Quantized Three-Ion-Channel Neuron Model for Neural Action Potentials

Tasio Gonzalez-Raya1, Enrique Solano1,2,3, and Mikel Sanz1

1Department of Physical Chemistry, University of the Basque Country UPV/EHU, Apartado 644, 48080 Bilbao, Spain
2International Center of Quantum Artificial Intelligence for Science and Technology (QuArtist) and Physics Department, Shanghai University, 200444 Shanghai, China
3IKERBASQUE, Basque Foundation for Science, Maria Diaz de Haro 3, 48013 Bilbao, Spain

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.


The Hodgkin-Huxley model describes the conduction of the nervous impulse through the axon, whose membrane's electric response can be described employing multiple connected electric circuits containing capacitors, voltage sources, and conductances. These conductances depend on previous depolarizing membrane voltages, which can be identified with a memory resistive element called memristor. Inspired by the recent quantization of the memristor, a simplified Hodgkin-Huxley model including a single ion channel has been studied in the quantum regime. Here, we study the quantization of the complete Hodgkin-Huxley model, accounting for all three ion channels, and introduce a quantum source, together with an output waveguide as the connection to a subsequent neuron. Our system consists of two memristors and one resistor, describing potassium, sodium, and chloride ion channel conductances, respectively, and a capacitor to account for the axon's membrane capacitance. We study the behavior of both ion channel conductivities and the circuit voltage, and we compare the results with those of the single channel, for a given quantum state of the source. It is remarkable that, in opposition to the single-channel model, we are able to reproduce the voltage spike in an adiabatic regime. Arguing that the circuit voltage is a quantum variable, we find a purely quantum-mechanical contribution in the system voltage's second moment. This work represents a complete study of the Hodgkin-Huxley model in the quantum regime, establishing a recipe for constructing quantum neuron networks with quantum state inputs. This paves the way for advances in hardware-based neuromorphic quantum computing, as well as quantum machine learning, which might be more efficient resource-wise.

► BibTeX data

► References

[1] A. L. Hodgkin and A. F. Huxley, ``Currents carried by sodium and potassium ions through the membrane of the giant axon of Loligo'', J. Physiol. 116, 449 (1952).

[2] A. L. Hodgkin and A. F. Huxley, ``The components of membrane conductance in the giant axon of Loligo'', J. Physiol. 116, 473 (1952).

[3] A. L. Hodgkin and A. F. Huxley, ``The dual effect of membrane potential on sodium conductance in the giant axon of Loligo'', J. Physiol. 116, 497 (1952).

[4] A. L. Hodgkin and A. F. Huxley, ``A quantitative description of membrane current and its application to conduction and excitation in nerve", J. Physiol. 117, 500 (1952).

[5] M. I. Rabinovich, P. Varona, A. I. Selverston, H. D. I. Abarbanel, ``Dynamical principles in neuroscience'', Rev. Mod. Phys. 78, 1213 (2006).

[6] S.-G. Lee, A. Neiman, and S. Kim, ``Coherence resonance in a Hodgkin-Huxley neuron", Phys. Rev. E 57, 3292 (1998).

[7] Y.-Q. Wang, David T. W. Chik, and Z. D. Wang, ``Coherence resonance and noise-induced synchronization in globally coupled Hodgkin-Huxley neurons", Phys. Rev. E 61, 740 (2000).

[8] C. Zhou and J. Kurths, ``Noise-induced synchronization and coherence resonance of a Hodgkin-Huxley model of thermally sensitive neurons", Chaos 13, 401 (2003).

[9] L. A. da Silva and R. D. Vilela, ``Colored noise and memory effects on formal spiking neuron models", Phys. Rev. E 91, 062702 (2015).

[10] E. Yilmaza, V. Baysala, and M. Ozer, ``Enhancement of temporal coherence via time-periodic coupling strength in a scale-free network of stochastic Hodgkin-Huxley neurons", Phys. Lett. A 379, 1594 (2015).

[11] X.-M. Guo, J. Wang, J. Liu, H.-T. Yu, and R. F. Galán, ``Optimal time scales of input fluctuations for spiking coherence and reliability in stochastic Hodgkin-Huxley neurons", Phys. A 468, 381 (2017).

[12] H.-T. Yu, R. F. Galán, J. Wanga, Y.-B. Cao, and J. Liu, ``Stochastic resonance, coherence resonance, and spike timing reliability of Hodgkin-Huxley neurons with ion-channel noise", Phys. A 471, 263 (2017).

[13] Y.-H. Hao, Y.-B. Gong, X. Lin, Y.-H. Xie, and X.-G. Ma, ``Transition and enhancement of synchronization by time delays in stochastic Hodgkin-Huxley neuron networks", Neurocomputing, 73, 2998 (2010).

[14] L. O. Chua, ``Memristor-The missing circuit element", IEEE Trans. Circuit Theory 18, 507 (1971).

[15] L. O. Chua, V. Sbitnev, and H. Kim, ``Hodgkin-Huxley axon is made of memristors'', Int. J. Bifurcation Chaos 22, 1230011 (2012).

[16] M. Mohseni, P. Rebentrost, S. Lloyd, and A. Aspuru-Guzik, ``Environment-assisted quantum walks in photosynthetic energy transfer'', J. Chem. Phys. 129, 174106 (2008).

[17] M. Mohseni, Y. Omar, G. S. Engel, and M. B. Plenio, Quantum effects in biology (Cambridge University Press, Cambridge, 2014).

