quantum engineering of superconducting...

William D. Oliver

Quantum Engineeringof Superconducting Qubits

EQuS @ RLE . Engineering Quantum Systems

Plasma Science and Fusion Center – IAP Seminar

Engineering Quantum Systems (EQuS) Group, MITQuantum Information and Integrated Nanosystems (QuIIN) Group, MIT-LL

10 January 2018

SNEQSE- 2WDO 11/04/17

Computing Development Timeline

2

Quantum computing is transitioning from scientific curiosity to technical reality

A new discipline – quantum engineering – is emerging to bridge this gap.2

Classical (Electronic) ComputingFirst vacuum tube

(1907)ENIAC

(1946)

First fully transistor-based computer: TX-0

(1953)

Transistor invented(1947)

4.5M transistors: Pentium(1998)

30k transistors: i8088(1971)

5B transistors: Xeon(2014)

Quantum Computing

Quantum computer proposed

(1981)

Shor’s algorithm & quantum error

correctionproposed(1994-95)

Milestones in Fundamental

Elements(2012-2016)

Quantum anneling& adiabatic QC

proposed(1998-2000)


Superconducting qubits Quantum optics

Canada• Inst. for Quantum Computing (est. 2002)

– U. Waterloo and Perimeter Institute

China• Key Lab, Quantum Information, CAS (2001)• Key Lab, Solid-State Microstruct. (2004)• Q-comm on satellite

NV centersIon trap qubits Semiconducting qubits

Worldwide Investment(not an exhaustive list)

Singapore• Research Center on Quantum Information Science and Technology (est. 2007)

Australia• ARC Centers of Excellence

– Center for Quantum Computing Technology (est. 2000) – Engineered Quantum Systems (est. 2011)– $46M investment (banking / Government, 2015)

Japan• Gate-based QC

– RIKEN, universities, … • Coherent computing: ImPACT program

– Universities (Tokyo, Osaka, Kyoto, …)– Govt. labs (NICT, NII, NTT, RIKEN, …)– Industry (Mitsubishi, NEC, Toshiba, …)

Europe• Austria: Institute for Quantum Optics and Information (est. 2003)• Netherlands: QuTech (2014)…$50M investment from Intel• United Kingdom: National Quantum Technologies Program (2014)• EU: Quantum Flagship (2016)

United States• Joint Quantum Institute (est. 2007)

– Maryland / NIST / LPS (NSA)– Ions, neutral atoms, optical, superconductors

• Multi-agency government investments– Universities, DOE, DOC, DoD, NSA, industry …– Basic research and systems programs

IonQ

Q-Ctrl

Potential value of quantum computing for economic and information security is driving significant worldwide investment – currently estimated at $4 billion / year.


Outline

• Introduction to quantum computing

• Superconducting qubits

• Quantum engineering– State of field

– Quantum control & filter engineering

– 3D integration

C. Macklin et al., Science (2015)

Dispersive Engineered TWPA 5x5 mm2 silicon chip


How is a Quantum Computer Different?

Quantum computers rely on encoding information in a fundamentally different way than classical computers

Quantum ComputerClassical Computer“Bit” : classical bit

(transistor, spin in magnetic memory, …)“Qubit” : quantum bit

(any coherent two-level system)

• Superposition states• Probabilistic measurement:

Ex: If |𝜶| = |𝜷|, 50% | 𝟎 , 50% | 𝟏

• Discrete states• Deterministic measurement:

Ex: Set as 1, measure as 1

0 1

| 𝝍 = 𝜶𝟏𝟎

+ 𝜷𝟎𝟏

𝜶| 𝟎 + 𝜷| 𝟏

| 𝟏

Superposition:

Fundamental logic element

State

Measurement

“Or” | 𝟎

| 𝟎

| 𝝍

| 𝟏“And”


How is a Quantum Computer Different?

