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Thomas Ohki, Group Leader

NY CREATES Emerging

Technologies Seminar Series talk

March 4, 2021

Quantum Engineering and Computing Group

Quantum Engineering & Computing Group BBN entered the “quantum frontier” in 2000

Demonstrated the first metropolitan scale quantum key distribution (secure optical comms)

Formed quantum research group in 2008 spurred by large DARPA quantum computing project

Nucleated efforts around superconducting quantum and classical computing and integrated

photonics

Currently have world-class cryogenic measurement labs, superconducting device fabrication,

quantum optics labs and QIS theory group

QEC focus is bringing research/basic physics to application demonstrations

~20 staff; mix of physicists, RF and software engineers, visiting scientists and interns

Resources include other Raytheon facilities and staff in addition to the Cambridge labs

Very active and necessary collaborations with academia, government labs and other industry

>20 publications/year (including Science, Nature, Phys. Rev. Lett., IEEE journals …)

Experimental Graham Rowlands KC FongMatt Ware Leonardo RanzaniBrian Hassick Guilhem RibeillAndrew Wagner Minh-Hai NyugenMartin Gustafsson Mohammed SoltaniAnshuman Singh Allen KreiderThomas Ohki

TheoryHari KroviLuke GoviaZac Dutton

Program managamentRich LazarusAkarsha RamaniCynthia Walsh

Alumni Chris Fuchs (Umass Bos), Chris Lirakis (IBM), Hanhee Paik (IBM), Colm Ryan (AWS), Blake Johnson (IBM), Saikat Guha (U of Arizona), Marcus Silva (Microsoft), Jon Habif (ISI), Dan Greenbaum (STR), Borja Peropadre (Zapata), Diego Riste (Keysight)

Many interns and visiting scientists over the years

Quantum Engineering and Computing Group

Optical and Microwave Photonics

Optical signal processing

Optical sensors

Optical comms

Quantum networking

Advanced Materials

2D materials and other “quantum” materials

Novel quantum bits materials

Single Photon Detectors

Spintronic devices

Quantum Computing and Networking

Quantum Control systems

Quantum Algorithms

Quantum Circuit Fabrication

Quantum Repeaters

Neuromorphic/Energy Efficient

Energy-efficient cryogenic logic

Energy efficient memory

Reservoir computing

Quantum reservoir computing

Quantum Engineering & Computing Group

Outline

• Josephson Junction oscillators

• Regimes of operation

• Quantum computing

• Quantum oscillator

• Qubits

• Classical oscillator

• Amplifiers and other microwave components

• Control and readout cryo electronics

• Reservoir computing

• Classical oscillator networks

• Quantum oscillator

Josephson Junction

Two superconductors interrupted by a tunnel barrierMost commonly Al-AlOx-Al: easy to grow oxide in situ

Superconductor wavefunction (phase) can tunnel across barrier.

Cooper pairs tunnel for free, energy cost associated with electron tunneling exponentially

dependent on barrier thickness.

Jj

1 um

Overview of Josephson Junction Oscillators

Josephson Junctions governed by two

relationships:

𝐼(𝑡) = 𝐼𝑐sin(𝜙 𝑡 )

𝑉 𝑡 =ℏ

2𝑒

𝑑𝜙(𝑡)

𝑑𝑡=

ℏ

2𝑒𝐼𝑐cos(𝜙)

𝑑𝐼

𝑑𝑡

Superconductor

Weak Link

Superconductor𝐼, 𝑉

|Ψ1⟩

|Ψ2⟩

𝜙 = 𝜙2 − 𝜙1

=Nonlinear Inductor, LJ

Equations of motion

𝑈(𝜙)

𝜙

0.8 𝐼𝑐1.2 𝐼𝑐

2.5 𝐼𝑐

1.6 𝐼𝑐

The dynamics are analogous to a pendulum where the current

is a direct torque. Oscillations can be highly non-sinusoidal.

