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 13 th 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 spin models – 3D Transmons 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 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 Observed Q’s > 10 6 b 𝐹 a Reagor et.al. Appl. Phys. Lett. 102, 192604 (2013)

Quantum Circuits Energy Around a resonance: 𝐷 → Φ ← 𝑀 𝑅 2 1 Classical drive 0 Φ 2 2 𝑅 Φ 𝐼 = 2 𝐷 + 2 𝑀 ℏ Φ = 𝑗 ℏ 𝑎 0 𝑏 + 𝑏 † 𝑏 − 𝑏 † 𝑅 = 2 𝑎 0 2 𝑀 𝑎 0 = 𝐷 ⟶ 1 … 100 Ω 𝑏 † 𝑏 + 1 𝐼 = ℏ𝜕 0 2 1 𝜕 0 = 𝑀𝐷 ⟶ 4 … 10 𝐻𝐼𝑨 Quantum Harmonic Oscillator

Qubits – 3D Transmon

Josephson Junction Superconductor(Al) Insulating barrier 1 nm Superconductor (Al) 𝐼 = −𝐹 𝑘 cos 𝜒 2 𝑅 𝐼 = −𝐹 𝑘 cos 𝜒 + 2 𝐷

Superconducting Qubits - Transmon Energy Transmon 2 C 1 0 Φ 2 2 2 4 2 𝑅 Φ 𝑅 − 2𝑓 Φ 𝜒 = 2𝑓 𝐼 = −𝐹 𝑘 cos 𝜒 + ≈ + ℏ Φ 2 𝐷 Σ 2 𝑀 𝑘0 2 𝐷 Σ ℏ 24 𝑀 𝑘0 Using the same replacement rules as for the Harmonic Oscillator 𝐼 = ℏ𝜕 0 𝑐 † 𝑐 − 𝐹 𝑑 2 𝑐 † 𝑐 2 𝜕 0 = 5 − 10 𝐻𝐼𝑨 𝐼 = ℏ 𝜕 0 2 𝜏 𝑨 𝐹 𝑑 = 300 𝑁𝐼𝑨 = 𝛽 Koch et.al. Phys. Rev. A 76, 042319

Transmon coupled to a Resonators C c C q C r L r E j 𝐹 𝑏 𝐹 𝑐 𝐼 = ℏ 𝜕 𝑟 2 𝜏 𝑨 + ℏ𝜕 𝑠 𝑏 † 𝑏 𝐼 𝑗𝑜𝑢 = ℏ𝑕(𝑏 † 𝜏 − + 𝑏𝜏 + ) 𝑕 = 50 − 250 MHz Jaynes Cummings Hamiltonian driving, readout, interactions

Transmon - Transmon coupling C c C q1 C q2 E j1 E j2 𝐹 𝑐 𝐹 𝑏 Direct capacitive qubit-qubit interaction 𝐼 𝑗𝑜𝑢 = ℏ𝐾(𝜏 + 𝜏 − + 𝜏 − 𝜏 + ) 𝐾 = 50 − 250 MHz

3D Transmon coupled to a Resonator Large mode volume compensated by large 𝐹 𝑟𝑣𝑐𝑗𝑢 “ Dipolemoment ” of the qubit 𝐹 𝑑𝑏𝑤 ~ mm 𝑈 1 , 𝑈 2 ≤ 100 𝜈𝑡 Observed Q’s up to 5 M

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 quantum simulator for the system of interest.

The basic idea & some systems of interest… Spin chain physics 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 2 cos(𝜄 1 − 𝜄 2 ) − 3 cos 𝜄 1 cos 𝜄 2 𝐾 𝑠, 𝜄 1 , 𝜄 2 = 𝐾 0 𝑒 𝑛 + 𝐾 𝑑𝑏𝑤 𝑠 3

Interaction tunability 𝑭 • 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 𝐾 𝜄 1 , 𝜄 2 − + ℎ. 𝑑. + 𝑇 𝑨 𝐼 = 𝑇 𝑗 + ℎ 𝑘 𝑇 𝑗 𝑘 3 𝑠 𝑗,𝑘 𝑗,𝑘 𝑗 In Collaboration with M. Dalmonte & D. Marcos & P. Zoller

