Coherent feedback control and autonomous quantum circuits
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1 Coherent feedback control and autonomous quantum circuits Hideo Mabuchi Stanford University DARPA-MTO AFOSR, ARO, NSF
2 Feedback (control) motifs in circuit design Stabilization (robustness) v 2 = v 1 GR 2 R 1 + R 2 + GR 1! R 2 R 1 v 1 SS RR QQ 1 1 hold Synthesis undef Steady-state analysis can be intuitive, but need theory for dynamics (transients), noise
3 Nanophotonic integration: on the roadmap? Y. Vlasov, CLEO Plenary (2012) switching/routing, combinational logic, cache management, error correction?
4 Spontaneous switching in attojoule bistability J. Kerckhoff, M. A. Armen and HM, Opt. Express 19, (2011) Cs P. W. Smith, Phil. Trans. R. Soc. Lond. A 313, 349 (1984)
5 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 HM, Appl. Phys. Lett. 98, & 99, (2011) PLINC: Photonic Logic via Interferometry with Nonlinear Components 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 + highperformance numerical simulation for analysis and design of functional circuits 4. Validate key coherent feedback concepts in singleatom cavity QED experiments In1 In2 ¼/4 w ¼/4 µ x Out1 µ Out2
6 Attojoule nanophotonic switch stabilization β HM, Appl. Phys. Lett. 98, (2011) β ϕ 0 P Nonlinear dynamic controller ϕ(p)
7 Attojoule nanophotonic switch stabilization HM, Appl. Phys. Lett. 98, (2011) β ϕ 0 P Nonlinear dynamic controller ϕ(p)
8 Combinatorial logic: a PLINC NAND gate HM, Appl. Phys. Lett. 99, (2011) Out1 In1 w z Out2 In2 In2 Out1 In1 ¼/4 w µ x µ ¼/4 Out2
9 Quantum models for attojoule photonic switching HM, Appl. Phys. Lett. 99, (2011) N. Tezak, A. Niederberger, D. S. Pavlichin, G. Sarma and HM, Phil. Trans. Roy. Soc. A 370, 5270 (2012) SR NAND latch Hierarchical Design NAND gate
10 QHDL / Modelica workflow N. 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, (2013)
11 Quantum noise in large-scale coherent circuits C. Santori et al. (HP Labs + Stanford), Phys. Rev. Appl. 1, (2014) 4-bit ripple counter = 4 flip-flops = 88 resonators
12 Message passing in nanophotonic circuits D. Pavlichin and HM, New J. Phys. 16, (2014)
![Appl. 4, 024016 (2015) Re[α] 30](/docs-images/87/95989800/images/13-4.jpg "20 10 0 10 20 30 40 50 0 2500")
![Im[β out] 20 10 0 500 0 50 100](/docs-images/87/95989800/images/13-6.jpg "Re[β out] 150 200 0 0 10002000")
13 Limit-cycle oscillators, synchronization and Ising-XY N=2-5 Free-Carrier Ising Machine Ryan Hamerly and HM, Phys. Rev. Appl. 4, (2015) Re[α] t N c Energy U Im[β out] Re[β out] N ph Time t Gon Frustrated 16- Gon 10 2 Energy U U min Time t Time t Role of entanglement? Y. Yamamoto et al., PRA 92,
14 Coherent perceptron for all-optical machine learning N. Tezak and HM, EPJ Quantum Technology 2:10 (2015)
15 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 B. Park et al., 2011 IEEE Sensors J
16 Quantum error correction circuits physicsworld.com (UCSB) superconducting trio get entangled