𝛽𝑐

𝜔𝑐2

𝑑2𝜙(𝜏)

𝑑𝜏2+

1

𝜔𝑐

𝑑𝜙(𝜏)

𝑑𝜏+ sin𝜙 = 𝐼/𝐼𝑐

𝛽𝑐 = 𝜔𝑐𝑅𝑛𝐶, 𝜔𝑐 =2𝜋𝐼𝑐𝑅𝑛Φ0

0.0 𝐼𝑐

Environment

𝑈 𝜙 = −Φ0 𝐼𝐶 cos𝜙 − Φ0𝐼𝜙

IV and particle in well

Supercurrent branch

Energy Level Quantization at Zero Bias

Superconducting qubit = + nonlinear L

Josephson junction: only lossless, nonlinear electrical element

LC oscillator

𝜔𝑝 =𝐼𝑐Φ0𝐶

Cavity Quantum Electrodynamics (cQED)

2g = vacuum Rabi freq. ~Cc

k = cavity decay rate ~ QLC

g = “transverse” decay rate ~QNL-LC

† †12

ˆ ( )( ) ˆ2

azr a a a agH H Hk g

Quantized FieldElectric dipole

Interaction2-level system

Jaynes-Cummings Hamiltonian

Strong Coupling = g > k , g , 1/t

t = transit time ~ if LC is tunable this

is the time it is near resonance

Dissipation

Non-linear LC LC

Cc

Blais et al., Phys. Rev. A (2004)

Superconducting Qubit Circuits

Superconducting qubits

• Anharmonic oscillator mimics artificial

atom

• Manipulated with resonant microwave

fields, 4-8 GHz

• Connect via linear microwave resonators

BBN 10-qubit processor

Qubit

Coupler

Readout

Non-linear LCQubit

LC Coupler

Cc Cc

LC Readout

Cc Cc

I/O

Non-linear LCQubit

Quantum Limited Amplifiers (QLA)

DAC ADC

4K

10mK

77K

QB

6 GHz LO

100 MHz IF

QLA

G > 20dB

Tn < 150mK

BW ~500 MHz

PSAT >-100 dBm

HEMT 3K Tn G> 30dB

Cryogenic

isolators

Very challenging requirements for

amplifier chain requires QLAs at 10 mK

Single qubit example - single I/O channel

Qubits

Still in the well but a classical oscillator

Quantum Limited Amplifier

Parametric process and gain

Non-linear LC resonance fLC

J. Aumentado, "Superconducting Parametric Amplifiers: The State of the Art in Josephson

Parametric Amplifiers," in IEEE Microwave Magazine, vol. 21, no. 8, pp. 45-59, Aug. 2020

Superconducting Parametric LNAs

RTN-BBN Josephson Parametric Amplifier

• Broadband on-chip input transformer

• Low loss SiN dielectric processing

• Flux pumped

Large-area JJ

Broadband

match network

RF in/out

Pump + bias

2-10 GHz 4:1

Circuit schematic

Josephson Parametric Amplifier (JPA)20dB gain over 100’s MHZ BW

SNR

improvement

Qubit measurement

SNR improvement

Qubit as calibrated power source:

Measured TN = 295 mK

HEMT only: TN = 15 K

Specifications at 25 mK

Cross-checked system TN

with Y-factor meas.

fc = 6 GHz

Integrated Cryogenic Components and Logic:Utility in systems >1000 qubits

Google 50 qubit system

Pushing the control hardware down the fridge

Quantum Devices

Digital SFQ

(logic/ADC)

SMMIC

(QLA and

switches)

MUX and DeMUX

Quantum

Packaging

I/O via Optical

MUXING,

analog field

generation

CryoCMOS,

limited DSP

Cryomemory

77K

RT

4K

0.1K

0.01K

Thermal bottleneck for

RT to 4K interconnects

Algorithms drive

cryogenic

control/memory

requirement

Customized

components designed

to system

not general purpose or

wideband

Glossary:

MUX-multiplexing

DSP-digital signal

processing

SFQ-Single Flux Quantum

SMMIC-Superconducting

monolithic microwave ICs

Cryogenic Control and Readout

Exploding interest in novel architectures for cryogenic control

and readout of qubits

• Interesting at the few-qubit scale

• Useful at the NISQ scale

• Necessary for a general-purpose quantum computer

Leverage progress in cryo-electronics

• SFQ-family/RQL development

• Cryo-CMOS / FD-SOI / SiGe / III-V devices…

• Digital cryogenic readout (JPM, etc…)