Quantum computers rely on encoding information in a fundamentally different way than classical computers

Quantum ComputerClassical ComputerFundamental logic element

f(000)

f(001)

000

001

Computing

000

001

+ f(000)

f(001) +

𝜶′𝜶

𝜷 𝜷′

• N qubits: 2N components to one state

• Quantum parallelism & interference

• N bits: One N-bit state

• Change a bit: new calculation (classical parallelism)

000, 001, …, 111 (N = 3) 𝜶 𝟎𝟎𝟎 + 𝜷 𝟎𝟎 𝟏 + ⋯+ 𝜸|𝟏𝟏 𝟏 (N = 3)

+

+… …

“Bit” : classical bit(transistor, spin in magnetic memory, …)

“Qubit” : quantum bit(any coherent two-level system)


Three Atoms…Eight Classical States

• For three qubits, eight possible states

4321

cccc

8765

cccc

This state requires eight complex numbers to specify it

87654321

,,,,,,, cccccccc

coupling coupling

atom 1 atom 2 atom 3

3-atom system(8 states)

c1

c2

c3

c4

c5

c6

c7

c8


Quantum Parallelismcoupling coupling


3-atom system

c1

c2

c3

c4

c5

c6

c7

c8

3-atom system

c1

c2

c3

c4

c5

c6

c7

c8

before pulse after pulse

Operates on entire system

simultaneously

State amplitudes are shuttled between

states

QuantumParallelism

EM pulse flips spin of atom 1(p-pulse)


Quantum Interferencecoupling coupling


3-atom system

+

3-atom system

c5

c6

c7

c8

c1

c2

c3

c4


c5

c5

EM pulse puts spin of atom 3into superposition

(p/2-pulse)

| 𝟏

| 𝟎

+




_

3-atom system

c5

c6

c7

c8

c1

c2

c3

c4


c5 + c6

c5 - c6

3-atom system


(p/2-pulse)

| 𝟏

| 𝟎

+-

+




3-atom system

c5

c6

c7

c8

c1

c2

c3

c4


c5 + c6

c5 - c6

3-atom system


(p/2-pulse)

_

+

if c5=c6no amplitude

in state

QuantumInterference




3-atom system

c5

c6

c7

c8

c1

c2

c3

c4


c5 + c6

c5 - c6

c7 + c8

c7 - c8

3-atom system

c1 + c2

c1 - c2

c3 + c4

c3 - c4Quantum

Parallelism

if c5=c6no amplitude

in state

QuantumInterference


(p/2-pulse)

_

+


0 1 X0 1

Gate-Based Approach:Single-Qubit Operation

X-gate: p-pulse around x-axis

Classical NOT-gate Quantum NOT-gate example: X-gate

Bloch Sphere Driving Field (envelope only)

0 1X-gate applied to qubit along +Z:


0 1 X0 1

Gate-Based Approach:Single-Qubit Operation

X-gate: p-pulse around x-axis

Classical NOT-gate Quantum NOT-gate example: X-gate

Bloch Sphere Driving Field (envelope only)

0 1 0 1 X-gate applied to arbitrary qubit state:


Gate-Based Approach:Two-Qubit Controlled-NOT

Rotation of QB-y depends on the state of QB-x

in yx0 1 0

For example:

out x y x y0 0 1 1

Results in an entangled state

(cannot be factored)

Universal gate-based quantum computation is achievable with a small set of single and two-qubit gates.

Quantum CNOT-gate

CNOT

in

out

QB-x

QB-y

“control” qubit

“target” qubit

“control” bit

“target” bit

Classical XOR-gate

0011

0101

0011

0110


time

Computer

Algorithm

…000

Yin =

+

+

001

010

+ 011

Input state

Measurement

0 1

Output state

000

001

010

011

…

’ ~ 0

Algorithm encodes answer

into single output state

with high probability

’ ~ 1

g’ ~ 0

d’ ~ 0

Quantuminterference

Quantum Algorithm (Gate Model)

…

000

001

010

011

Quantum interference

g

d

000

001

010

011

…

Single-qubitoperations

Coupled-qubitoperations


Intuitive Figure of Merit for Qubit Quality

Coherence time: The qubit’s lifetime

Gate time: Time required for a single operation

Time

State lost

Environmental disruptions

• Fast operations are desired; Classical processor: ~1 GHz (1 ns per op.)

