Coherent feedback control and autonomous quantum circuitsHideo MabuchiStanford University

DARPA-MTOAFOSR, ARO, NSF

http://www.rfdesignline.com/howto/209400216

�𝑺𝑺 �𝑹𝑹 𝑄𝑄

1 1 hold

0 1 → 1

1 0 → 0

0 0 undef

Feedback (control) motifs in circuit design

Stabilization(robustness)

Synthesis

Steady-state analysis can be intuitive, but need theory for dynamics (transients), noise

v2 = ¡v1GR2

R1 + R2 + GR1

! ¡R2

R1v1

Nanophotonic integration: on the roadmap?Y. Vlasov, CLEO Plenary (2012)

switching/routing, combinational logic, cache management, error correction…?

Spontaneous switching in attojoule “bistability”

Cs

J. Kerckhoff, M. A. Armen and HM, Opt. Express 19, 24468 (2011)

P. W. Smith, Phil. Trans. R. Soc. Lond. A 313, 349 (1984)

Ultra-low power nanophotonic circuit theory

PLINC exploits cavity-enhanced nonlinearity and circuit-scale

optical coherence to implement attojoule photonic logic

PLINC is a natural scheme for near-future integrated

nanophotonics, testable today using single-atom cavity QED

PLINC circuit theory = coherent-feedback quantum control

In1

In2 Out1

w x

¯

¯ ’

Out2

µ

µ ’

¼/4

¼/4

1. Develop QHDL, a subset of industry-standard VHDL for the specification of PLINC circuits

2. Develop software for compiling QHDL into rigorous quantum optical models

3. Use QHDL toolbox + high-performance numerical simulation for analysis and design of functional circuits

4. Validate key coherent feedback concepts in single-atom cavity QED experiments

HM, Appl. Phys. Lett. 98, 193109 & 99, 153103 (2011)

PLINC: Photonic Logic via Interferometry with Nonlinear Components

β

β

ϕ(P)ϕ0 P

Nonlinear dynamiccontroller

Attojoule nanophotonic switch stabilizationHM, Appl. Phys. Lett. 98, 193109 (2011)

-5 -4 -3 -2 -1 0 1 2 3 4 5-5

-4

-3

-2

-1

0

1

2

3

4

5

0 1 2 3 4 5 6 7 8 9 10

0

1

2

3

4

5

6

7

8

9

10

β

ϕ(P)ϕ0 P

Nonlinear dynamiccontroller

Attojoule nanophotonic switch stabilizationHM, Appl. Phys. Lett. 98, 193109 (2011)

In1

In2 Out1

w x

¯

¯ ’

Out2

µ

µ ’

¼/4

¼/4

In1

In2

Out1

w z Out2

Combinatorial logic: a PLINC NAND gateHM, Appl. Phys. Lett. 99, 153103 (2011)

Hierarchical Design

SR NAND latch

NAND gate

Quantum models for attojoule photonic switchingHM, Appl. Phys. Lett. 99, 153103 (2011)

N. Tezak, A. Niederberger, D. S. Pavlichin, G. Sarma and HM, Phil. Trans. Roy. Soc. A 370, 5270 (2012)

http://mabuchilab.github.com/QNET/

QHDL / Modelica workflowN. Tezak, A. Niederberger, D. S. Pavlichin, G. Sarma and HM, Phil. Trans. Roy. Soc. A 370, 5270 (2012)

G. Sarma, R. Hamerly, N. Tezak, D. S. Pavlichin and HM, IEEE Photonics J. 5, 7500111 (2013)

http://mabuchilab.github.com/QNET/

Quantum noise in large-scale coherent circuitsC. Santori et al. (HP Labs + Stanford), Phys. Rev. Appl. 1, 054005 (2014)

4-bit ripple counter

= 4 flip-flops

= 88 resonators

D. Pavlichin and HM, New J. Phys. 16, 105017 (2014)

Message passing in nanophotonic circuits

Ener

gyU

101 102

Time t

N=2-5 Free-Carrier Ising Machine

100 101 102 103

Time t

10-1

100

101

102

Ener

gyU−

Um

in

16-Gon

100 101 102 103

Time t

10-1

100

101

102

Frustrated 16-Gon

20 40 60 80t

100 120 140

30201001020304050

0

Re[

α]0 50 100

Re[βout]150 200

20

10

0

40

30

50

Im[β

out]

0 10002000300040005000Nph

0

500

1000

2500

2000

1500

Nc

Limit-cycle oscillators, synchronization and Ising-XYRyan Hamerly and HM, Phys. Rev. Appl. 4, 024016 (2015)

Role of entanglement? Y. Yamamoto et al., PRA 92, 043821

Coherent perceptron for all-optical machine learningN. Tezak and HM, EPJ Quantum Technology 2:10 (2015)

Embedded photonic signal-processing• MHz-GHz natural bandwidths

• Coherent ) very low dissipation (power in ¼ power out)

• Homogeneous platforms: nano/micro-photonic circuits; fiber sensor networks?