Engineering challenges of cryogenic control: • Power dissipation for <1mW per qubit

• Reliability and scale of SFQ circuits

• Device and timing models, cryo PDKs not available from foundries

• Fast low-power memory for DACs/SFQ drivers and execution of

algorithms

• Serious architecture questions

Newer energy efficient circuits matured in government programs eg. IARPA C3

Quantum science and technology 3 (2), 024004

Reminder: Dynamics of Finite Voltage Operation

𝑈(𝜙)

𝜙

0.8 𝐼𝑐1.2 𝐼𝑐

2.5 𝐼𝑐

1.6 𝐼𝑐

The dynamics are analogous to a pendulum where the current

is a direct torque. Oscillations can be highly non-sinusoidal.

𝛽𝑐

𝜔𝑐2

𝑑2𝜙(𝜏)

𝑑𝜏2+

1

𝜔𝑐

𝑑𝜙(𝜏)

𝑑𝜏+ sin𝜙 = 𝐼/𝐼𝑐

𝛽𝑐 = 𝜔𝑐𝑅𝑛𝐶, 𝜔𝑐 =2𝜋𝐼𝑐𝑅𝑛Φ0

0.0 𝐼𝑐

Environment

𝑈 𝜙 = −Φ0 𝐼𝐶 cos𝜙 − Φ0𝐼𝜙

Coupling these oscillators

Single flux quantum

Coupled damped oscillators

torsion spring coupled pedula analogy

Simple Circuits for Qubit ControlControl

Coherent control demonstrated and benchmarked with 3% error E. Leonard J … BLT PLourde, R McDermott Phys.

Rev. Applied 11, 014009 (2019)Old experiment:

D. S. Crankshawet al, An RSFQ variableduty cycle oscillator for driving a superconductive qubit ,IEEE Trans. Appl. Supercond.13, 966 (2003).

Single flux quantum

• Digital I/0 for easy low speed digital interface

• This specific example

• DC-5 GHz operation speed capability

• 30 A/cm2 specialized Nb SFQ/qubit process

• Qubit flux state readout speed is 30 ps

-Copper cooling fins

-SiOx dielectric

-Nb trilayer

Simple Circuits for Qubit Readout

Ohki et al, manuscript in prep

Simple Circuits for Cavity Qubit Readout

A. Opremcak … BLT PLourde, R McDermott

Phys. Rev. X 11, 011027 (2021)

Revisit simple coupled oscillator JTL

A parallel, inductively coupled JJ array obeys the

spatially discretized (modified) Sine-Gordon Equation

The discrete system supports rich soliton dynamics —

annihilation, pair creation, and pass-through — all of which:

have been observed in experiment.

𝑑2𝜙

𝑑𝑥2

𝛽𝑐

𝜔𝑐2

𝑑2𝜙(𝜏)

𝑑𝜏2+

1

𝜔𝑐

𝑑𝜙(𝜏)

𝑑𝜏+ sin𝜙 =

1

2𝜋𝛽𝐿𝜙𝑛−1 − 2𝜙𝑛 + 𝜙𝑛+1 + 𝐼/𝐼𝑐

𝛽𝐿 =𝐿𝐼0Φ0

Single flux quantum

K. Nakajima, et al. Phys. Rev. Lett. 65, 1667–1670 (1990).

K. Nakajima et al. J. of Appl. Phys. 45, 3141 (1974).

Coulombe, J. C., York, M. C. A. & Sylvestre, J. PLoS ONE 12, e0178663 (2017).

Similarities to other reservoir computing implementations:

Nearly identical to MEMS reservoirs, which have Duffing

nonlinearity instead of full sinusoidal nonlinearity.

