎+𝜎− + 𝜎−𝜎+)
Cq1Ej1
𝐸𝑏
Cq2
Cc
Ej2
𝐸𝑎
Direct capacitive qubit-qubit interaction
𝐽 = 50 − 250 MHz
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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
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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)
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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
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The basic idea & some systems of interest…
2D spin lattice Open quantum systemsSpin chain physics
…spins …interactions
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Finite Element modeling - HFSS
Eigenmodesof the system:
Phys. Rev. B 92, 174507 (2015)
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Qubit – Qubit interaction
𝐽 𝑟, 𝜃1, 𝜃2 = 𝐽0𝑑𝑚2cos(𝜃1 − 𝜃2) − 3 cos 𝜃1 cos 𝜃2
𝑟3+ 𝐽𝑐𝑎𝑣
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Interaction tunability
𝑬
• Qubit - Qubit angle and position• tailor interactions
• Qubit - Cavity angle• tailor readout & driving• measure correlations
Spin chain physics
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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
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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?
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Simulating dipolar quantum magnetism
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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
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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
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Adiabatic state preparation
System size: L = 6, 2J2 = J1 =2p 100 MHz,
Including disorder dh/J1=0.25
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Experimental progress
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Experimental progress - Qubits
Single qubit control, frequency tunable
T1≈ 40 µ𝑠, T2 ≤ 25 µ𝑠
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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
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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
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Tuning fields with a Magnetic Hose
Long-distance Transfer and Routing of Static Magnetic FieldsPhys. Rev. Let. 112, 253901(2014)
SC steel
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Experimental progress - Magnetic Hose
𝑇1 ≥ 15 µ𝑠
Purcell limited
𝑇2 < 15 µ𝑠
depends on flux bias
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Experimental progress - Magnetic Hose
readoutflux pulse
50ns
p pulse t
Trise < 50 ns
Not perfectly compensated
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Experimental progress – Waveguides
High Q Stripline resonators for waveguides
AIP Advances 7, 085118 (2017)
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Experimental progress - Waveguides Waveguides with resonators and qubits
Qubits Resonators
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• 3D Transmons behave like dipoles
Conclusion
• Circuit QED
• Simulate models on 1D and 2D lattices
• Work in progress
LrCrCq
Cc
Ej
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OscarGargiulo
Phani R.Muppalla
ChristianSchneider
DavidZöpfl
StefanOleschko
MichaelSchmidt
AlekseiSharafiev
Quantum Circuits Group Innsbruck – April 2017
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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
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Resonators and CavitiesCoplanar Waveguide Resonators
𝐸
Ground PlaneMicrowaves in
out
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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)
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Circuit model explanation
J < 0
J > 0
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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
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Josephson Junction
Superconductor(Al)
Superconductor (Al)
Insulating barrier1 nm
500nm
Junction fabrication:• thin film deposition• Shadow bridge technique
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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)