Static properties of the model Disorder influence on the Order parameter and Bond Correlation Bond Correlation CP DP SF 𝑀−1 𝛽 = −1 𝑘 𝑇 𝐶 𝑨 = 𝐸 𝑀/2 𝐸 𝛽 = 𝛽 𝑇 𝛽 𝑨 𝛽 𝛽 = 𝑦, 𝑨 𝐸 𝐸 𝑘 𝑘 𝑘 𝑘+1 𝑘=1 Bond order parameter shows formation of triplets for J 2 /J 1 =0.5

Adiabatic state preparation System size: L = 6, 2J 2 = J 1 =2 p 100 MHz, Including disorder d h/J 1 =0.25

Experimental progress

Experimental progress - Qubits  Single qubit control, frequency tunable T 1 ≈ 40 µ𝑡 , T 2 ≤ 25 µ𝑡

Experimental progress - Qubits  Multiple qubits and interactions 𝐼 𝑗𝑜𝑢 = ℏ𝐾(𝜏 + 𝜏 − + 𝜏 − 𝜏 + ) 6.85 Frequency (GHz) 6.81 𝐾 ≈ 70 MHz 2 J 6.77 B-field (a.u.)

Qubit measurements & state preparation • During the simulation: 𝜕 𝑗 = 𝜕 𝑘 ∀ 𝑗, 𝑘 • We want to measure: 𝑛 ⨂𝜏 𝑛 𝜏 𝑗 𝑘 • 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 𝑈 1 ≥ 15 µ𝑡 Purcell limited 𝑈 2 < 15 µ𝑡 depends on flux bias

Experimental progress - Magnetic Hose 50ns p pulse flux pulse readout t Not perfectly compensated T rise < 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 C c C q L r E j C r • 3D Transmons behave like dipoles • Simulate models on 1D and 2D lattices • Work in progress

Quantum Circuits Group Innsbruck – April 2017 Michael Aleksei Stefan Schmidt Sharafiev Oleschko Phani R. Christian David Oscar Muppalla Schneider Zöpfl Gargiulo

Quantum Circuits Around a resonance: 𝐷 → Φ ← 𝑀 𝑅 x 2 𝑛 + 𝑛𝜕 2 𝑞 2 𝑦 2 2 2 𝑅 Φ 𝐼 = Lagrangian  𝐼 = 2 𝐷 + 2 2 𝑀  energy in magnetic field potential energy  energy in electric field kinetic energy

Resonators and Cavities Coplanar Waveguide Resonators out 𝐹 Ground Plane Microwaves in

Why interfaces matter… dirt happens E d Nb - - + + a -Al 2 O 3 “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 ( tan d ≈ 10 -2 ) would limit Q ≈ 10 5 as shown in: Increase spacing Gao et al. 2008 (Caltech) O’Connell et al. 2008 (UCSB) decreases energy on surfaces 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) Ψ 𝐵 Insulating barrier 1 nm Ψ 𝐶 Superconductor (Al) 𝜒 = 2𝑓 ℏ 𝑊(𝑢) 𝐽 𝜒 = 𝐽 𝑑 sin 𝜒 Josephson relations: Josephson Junction Regular inductance 𝑘𝑘 = ℏ 1  𝑀 = 𝑀 𝑊 𝐽 𝑊 𝐽 2𝑓 𝐽 𝑑 cos 𝜒 𝐹 = Φ 2 𝜒 2 𝜒 4  𝐹 = −𝐹 𝑘 cos 𝜒 ≈ 𝐹 2 −𝐹 12 + ⋯ 2 𝑀 𝑘 𝑘 𝜒 = 2𝑓 ℏ Φ = 2𝜌 Φ Φ 0

Josephson Junction Superconductor(Al) Insulating barrier 1 nm Superconductor (Al) Junction fabrication: • thin film deposition • Shadow bridge technique 500nm

Charge Qubit Coherence 10 4 10 6 Transmon 3D Fluxonium 3D Transmon Sweet Spot (Yale, ETH) (Yale) (Yale, IBM, Delft) (Saclay, Yale) 10 5 10 3 # Operationen Kohärenz Zeit (ns) Charge Echo (NEC) Improved 3D Transmon (Yale, IBM, Fluxonium Nakamura Delft) (Yale) (NEC) 1 100 10 0.1 Jahr