Most lenient threshold for quantum error correction (to sustain computation): >103 operations per qubit lifetime

( * Rigorous metric: gate & readout fidelity > 99.5%, that is, < 0.5% error per operation)

State decayingQuantum state

One Figure of Merit * : (Coherence time) / (Gate time)


1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

1.E+05

1.E+06

1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 1.E+08 1.E+09

Series1

Qubit Modalities

Gate Speed (Hz)

Figu

re o

f Mer

it: C

oher

ence

Tim

e / G

ate

Tim

eNuclear Spin

in Silicon

Ensemble NMR

Optical Quantum Dot

Trapped Ion

Neutral Atoms

Viable qubit for scalingNot yet demonstrated to be viable

lowest thresholdfor quantum error correction

Electron Spin in Silicon

Solid State Quantum Dots

NV-Centers in Diamond

Superconducting Qubits

BestPerformanceTrapped-Ion Qubit

Gate time: 10-100 msCoherence time: 1-50 s

Gate time: 10 nsCoherence time: 100 ms

Superconducting Qubit

1 mm

|𝟎 = |𝟏 =| |

faster gates & RO

higherfidelity


Quantum Computing Approaches

2048102451225612864

Bit-length of RSA Key

1 hour

1E-12

1E-06

1E+00

1E+06

1E+12

1E+18

age of theuniverse

4096

QuantumClassical

Proc

essi

ng T

ime

(h

ours

)

Key Annealing Applications:• Supply transport optimization• Sensor & satellite tasking• Pattern recognition (surveillance)

Shor’s Algorithm for Prime Factorization:RSA Key Decryption

Gate-Based Quantum Computer Quantum Annealing Computer

Key Gate-Based Applications:• RSA key decryption• Unsorted database searching• Quantum simulation

Travelling Salesman Problem:Route Optimization

Quantum speed-up exists over known classical algorithms

Unknown if quantum speed-up exists with this approach


Outline





– 3D integration




• Linear resonant circuit– Low loss: Q >> 1

How to Build an Artificial Atom

0

1

2 LC

p CL

Linear Resonant Circuit


Normal

• Dissipationless (R=0 @ DC)

• Phase coherent

http://iqc.uwaterloo.ca/faculty-research/nanoelectronics-based-quantum-information-processing/files/useqip_sc_lupascu.pdf

Superconductivity

Superconducting

also NbN, TiN, NbTiN, …

http://hyperphysics.phy-astr.gsu.edu/hbase/tables/supcon.html


• Linear resonant circuit– Low loss: Q >> 1– Low temperature: kT << h0

– Linear elements: harmonic


0

1

2 LC

p CL


Energy Spectra of Quantum LC Circuit

Energy0

h

0h

0h

~1/Q

0

1

2

3

quantized electricalharmonic oscillator

(e.g., quantized EM field)

2 21 1ˆ ˆ ˆ2 2

H CV LI

V

I

ˆ ˆ, 0I V

Capacitiveenergy

Inductiveenergy

capacitor voltage (momentum p)

inductor current (position q)

current and voltage do not commute(cannot measure simultaneously with arbitrary precision uncertainty relation)

M.H. Devoret, Les Houches (1995)


250 nm

Josephson Junctions (JJs)Nonlinear inductors

RL

SIS (Josephson) Junction~ 1 nm

sinc

II Current:

Voltage:dt

dV

p2

0

Ic is the critical current, which depends on superconductor material and insulator thickness0 = h/2e is the superconducting flux quantum and has value 2.07x10-15 Wb = 2.07 mA · pH = 2.07 mV · ps

SEM of Al shadow-evaporated Josephson junction

insulatorsuperconductor

superconductor~ 1

nm Inductance:J

dIV L

dt


• Linear resonant circuit– Low loss: Q >> 1– Low temperature: kT << h0

– Linear elements: harmonic


0

1

2 LC

p CL



Energy0

h

0h

0h

~1/Q

0

2 cosJ

C

LIp

Josephson Junction: Nonlinear Inductor

sinC

I I 0

2

dV

dt

p

CLJ

• Nonlinear resonant circuit– Josephson tunnel junction– Anharmonic– Solid-state artificial atom


Energy

CI VI ,,

Qubit

23h

12h

01h

0

1

2

3

0

1

2

3


Device Testing in a Dilution RefrigeratorTemperature = 20 mK

11 resonator pkgs (5 res. / package)

Isolators / circulators

Mixing chamber plate (10 mK)

Microwave linesand attenuators

Microwave switches

3 qubit pkgs (2 qubits / pkg)

Filters and biasing lines

5 GHz has a thermal energy of 250 mK operate at 20 mK.Commercially available, turn-key dilution refrigerators.


5 mm 0.5 mm 0.5 mm

Why Superconducting Qubits: Lithographic scalability

200-mm wafers(49 Reticles 16 chips)

-1

0

1

0

0.5

Magnetic Flux (/0)