Coupled mechanical oscillators

Run the system and obtain

signals 𝑋

Calculate the explicit output weights

𝑾𝑜𝑢𝑡

Run the system and multiply by weights

Traditional Artificial NN Approach Reservoir Approach

Backpropagation Forward Evolution

Run the system and obtain outputs1

Propagate errors backwards to converge on

weights2

3 Run the system with final trained weights

1

2

3

What is reservoir computing?

What can a reservoir do?

Mackey-Glass Reservoir• Many things normal neural networks can

do

• Classification (image, speech, etc.)

• Excellent for processing time-domain data

• Nonlinear forecasting

• Nonlinear control

To emulate a chaotic delay-differential

equation (Mackey-Glass), train the reservoir

for some interval on the output of the above

differential equation, then feed the reservoir’s

output back into itself.

𝑑𝑥

𝑑𝑡= 𝛽

𝑥𝜏1 + 𝑥𝜏

𝑛 − 𝛾𝑥

Let nature do the computation for us: the evolution of physical systems provides reservoir functionality. Fixed random weights can be ”baked in” or provided by natural variation in physical system parameters. No weight memory is required, and computation can take place at the natural speed of a physical systems.

Only requirements are that response must be nonlinear, repeatable, and complex (i.e. system has high dimensionality), as well as exhibit fading memory..

Enhanced dimensionality can also be provided by quantum systems.

𝑾𝑜𝑢𝑡 = 𝒀𝑡𝑎𝑟𝑔 𝑿𝑇 𝑿𝑿𝑇 + 𝛼2𝑰 −𝟏

𝒀𝑔𝑢𝑒𝑠𝑠 = 𝑾𝑜𝑢𝑡 𝑿𝑡𝑒𝑠𝑡

One of the first physical reservoirs was a shallow water tank on an overhead projector.

Fernando, Sampsa "Pattern recognition in a bucket." European conference on artificial life., 2003.

Weights are an explicit function of outputs. Use either Moore-Penrose pseudo-inverse or Ridge Regression.

Input DataServo Motor Control

Output Data

Pixel data from ripples

Weigh

t Mu

lt

Result

Physical Systems: a wide variety of implementations

FPGAMemristorMEMS Spintronic

Physical Systemsas Reservoirs

System throughput is determined by the natural physical timescales

Optical

and many others…

Are highly nonlinear

Are easy to couple (R, L, or C)

Operate at extremely high speeds (>100 GHz)

Can interface directly to superconducting logic

1

2

3

Superconducting Circuits as Reservoirs

Superconducting oscillators are a good

candidate for a hardware reservoir, in particular

because they:

High Level Reservoir Design

Josephson Junction

Easy coupling eliminates the need for virtual

nodes, which degrade system throughput. This

makes scaling straightforward.

High speeds enable channel equalization for 5G

networking, or accelerate lower rate tasks by

many orders of magnitude.

Superconducting logic provides ADCs, counters,

integrators, decimators, and filters that operate

at 50+ GHz. Eliminating bottlenecks.

4

1b/s 1Kb/s 1Mb/s 1Gb/s

Memristor

Data Rates For Physical Reservoirs

Photonic

Spin TorqueMEMS

CMOS/FPGA SC (BBN)

The Josephson Transmission Line ReservoirUse this Josephson transmission line (JTL) as a

reservoir, and drive using a parallel input scheme

as in Coulombe et. al. 2017.

All junctions are put into an auto-oscillatory state

with a current bias 𝐼𝑏 > 𝐼𝑐 to which the input signal

𝐼𝑠(𝑡) is added. The dynamics show complex

wavelike propagation of signals throughout the line.

Some heterogeneity is required, either by driving

a subset of JJs or by introducing some spread in 𝐼𝑐or another circuit parameter.

The sample-and-hold time can be as short as 15

ps depending on the choice of junction parameters.

But, this timescale can be extended.

But what about readout?

Coulombe, J. C., York, M. C. A. & Sylvestre, J. PLoS ONE 12, e0178663 (2017). G Rowlands,… TAO “Reservoir Computing with Superconducting Electronics” arXiv:2103.02522

Application: High Rate Channel Equalization

100 Gb/s Channel Equalization

Recover the original symbols for a 4PAM modulation

scheme in a nonlinear channel subject to multipath

interference* and additive white Gaussian noise (AWGN).

