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Towards modeling of classical and quantum mind in superconductor

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The usage of RSQF [1] instead of semiconductor electronics allows reduction of energy use up to 6 orders of magnitude. It is reported that 10^5 Josephson junctions in RSQF architecture
have been implemented on one chip by AIST. Certain steady development of superconducting quantum computer is observed and it is thus promising implementation of quantum Turing
machine [2]. Quantum state is fragile against decoherence and quantum computing chip is thus small and costly [3]-[4]. Therefore big quantum computer is unlikely and one needs to
use both superconducting classical and quantum chips. Flux superconducting qubit can be integrated with RSQF electronics on one chip [5]. Thus qubit state can be set and read by RSFQ chips [5]. In that framework we obtain hybrid classical-quantum superconducting computer on big scale on the same chip. This drives need for mixed classical-quantum computer algorithms robust against various types of noise. Since Josephson junctions in RSQF architecture can simulate Spiking Neural network [6]-[7] it is possible to represent classical mind in superconductor in analogy to semiconductor SPINNAKER [2]. Limited tests on hypothesis of quantum features in human brain become accessible. Therefore it is possible to obtain hybrid classical-quantum mind implemented in superconductor what can be represented by classical-quantum neural networks. We present the methodologies necessary to model proposed system and design new experiments that can be conducted using London, Ginzburg-Landau, Bogoliubov-de Gennes & non-equilibrium Green formalisms implemented in numerical relaxation method. Execution of quantum algorithms is expected to be traced. New hardware architectures [8] and various approaches are analyzed [9]-[11].

References:

1. K. K. Likharev, NATO ASI Series, Series E: App. Sci. 251, 221 (1993).
2. J. Q. You, F. Nori, Phys. Today 58, 11, 42 (2005).
3. B. Foxen et al., Quantum Sci. Technol. 3, 014005 (2018).
4. J. Martinis, www.technologyreview.com/s/544421/googles-quantum-dream-machine (2017)
5. N. V. Klenova et al., Low Temp. Phys. 43, 789 (2017).
6. P. Crotty, et al., Phys. Rev. E 82, 011914 (2010).
7. T. Hirose, et al., Physica C 463–465, 1072 (2007).
8. A. Grübl, PhD thesis, Heidelber University (2010).
9. K. Pomorski, et al., arxiv.org/abs/1607.05013 (2016).
10. J. M. Shainline, et al., Phys. Rev. App. 7, 034013 (2017).
11. Z. He, D. Fan, arxiv.org/pdf/1705.02995.pdf (2017).

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Towards modeling of classical and quantum mind in superconductor