Ener

gy

|0

|1

Qubit Design Determines Energy Levels of “Artificial Atom”• Manufactured/designed “atoms”

• Lithographic scalability (silicon)

Transmon capacitorand control lines

5-Transmon chip withreadout resonators

Tunable transmon qubit loop with junctions

Josephson junctions(aluminum)

5 mm

250 nm


Why Superconducting Qubits: Nanosecond-scale gate operations

Dual-Channel, 2GS/s, 14-bit AWG Qubit Control via Microwave Pulses• Manufactured/designed “atoms”

• Lithographic scalability (silicon)

• RF and microwave control

• 100-MHz gate operations


Why Superconducting Qubits: Remarkable improvements in qubit coherence

“Moore’s Law” for T2

Oliver & Welander, MRS Bulletin (2013)

Blue: MIT & LL

lowest thresholdsfor quantum error correction

several groups 100-150 us(Delft, IBM, MIT, Yale, …)

NIST/IBM, Yale, ...

MIT-LL Nb Trilayer

• Remarkable improvement in T1,2

– Materials– Fabrication– Design

• All major qubit types at MIT– Flux qubit: T2 = 23 us– 2D transmon: T2 = 100 us– 3D transmon: T2 = 150 us– C-shunt flux qubit: T2 = 100 us

• Planar resonators– TiN Q > 2 M– Al & Nb Q > 1 M


Outline





– 3D integration




Engineering Quantum Systems

Physics Materials &Fabrication

LogicalPrimitives

QuantumTestbeds

Predictions ofPerformance

• Hamiltonian simulations and design tools• New algorithms & error correction • Benchmarking, validation, verification• Simulation and design tools

• Integrated control electronics and optics• Control electronics, cryogenic CMOS, SFQ• Calibration and benchmarking• Optimal control & dynamical error suppression

2-10 QubitExperiments

• High-coherence materials, fabrication and 3D integration• Thermal, mechanical, electromagnetic management• Integrated electronics and optics• Advanced packaging and signal routing

• Fault-tolerant implementations• Quantum error correction• Logical controller, compiler, scheduler

FutureQuantumProcessor

Future quantum processor demonstrations will stand on physics, computer science, and engineering foundation

ComputerScience

Control &DSP

Analog & Digital Circuits

ComputerArchitecture


Architectural Layers of a QIP

Layered ArchitectureSoftware: algorithm & interface

Hardware: physical qubitsN.C. Jones PRX 2, 031007 (2012)


Layered ArchitectureCompiler & firmware:

Dedicated to achieving fault-tolerant

logical operations via error mitigation,

detection, and correction

N.C. Jones PRX 2, 031007 (2012)

logicaloperation

+error

correction

errordetection

+error

mitigation

physical qubits(faulty)

logical qubits(robust)



Layered Architecture

N.C. Jones PRX 2, 031007 (2012)


Qubit Error DetectionUCSB / Google Group,

IBM & Delft demonstrations

J. Kelley et al., Nature 519, 66-69 (2015)

Also: A.D. Corcoles et al., & Riste et al., Nature Comm. (2015)




N.C. Jones PRX 2, 031007 (2012)

Capacitively shunted flux qubitT1 = 50 ms ; T2 = 100 ms

F. Yan et al., Nature Comm. 7, 12964 (2016)


Layered ArchitectureEngineered Error Mitigation:

Dynamical Decoupling

Eg. Lacrosse Cradling


N.C. Jones PRX 2, 031007 (2012)


Quantum Control Demonstration:Reducing Decoherence During Free Evolution

Transverse Relaxation: T2* ~ 2.5 us

Linewidth: T2* = 1/(p FWHM) ~ 1.75 us

Rabi approximately T1- limited: TR ~ (4/3) T1

Echo approximately T1- limited: T2E ~ 2 T1

Gate fidelty (rand. benchmkg): F = 99.75%

Longitudinal Relaxation: T1 = 12 us

Nature Physics 7, 565 (2011)

http://lanl.arxiv.org/abs/1101.4707


Free evolution of the phase

dephasing

Qubit Dephasing and Filter Function



dephasing


010

exp ( ) exp ( )i

i t dtE t



dephasing

for Gaussian-distributedfluctuations


Martinis et al., PRB 67, 094510 (2003), Ithier et al., PRB 72, 134519 (2005); Yoshihara et al., PRL 97, 167001 (2006), Cywinski et al. PRB 77, 174509 (2008)