* We use the common channel in the RC literature, but drop the acausal FIR coefficients.

Compare to:

Adaptive LMS (least mean-square) filter

Limit with perfect channel inverse

Limit for full channel with no equalization

1

2

3

Performance we find the N=40 JTL reservoir can

equalize at a rate of 100 Gb/s (50 GS/s) and outperform

LMS results with only 104 training samples.

Application: High Rate Channel Equalization

100 Gb/s Channel Equalization

Recover the original symbols for a 4PAM modulation

scheme in a nonlinear channel subject to multipath

interference* and additive white Gaussian noise (AWGN).

* We use the common channel in the RC literature, but drop the acausal FIR coefficients.

The reservoir implements a perfect inverse filter:

looking at the performance of a manually constructed

inverse, we see the same performance.

All of the reservoirs we’ve implemented

(superconducting and others) saturate at this

performance: this implies that accuracy among

different reservoirs is likely to be similar. One may as

well choose a reservoir with the best efficiency,

speed, or some other desirable quality. Lee, J. et al. Deep Neural Networks as Gaussian

Processes. arXiv:1711.00165 [cs, stat] (2018).

Other Applications: Higher Order Parity

𝑃 𝑛, 𝑡 =ෑ

𝑖=0

𝑛−1

𝑢[𝑁 − 𝑖 + 𝑡 ]

Calculate the higher order parties for a bitstream

played serially through the reservoir. This is known to

be a difficult problem in machine learning.

Performance: we find a N=45 JTL reservoir can calculate

parity at a rate of 50 Gb/s with a memory capacity

comparable to those seen in the RC literature.

Coulombe, J. C., York, M. C. A. & Sylvestre, J. PLoS ONE 12,

e0178663 (2017).

Dion, G., Mejaouri, S. & Sylvestre, J. Journal of Applied

Physics 124, 152132 (2018).

Accuracy vs. Delay

50 Gb/s High Order Parity Check

.

Spoken digit classification using freely available

AudioMNIST dataset [1]. Used 16 female and male

speakers, trained on 10 utterances, tested on 10

utterances.

[1] https://arxiv.org/abs/1807.03418

Performance: with N=5 reservoir, data rate

upconversion

Early results: 70% accurate spoken digit

identification at ~109 faster than real time.

Towards Experiments: Chip Designs

Output Stage

TFF + SFQ/DC for 2x decimation

and NRZ conversion

SC Reservoir

JTL with large shunt capacitors slows

down pulse propagation times..

The BBN ”Fresh Pond” Architecture

Quantum Oscillators for Quantum Reservoir Computing

Single Oscillator Devices

QUANTUM RESERVOIRS• Potential quantum advantage from exponentially larger reservoir state-space or Hilbert Space, and entanglement.• Largely unexplored in current quantum technology.• May uniquely leverage current quantum computing capabilities: resilient to noise, low control requirements.

L. C. G. Govia,… TAO “Reservoir computing with a single

nonlinear oscillator” Phys. Rev. Research 3, 013077 (2021)

B. Kalfus,… TAO, LCGG. “Neuromorphic computing with a

single qudit” arXiv:2101.11729 (2021)

Performance of Quantum RC

Sine phase estimation

Sine amplitude and phase estimationNext, how would more oscillators perform? Experiments?

L. C. G. Govia,… TAO

“Reservoir computing

with a single nonlinear

oscillator” Phys. Rev.

Research 3, 013077

(2021)

B. Kalfus,… TAO, LCGG.

“Neuromorphic computing

with a single qudit”

arXiv:2101.11729 (2021)

Summary

• Josephson Junction oscillators are extremely versatile

• Many other applications not discussed

• Quantum computing

• Just a simple single Jj nonlinear oscillator is the basis for a

huge industry now based on superconducting quantum

computing: IBM, Google etc.

• Reservoir computing

• Lots of promise for reservoir computing hardware

• Superconductors may provide an advantage for specific use

case/operation environment

• Could leverage huge investments in QC technology

Acknowledgements and Collaborations

Thank you!