J. Vuckovic et al., 2011 New J. Phys. 13 055025 B. Park et al., 2011 IEEE Sensors J. 11 2643

Quantum error correction “circuits”

http://openbookproject.net/electricCircuits/Digital/DIGI_15.htmlphysicsworld.com (UCSB)

“superconducting trio get entangled”

Coherent-feedback autonomous quantum memoryJ. Kerckhoff, H. Nurdin, D. Pavlichin and HM, PRL 105, 040502 (2010)

J. Kerckhoff, D. S. Pavlichin, H. Chalabi and HM, New J. Phys.13, 055022 (2011)

R

OUT

OUTPOWER

in

SET in

RESETin

A. Faraon et al. New J. Phys. 15 025010 (2013)

B3

B1

R12

R11 B5

Q32

Q11

Q13

Q22

Q21

Coherent-feedback network “wiring diagram”J. Kerckhoff, H. Nurdin, D. Pavlichin and HM, Phys. Rev. Lett. 105, 040502 (2010)

J. Gough and M. R. James, IEEE Trans. Automat. Contr. 54, 2530 (2009)L. Bouten, R. van Handel and A. Silberfarb, Journal of Functional Analysis 254, 3123 (2008)

Gp = R12 / B3 / ((Q13 / Q21) ¢ (1; 0; 0)) / B1

Gf = (Q11 ¢ Q32 ¢ Q22) / (B5 ¢2 (1; 0; 0)) / (R11 ¢ (1; 0; 0))

N = Gp ¢ Gf ¢ Gp0 ¢ Gf

0 ¢ G¡

Network component modelsL. Bouten, R. van Handel and A. Silberfarb, J. Funct. Anal. 254, 3123 (2008) J. Kerckhoff, L. Bouten, A. Silberfarb and HM, Phys. Rev. A 79, 024305 (2009)

H. Mabuchi, Phys. Rev. A 80, 045802 (2009)

RSET in

RESET in

POWERin

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RESET in

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set

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er

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jei

jgijhi

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jei

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j®i 7! j ¡ ®i

j®i 7! j®ij+i

j®i 7! j ¡ ®ij¡i

Probe interaction: Z- (Duan-Kimble/Nielsen) or X-parity (Kerckhoff)

Closed-loop master equation; simulationsJ. Kerckhoff, H. Nurdin, D. Pavlichin and HM, PRL 105, 040502 (2010)

_½t = ¡i[H; ½t] +

7X

i=1

µLi½tL

¤i ¡

1

2fL¤iLi; ½tg

¶

H =p

2­¦(R1)g ¦

(R2)h X1 +

p2­¦

(R1)h ¦(R2)

g X3 ¡ ­¦(R1)g ¦(R2)

g X2

L1 =®p2f¾(R1)

hg (1 + Z1Z2)

+¦(R1)h (1¡ Z1Z2)g

L2 =®p2f¾(R1)

gh (1¡ Z1Z2)

+¦(R1)g (1 + Z1Z2)g

L3 =®p2f¾(R2)

hg (1 + Z3Z2)

+¦(R2)h (1¡ Z3Z2)g

L4 =®p2f¾(R2)

gh (1¡ Z3Z2)

+¦(R2)g (1 + Z3Z2)g

Autonomous quantum circuit design automationJ. Kerckhoff, D. S. Pavlichin, H. Chalabi and HM, New J. Phys.13, 055022 (2011)

G. Sarma, R. Hamerly, N. Tezak, D. S. Pavlichin and HM, IEEE Photonics 5, 7500111 (2013)G. Sarma and HM, New J. Phys. 15 035014 (2013)

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00100 00001

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10000 01000

10100 01001

11100 11001

10010 01010

M12+ M23+

M12+

M23+M12- M23-

M12-M23-

X1+ X3+

X1- X3-

X2+

X1- X3-

X2- X2-

code separability, subsystem structurel

robust circuit layout

Classical computation Fully-quantum computation

?

Computational power of semi-quantum architectures?

Decoherence-dependent complexity of classically simulating quantum models?

Dimensional reduction of open quantum networksN. Tezak, R. Hamerly, D. Pavlichin, G. Tabak; N. Amini (CNRS); M. Maggione (Johns Hopkins)

• MIT curriculum ca. 2010

• How will it look in 2030?

Abstraction is fundamental to modern engineering

Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare(http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on 3/17/09.

There is no simplequantum amplifier

abstraction!

Typical qubits andquantum circuits

Quantum/classicalprobability

Quantum andnanoscale device

physics

Vast majority of work in “quantum

engineering” today

?

Mabuchilab.wordpress.com

Kinetic (as opposed to equilibrium) hysteresisJ. Kerckhoff, M. A. Armen and HM, Opt. Express 19, 24468 (2011)

Phase switching in single-atom cavity QED

Cs

• single-atom cavity QED w/ strong driving• spontaneous dressed-state polarization• random binary phase-shift keying• switching dissipates » 0.23 aJ per edge

J. Kerckhoff, M. A. Armen, D. S. Pavlichin and HM, Opt. Express 19, 6478 (2011)