010

exp ( ) exp ( )i

i t dtE t

22

01

2exp

2N

Ed S g t



dephasing

sensitivity of qubit energy to fluctuations




010

exp ( ) exp ( )i

i t dtE t

22

01

2exp

2N

Ed S g t



dephasing

sensitivity of qubit energy to fluctuations

strength (variance) of fluctuations




010

exp ( ) exp ( )i

i t dtE t

22

01

2exp

2N

Ed S g t



dephasing

sensitivity of qubit energy to fluctuations Filter functionshapes noise



Engineered filter function depends on pulse sequence and windows the PSD S()


010

exp ( ) exp ( )i

i t dtE t

22

01

2exp

2N

Ed S g t

strength (variance) of fluctuations


NO Dynam. Decoup.

Dynamical Decoupling: Noise Shaping Filters

(Ramsey, N=0)t

Xp/2 Xp/2

Frequency (MHz)

= 1 ms, p = 0 RamseySpin echo

S ~ 1/f

Filte

r Fun

ctio

n

0

1

0 54321

0.8

0.2

0.4

0.6

Nature Physics 7, 565 (2011); PRL 110, 040502 (2013)


t

Xp/2 Xp/2

Frequency (MHz)


S ~ 1/f

Filte

r Fun

ctio

n

NO Dynam. Decoup.(Ramsey, N=0)

WITH Dynam. Decoup.(spin echo, N=1)

t

Xp

Xp/2 Xp/2

/2 /2 0

1

0 54321

0.8

0.2

0.4

0.6

Dynamical Decoupling: Noise Shaping Filters with 1 p-pulse



Frequency (MHz)


S ~ 1/f

Filte

r Fun

ctio

n g(

t)

0.8

0.2

0.4

0.6

0

1

0 54321

NO Dynam. Decoup.(Ramsey, N=0)

WITH Dynam. Decoup.(CPMG, N=2)

t

Xp/2 Xp/2

t

Xp

Xp/2 Xp/2

/4 /2

Xp

/4

Dynamical Decoupling: Noise Shaping Filters with 2 p-pulses





N.C. Jones PRX 2, 031007 (2012)

Engineered Error Mitigation:Dynamical Decoupling

(improves the physical qubit error rate)

J. Bylander et al., Nature Phys. 7, 565 (2011)


Outline





– 3D integration




Frequency-Tunable Transmons

Single Qubit Gates Coupled Qubit Gates

M. Kjaergaard, P. Krantz, T. W. Larsen, M. Kimchi-Schwarz, D. Rosenberg, J. Yoder, D. Kim, S. Gustavsson & W. D. Oliver

SWAP

5-Transmon Chip

C-phase

High coherence times, but single-layer process.Routing I/O to 2D array is challenging.


Quantum-to-Classical Interface Today(few-qubit experiments)

Superconducting qubits in a dilution refrigerator

Quantum-to-Classical Interface as it looks today…

Trapped ionson an optical table

Need an extensible approach to realize practical quantum information processors

Superconducting Qubits Trapped Ion Qubits


3D Integration for Quantum ProcessorsIARPA Quantum Enhanced Optimization

SiliconMCM

Coplanar WaveguideTransition to MCM

Ribbon Bonds

RF Wiring Harness

QubitChip

Printed CircuitBoard

Metal Carrier

Microbumps

dc Wiring Harness

Wire Bonds

Interposer

Readout/interconnect

Qubitchip

Parametric readout amplifiersand qubit bias/control routing

Qubit 1

~100 mm

High-Q metal

Thick ground plane

Qubit 2

Qubitbias

Fewmm

Large, isolated qubit mode

volume Coupling

Through-silicon vias

In bumps

3-Stack enables high connectivity while maintaining high qubit coherence



SiliconMCM


Ribbon Bonds

RF Wiring Harness

QubitChip


Metal Carrier

Microbumps

dc Wiring Harness

Wire Bonds

Interposer


Qubitchip


Qubit 1

~100 mm

High-Q metal

Thick ground plane

Qubit 2

Qubitbias

Fewmm


volume Coupling


In bumps

Coupled superconducting qubitsFlux qubits for quantum annealing

50-100 us coherence times: Z1-10 us coherence times: X & Z

Circuit-model QC50-100 us coherence times

Yan et al., Nature Comm. (2016)MIT / MIT-LL (2017)

Kelly et al., Nature (2015)

Qubit layer fabrication used for both gate-model and QA qubits (they are different!)