17 Coherent-feedback autonomous quantum memory J. Kerckhoff, H. Nurdin, D. Pavlichin and HM, PRL 105, (2010) J. Kerckhoff, D. S. Pavlichin, H. Chalabi and HM, New J. Phys.13, (2011) A. Faraon et al. New J. Phys (2013) SET in OUT RESET in R POWER in OUT
18 Coherent-feedback network wiring diagram J. Kerckhoff, H. Nurdin, D. Pavlichin and HM, Phys. Rev. Lett. 105, (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) R 11 B 5 Q 11 B 3 R 12 Q 13 B 1 Q 22 Q 21 Q 32 G p = R 12 / B 3 / ((Q 13 / Q 21 ) (1; 0; 0)) / B 1 G f = (Q 11 Q 32 Q 22 ) / (B 5 2 (1; 0; 0)) / (R 11 (1; 0; 0)) N = G p G f G p 0 G f 0 G
19 Network component models L. 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, (2009) H. Mabuchi, Phys. Rev. A 80, (2009) Probe interaction: Z- (Duan-Kimble/Nielsen) or X-parity (Kerckhoff) j i 7! j i j i 7! j i j+i jri jei jri jei j i 7! j i j i jhi jgi jhi jgi SET in OUT jei SET in RESET in R OUT OUT RESET in R set power jsi POWER in POWER in OUT jhi jgi
20 Closed-loop master equation; simulations J. Kerckhoff, H. Nurdin, D. Pavlichin and HM, PRL 105, (2010) _½ t = i[h; ½ t ] + 7X i=1 µ L i ½ t L i 1 2 fl i L i ; ½ t g H = p 2 (R 1) g (R 2) h X 1 + p 2 (R 1) h (R 2) g X 3 (R 1) g (R 2) g X 2 L 1 = p 2 f¾ (R 1) hg (1 + Z 1 Z 2 ) + (R 1) h (1 Z 1 Z 2 )g L 2 = p 2 f¾ (R 1) gh (1 Z 1Z 2 ) + (R 1) g (1 + Z 1 Z 2 )g L 3 = p 2 f¾ (R 2) hg (1 + Z 3 Z 2 ) + (R 2) h (1 Z 3 Z 2 )g L 4 = p 2 f¾ (R 2) gh (1 Z 3Z 2 ) + (R 2) g (1 + Z 3 Z 2 )g
21 Autonomous quantum circuit design automation J. Kerckhoff, D. S. Pavlichin, H. Chalabi and HM, New J. Phys.13, (2011) G. Sarma, R. Hamerly, N. Tezak, D. S. Pavlichin and HM, IEEE Photonics 5, (2013) G. Sarma and HM, New J. Phys (2013) M 12 + M X 1 - X 1 + X 3 + X M 12 - M 23 - M M 12 + code separability, subsystem structure l robust circuit layout M X 2 - X 1 - X 3 - X X M 12 -
22 Dimensional reduction of open quantum networks N. Tezak, R. Hamerly, D. Pavlichin, G. Tabak; N. Amini (CNRS); M. Maggione (Johns Hopkins) Classical computation Fully-quantum computation? Computational power of semi-quantum architectures? Decoherence-dependent complexity of classically simulating quantum models?
23 Abstraction is fundamental to modern engineering Quantum/classical probability Quantum and nanoscale device physics MIT curriculum ca Anant Agarwal and Jeffrey Lang, course materials for Circuits and Electronics, Spring MIT OpenCourseWare ( Massachusetts Institute of Technology. Downloaded on 3/17/09. How will it look in 2030? There is no simple quantum amplifier abstraction!? Typical qubits and quantum circuits Vast majority of work in quantum engineering today
24 Mabuchilab.wordpress.com
25 Kinetic (as opposed to equilibrium) hysteresis J. Kerckhoff, M. A. Armen and HM, Opt. Express 19, (2011)
26 Phase switching in single-atom cavity QED J. Kerckhoff, M. A. Armen, D. S. Pavlichin and HM, Opt. Express 19, 6478 (2011) Cs single-atom cavity QED w/ strong driving spontaneous dressed-state polarization random binary phase-shift keying switching dissipates» 0.23 aj per edge
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