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).

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. Table of contents
Spiking neural networks
RSQF electronics
Superconducting qubits
Quantum annealing
Hybrid classical-quantum algorithms
Variational approach in designing new circuits

3. Perceptron

5. Spiking neural network in biology

6. 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.

7. Simplified model of SNN

8. Gates for spikining neural network

9. [From presentation of Will Zeng (Rigetti)-Architectures for Hybrid
Quantum /Classical Computing]

10. Basic features of superconductor
No dissipation during current flow
Meissner effect
Macroscopic Quantum Effect

11. Definition of Josephson junction

13. Josephson junction neuron by P.Crotty, 2010

14. Josephson junction neuron waveform
[By Patric Crotty et al. Josephson junction simulation in neurons,

15. Bases of fluxon electronics

17. Artificial neural networks in superconductor
Articial neural network based on SQUIDs: demonstration of
network training and operation by F.Chiarello et al.

18. Basic superconducting qubit architectures

19. Gates between classical superconducting electronics and
Quantum computer electronics

20. Quantum vs classical annealing

21. Quantum annealing chip by D-wave company

23. By D-wave company.

25. 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].

26. Quantum mechanics vs Neural Networks
Quantum neural networks by A.Ezhov and Dan Ventura

27. 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 ...

28. 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..

29. 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.

30. Simple case of usage of relaxation method in
Ginzburg-Landau equations

31. Field Induced Josephson junctions
https://arxiv.org/abs/1607.05013

32. Variational approach towards superconducting electronics
https://arxiv.org/abs/1607.05013

33. 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.

34. Overlap of disciplines

35. 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...

36. [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