  1. 1. Towards modeling of classical and quantum mind in superconductor Krzysztof Pomorski1,6, Pawel Peczkowski2,5, Marcin Kowalik1, Przemyslaw Prokopow3 , Akira Fujimaki4 AGH-PL1, IFJ-PL2, RIKEN-JP3, Nagoya University-JP4, ICBM-PL5, University of Warsaw-PL6 May 3, 2018
  2. 2. Table of contents Spiking neural networks RSQF electronics Superconducting qubits Quantum annealing Hybrid classical-quantum algorithms Variational approach in designing new circuits
  3. 3. Perceptron
  4. 4. Spiking neural network in biology
  5. 5. Hodgkin-Huxley model where I is the current per unit area, and αi , αi and βi , βi are rate constants for the i-th ion channel, which depend on voltage but not time. ¯gn, ¯gn is the maximal value of the conductance. n, m, and h are dimensionless quantities between 0 and 1 that are associated with potassium channel activation, sodium channel activation, and sodium channel inactivation, respectively.
  6. 6. Simplified model of SNN
  7. 7. Gates for spikining neural network
  8. 8. [From presentation of Will Zeng (Rigetti)-Architectures for Hybrid Quantum /Classical Computing]
  9. 9. Basic features of superconductor No dissipation during current flow Meissner effect Macroscopic Quantum Effect
  10. 10. Definition of Josephson junction
  11. 11. Josephson junction neuron by P.Crotty, 2010
  12. 12. Josephson junction neuron waveform [By Patric Crotty et al. Josephson junction simulation in neurons,
  13. 13. Bases of fluxon electronics
  14. 14. Artificial neural networks in superconductor Articial neural network based on SQUIDs: demonstration of network training and operation by F.Chiarello et al.
  15. 15. Basic superconducting qubit architectures
  16. 16. Gates between classical superconducting electronics and Quantum computer electronics
  17. 17. Quantum vs classical annealing
  18. 18. Quantum annealing chip by D-wave company
  19. 19. By D-wave company.
  20. 20. Towards more efficient usage of quantum computer Figure: Example of non-efficient interface between classical semiconductor and superconducting computer. Definition of bad approach is when we try to combine two technologies that are not working in the same thermodynamic enviroments [as semiconductor technology with superconductor technology].
  21. 21. Quantum mechanics vs Neural Networks Quantum neural networks by A.Ezhov and Dan Ventura
  22. 22. Algorithms for hybrid classical-quantum computer 1. Movement of ion in potential trap can be captured by classical-quantum computer. The potential trap fields can be modeled by classical part of computer while energetic levels and dynamics of microstates in ion can be modeled by quantum chips. [hybrid classical-quantum computer simulating ion trap quantum computer] 2. Quantum ants [hypothetical concept proposed here and not yet implemented] with classical finite state machine in ant head and with quantum trajectories (when ants moves towards food place) 3. Simulations of quantum life. 4. Quantum chemistry... 5. Many others systems ...
  23. 23. Lattice of classical and quantum chips Massive classical chips are to be connected with ”diluted” quantum chips... Periodicity of the structure is assumed to be imposed. Quantum chips are to be insulated from outside enviroment by special shields..
  24. 24. Modeling of classical-quantum chip lattice Relaxation algorithm using quasi-one dimensional Ginzburg-Landau equations with addition to Bogoliubov-de Gennes equations is preassumed to be first working methodology.... modeling optimal or suboptimal design of hybrid classical-quantum computer. In relaxation method we adapt the scheme: δF δXi = ρi ∆Xi ∆t , (1) where Xi = (ψ, A, M) and ρi is some number characteristic for given field Xi . In practical way we compute fields Xi and its changes ∆Xi on finite lattice in fixed step ∆t (’virtual time step’), where ρi is some real valued constat. It is desirable to take initial guess of Xi fields distribution that is given by physical intuition.
  25. 25. Simple case of usage of relaxation method in Ginzburg-Landau equations
  26. 26. Field Induced Josephson junctions https://arxiv.org/abs/1607.05013
  27. 27. Variational approach towards superconducting electronics https://arxiv.org/abs/1607.05013
  28. 28. D-wave company and application of quantum annealing to train deep neural networks (classical-quantum chip architecture) Articial neural network based on SQUIDs: demonstration of network training and operation by F.Chiarello et al.
  29. 29. Overlap of disciplines
  30. 30. Bibliography [1]. Hybrid quantum circuit with a superconducting qubit coupled to a spin ensemble, Y. Kubo et al., https://arxiv.org/pdf/1110.2978 [2]. K.Pomorski, H.Akaikde, A.Fujimaki, Towards robust coupled field induced Josephson junctions, ArXiv:1607.05013, 2016 [3]. A. Stoica et al., Evolutionary design of electronic devices and circuits ,Proceeding of Evolutionary Computation, 1999. http://ieeexplore.ieee.org/document/782588/ [4]. J.Martinis materials: Design of superconducting computer [5]. Entanglement in a quantum annealing processor, arXiv:1401.3500v1 [quant-ph] 15 Jan 2014. [6]. Mimicking the Brain with Superconductors and LEDs https://physics.aps.org/synopsis-for/10.1103/ PhysRevApplied.7.034013 [7]. S. Anders et al, European roadmap on superconductive electronics status and perspectives, Physica C 470, 2010, http://www. sciencedirect.com/science/article/pii/S0921453410005332 [8]. Patrick Crotty, Dan Schult and Ken Segall, Josephson junction simulation of neurons, Physical Review E, Vol. 82, 2010, [9]. J.You, F.Nori, Physics Today, Superconducting Circuits and Quantum Information, 2015 + many others...
  31. 31. [10]. https://physicsandcake.wordpress.com/2009/07/20/ quantum-neural-networks-1-the-superconducting-neuron-model [11]. Application of Quantum Annealing to Training of Deep Neural Networks by Steven H. Adachi and Maxwell P. Henderson. [12]. Patent for hybrid classical quantum computer https://patents.google.com/patent/US20050273306 [13]. A Hybrid Classical/Quantum Approach for Large-Scale Studies of Quantum Systems with Density Matrix Embedding Theory by Nicholas C. Rubin

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