SiliconMCM


Ribbon Bonds

RF Wiring Harness

QubitChip


Metal Carrier

Microbumps

dc Wiring Harness

Wire Bonds

Interposer


Qubitchip


Qubit 1

~100 mm

High-Q metal

Thick ground plane

Qubit 2

Qubitbias

Fewmm


volume Coupling


In bumps

Readout/interconnect layer routes wires and amplifies signals8-layer planar Niobium process for efficient wire routing

M6

M5

JJ5

M7

Josephson JunctionTraveling Wave Parametric Amplifier

Macklin et al., Science 350, 307 (2015) Tolpygo et al., IEEE Trans. (2014)


SiliconMCM


Ribbon Bonds

RF Wiring Harness

QubitChip


Metal Carrier

Microbumps

dc Wiring Harness

Wire Bonds

Interposer


Qubitchip


Qubit 1

~100 mm

High-Q metal

Thick ground plane

Qubit 2

Qubitbias

Fewmm


volume Coupling


In bumps

Interposer isolates qubit from readout/interconnect layer.Superconducting through-silicon vias provide connectivity.

210 mm

Patterned TiN

Through-silicon via lined with TiN


Donna Yost, Justin Malek et al., (2017)


SiliconMCM


Ribbon Bonds

RF Wiring Harness

QubitChip


Metal Carrier

Microbumps

dc Wiring Harness

Wire Bonds

Interposer


Qubitchip


Qubit 1

~100 mm

High-Q metal

Thick ground plane

Qubit 2

Qubitbias

Fewmm


volume Coupling


In bumps

Tilt < 0.25 mrad

Fabricated In bumpsCross-section of

bump-bonded chips

3D image of bump-bonded chips

IR image of bump-bonded chips

Alignment ~1 µm

Indium bumps connect chips and provide electromechanical joining


Danna Rosenberg et al., npj Quantum Information (2017)


Packaged qubit with flip chip bonded on top

6 identical qubits coupled to quarter wave resonators

0 10 20 30 40 50

20

40

60

80

100

T1~19 ms

0 10 20 20 40 50

100

80

60

40

20

Sign

al [m

V]

Time (ms)

Coherence Times(T1, T2 ~ 15-25 ms)

D. Rosenberg, D. Yost, R. Das, L. Racz, et al. (2015)

Over past 12 months, have demonstrated four critical building blocksElectrical

conduction

Interposer

Qubit chip

Proximal surface

Qubit chip

Si chip

Inductive coupling

Interposer

Qubit chip

Capacitive coupling

Interposer

Qubit chip

Coherence times comparable to planar qubits of same design

3D IntegrationFlip-Chip Bonding


equs.mit.edu


Team and collaborators

MIT EQuS Group

sponsorship

NEC/RIKEN/Tokyo Fumiki Yoshihara (NICT)Yasunobu Nakamura

MIT Lincoln Laboratory

UC BerkeleyJohn ClarkeIrfan Siddiqi

Peter BaldoJeff BirenbaumVlad BolkhovskyGreg CalusineJohn ChiaveriniEric Dauler (GL)Rabi DasGeorge Fitch Mark Gouker (ADH)Gerry HollandDavid HoverJamie Kerman (co-PI)David KimJustin MallekKaren MagoonLee MaillhotAlex MelvilleJovi MiloxiPeter Murphy

Kevin ObenlandWilliam D. Oliver (co-PI)Brenda OsadchyJason PlantJeanne PorterLivia Racz (AGL)Danna RosenbergJeremy SageGabriel SamachAdam Sears

Rick SlatterySergey TolpygoSteve WeberTerry WeirWayne WoodsAlex WynnJonilyn YoderDonna YostScott Zarr

Amy GreeneBharath KannanUwe Luepke Tim MenkeJack QiuYoungkyu Sung

EQuS

Daniel CampbellMorten KjaergaardPhilip KrantzJoel WangFei Yan

Mirabella Pulido

Simon GustavssonTerry OrlandoWilliam D. Oliver

ChalmersJonas Bylander

JuelichGianluigi Catelani

Brian MillsFancisca VasconcelosMegan Yamoah

quantum engineering of superconducting...

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