superconducting qubits for analogue quantum...
Post on 13-Oct-2019
10 Views
Preview:
TRANSCRIPT
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)
top related