Design and analysis of autonomous quantum memories based on coherent feedback control

Transcription

1 Design and analysis of autonomous quantum memories based on coherent feedback control Hideo Mabuchi, Stanford University _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 SET in OUT jei SET in RESET in R OUT OUT RESET in R set power jsi POWER in POWER in OUT jhi jgi ARO, NSF, (DARPA-MTO)

2 Continuous syndrome detection Coherent feedback + (S,L,H) modeling Autonomous/Embedded

3 Quantum error correction circuits J. Vuckovic

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6 Continuous syndrome detection Coherent feedback + (S,L,H) modeling Autonomous/Embedded

7 Physical model of continuous Z measurement L-M. Duan and H. J. Kimble, Phys. Rev. Lett. 92, (2004) A. B. Nielsen, PRA 81, (2010) j i 7! j i j i 7! j i j+i! c j i 7! j i j i! c Idealization applies in the limit of large g, κ with g/κ fixed (QSDE limit theorem) Dispersive version with smaller phase shifts, A. B. Nielsen, PRA 81, (2010)

8 Parity measurement via sequential scattering J. Kerckhoff, L. Bouten, A. Silberfarb and HM, Phys. Rev. A 79, (2009) g=104, κ=23.4 MHz jª 0 i / (ju 1 i + jd 1 i) (ju 2 i + jd 2 i) / (ju 1 u 2 i + jd 1 d 2 i) + (ju 1 d 2 i + jd 1 u 2 i)

9 Discrete analogy: an odd but valid bit-flip circuit τ τ Syndrome measurement rate τ -1 limited by time required for CCNOT gates Further decrease in τ requires CCNOT! CCROT, statistical syndrome measurement Continuous limit obtained by taking τ! 0 with fixed information rate κ Continuous syndrome measurement: ancilla qubit stream laser beam gates Hamiltonian couplings time interval laser intensity reduced complexity ions/q-dots/nv-c s/circuit QED,

10 Error-state graph for the bit-flip code Continuous QND syndrome measurement ) Markov jump dynamics for error state Mapping of error state to syndrome is degenerate

11 Error-state tracking with a Wonham filter Ramon van Handel and HM, quant-ph/ Assertion (numerically testable via comparison to SME): optimal filter for the error state can be derived as a Wonham filter (Wonham, 1965) for the induced Markov jump process of the error state plant error-state observer M 1, M 2 nonlinear filter, much studied in hybrid stochastic control theory Filter stability results: P. Chigansky and R. van Handel, Model robustness of finite state nonlinear filtering over the infinite time horizon, Ann. Appl. Probab. 17, 688 (2007).

12 Jump dynamics of the error state Continuous syndrome measurement localizes the error state; bit-flip decoherence induces jump-like transitions Finite measurement strength/sensitivity gives rise to detection delay and quiescent fluctuations

13 Continuous syndrome detection Coherent feedback + (S,L,H) modeling Autonomous/Embedded

14 Coherent feedback vs. measurement feedback Coherent-feedback control Measurement-feedback control z u z u A ' laser PLANT CONTROLLER PLANT CONTROLLER y w y w Feedback signal is quantum Feedback signal is classical We are generally interested in (semi-)coherent quantum plant dynamics in both cases We are generally interested in real-time feedback, i.e., faster than open-loop T 1

15 Coherent-feedback quantum memory schematic J. Kerckhoff, H. Nurdin, D. Pavlichin and HM, PRL 105, (2010) Q3 j2 i Q2 R2 R1 j i j i Q1

16 Continuous syndrome detection Coherent feedback + (S,L,H) modeling Autonomous/Embedded

17 Network component models J. Kerckhoff, H. Nurdin, D. Pavlichin and HM, PRL 105, (2010) 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

18 Simplified four-state relay model jei jri SET in OUT RESET in jhi jgi POWER in OUT SET in RESET in R OUT OUT Idealized/abstracted component model, obtained rigorously in the small-volume limit: POWER in

19 Coherent-feedback network wiring diagram J. Kerckhoff, H. Nurdin, D. Pavlichin and HM, PRL 105, (2010) J. Gough and M. R. James, to appear in IEEE Trans. Automat. Contr. (2009); arxiv: v3 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

20 Closed-loop master equation; simulations 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) _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 ) g (R ) h X 1 + p 2 (R ) h (R ) g X 3 (R ) g (R ) g X 2 L 1 = p 2 f¾ (R ) hg (1 + Z 1 Z 2 ) + (R ) h (1 Z 1 Z 2 )g L 2 = p 2 f¾ (R ) gh (1 Z 1Z 2 ) + (R ) g (1 + Z 1 Z 2 )g L 3 = p 2 f¾ (R ) hg (1 + Z 3 Z 2 ) + (R ) h (1 Z 3 Z 2 )g L 4 = p 2 f¾ (R ) gh (1 Z 3Z 2 ) + (R ) g (1 + Z 3 Z 2 )g

21 Modeling propagation losses G. Sarma (unpublished) J. Vuckovic

22 Master equation simulations with losses G. Sarma (unpublished)

23 Coherent-feedback control James, Nurdin and Petersen, IEEE-TAC 53, 1787 (2008); HM, Phys. Rev. A 78, (2008) PD PBS HWP PZT2 z u z u w G K y 9 MHz 14 cm PLANT design c = p 2(k1 + k4) CONTROLLER PBS HWP 7 MHz 49 cm y w PZT1 optical feedback dynamic compensator

24 Coherent feedback control of optical bistability H. Mabuchi, Appl. Phys. Lett. 98, (2011) β ϕ 0 Nonlinear dynamic controller ϕ( ) 50 In2 Out1 45 ¼/4 In1 w µ x µ ¼/ Out

25 Coherent feedback control in nanophotonic circuits PLINC: Photonic Logic via Interferometry with Nonlinear Components 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 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

26 Quantum optical circuit modeling workflow N. Tezak, A. Niederberger, D. S. Pavlichin, G. Sarma and HM, arxiv: Comprehensive software package for automated network model analysis (based on custom code and open source software) Network Optimization Schematic Capture Quantum Hardware Description Language Quantum Network Model Visual circuit design allows for creation of large, complex networks. Plain text representation of circuit model. Can easily be published / shared among collaborators. Compile QHDL circuit file into mathematical model. Analyze/reduce model. Set up and run numerical simulations.

27 SR NAND latch Visual circuit design Hierarchical Design NAND gate Schematic Capture Export to QHDL Compute Model

28 A Quantum Hardware Description Language Subset of VHDL (VHSIC Hardware Description Language) Specification of a circuit in terms of: input/output ports, model parameters circuit schematic/netlist (structural VHDL) subcomponents as black boxes (Hierarchical Design Principle) Schematic Capture Export to QHDL Compute Model

29 Quantum optical circuit model Visual representation of algebraic network expression (automatically generated) Completely determines model Computer algebra approach for analytic model analysis/reduction/ optimization Automatically set up numerical simulation of model dynamics Schematic Capture Export to QHDL Compute Model

30 Continuous syndrome detection Coherent feedback + (S,L,H) modeling Autonomous/Embedded