[18] U. Alvarez-Rodriguez, M. Sanz, L. Lamata, and E. Solano, ``Artificial Life in Quantum Technologies'', Sci. Rep. 6, 20956 (2016).

[19] U. Alvarez-Rodriguez, M. Sanz, L. Lamata, and E. Solano, ``Quantum Artificial Life in an IBM Quantum Computer'', Sci. Rep. 8 14793 (2018).

[20] U. Alvarez-Rodriguez, M. Sanz, L. Lamata, and E. Solano, ``Biomimetic Cloning of Quantum Observables'', Sci. Rep. 4, 4910 (2014).

[21] E. Prati, ``Quantum neuromorphic hardware for quantum artificial intelligence'', J. Phys.: Conf. Ser. 880, 012018, (2017).

[22] N. Gomez, J. O. Winter, F. Shieh, A. E. Saunders, B. A. Korgel, and C. E. Schmidt, ``Challenges in quantum dot-neuron active interfacing", Talanta, 67, 462 (2005).

[23] M. Maeda, M. Suenaga, and H. Miyajima, ``Qubit neuron according to quantum circuit for XOR problem", Appl. Math. Comput. 185, 1015 (2007).

[24] M. Zak, ``From quantum entanglement to mirror neuron", Chaos, 34, 344 (2007).

[25] D. Ventura and T. Martinez, An Artificial Neuron with Quantum Mechanical Properties (Springer, Vienna, 1998), pp. 482-485.

[26] Y. Cao, G. G. Guerreschi, and A. Aspuru-Guzik, ``Quantum Neuron: an elementary building block for machine learning on quantum computers", arXiv: 1711.11240 (2017).

[27] N. Kouda, N. Matsui, and H. Nishimura, ``Learning performance of neuron model based on quantum superposition", IEEE RO-MAN, 112 (2000).

[28] G. S. Snider et al., ``From synapses to circuitry: Using memristive memory to explore the electronic brain'', Computer 44, 21 (2011).

[29] R. Berdan, E. Vasilaki, A. Khiat, G. Indiveri, A. Serb, and T. Prodromakis, ``Emulating short-term synaptic dynamics with memristive devices'', Sci. Rep. 6, 18639 (2015).

[30] Y. V. Pershin and M. Di Ventra, ``Neuromorphic, Digital, and Quantum Computation with Memory Circuit Elements'', Proc. IEEE 100, 2071 (2012).

[31] T. Serrano-Gotarredona, T. Masquelier, T. Prodromakis, G. Indiveri, and B. Linares-Barranco, ``STDP and STDP variations with memristors for spiking neuromorphic learning systems'', Front. Neurosci. 7, 2 (2013).

[32] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, ``Quantum Memristor", Sci. Rep. 6, 29507 (2016).

[33] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, ``Quantum Memristors with Superconducting Circuits", Sci. Rep. 7, 42044 (2017).

[34] M. Sanz, L. Lamata, and E. Solano, ``Quantum Memristors in Quantum Photonics", APL Photonics 3, 080801 (2018).

[35] T. Gonzalez-Raya, X. -H. Cheng, I. L. Egusquiza, X. Chen, M. Sanz, and E. Solano, ``Quantized Single-Ion-Channel Hodgkin-Huxley Model for Quantum Neurons'', Phys. Rev. Appl. 12, 014037 (2019).

[36] D. Yu, H. H.-C. Iu, Y. Liang, T. Fernando, and L. O. Chua, ``Dynamic Behavior of Coupled Memristor Circuits'', IEEE Trans. Circuits Syst. I 62, 1607 (2015).

[37] R. K. Budhathoki, M. Pd. Sah, S. P. Adhikari, H. Kim, and L. O. Chua, ``Composite Behavior of Multiple Memristor Circuits'', IEEE Trans. Circuits Syst. I 60, 2688 (2013).

[38] L. O. Chua, ``Resistance Switching Memories are Memristors'', Appl. Phys. A 102, 765 (2011).

[39] G. Alvarado Barrios, J. C. Retamal, E. Solano, and M. Sanz, ``Analog simulator of integro-differential equations with classical memristors'', Sci. Rep. 9, 12928 (2019).

[40] F. Silva, M. Sanz, J. Seixas, E. Solano, and Y. Omar, ``Perceptrons from Memristors'', Neural Networks 122, 273 (2019).

[41] M. Schuld, I. Sinayskiy, and F. Petruccione, ``An introduction to quantum machine learning", Contemp. Phys. 56, 172 (2015).

[42] J. Biamonte, P. Wittek, N. Pancotti, P. Rebentrost, N. Wiebe, and S. Lloyd, ``Quantum Machine Learning", Nature 549, 195 (2017).

[43] R. Kubo, ``Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems'', J. Phys. Soc. Jpn. 12, 570 (1957).

[44] G. Z. Cohen, Y. V. Pershin, and M. Di Ventra, ``Lagrange Formalism of Memory Circuit Elements: Classical and Quantum Formulation'', Phys. Rev. B 85, 165428 (2012).

[45] U. Vool and M. Devoret, ``Introduction to Quantum Electromagnetic Circuits'', Int. J. Circuit Theory Appl. 45, 897 (2016).

[46] B. Yurke and J. S. Denker, ``Quantum Network Theory'', Phys. Rev. A 29, 1419 (1984).

[47] M. Sanz, E. Solano, and I. L. Egusquiza, Beyond Adiabatic Elimination: Effective Hamiltonians and Singular Perturbation (Springer, Japan, 2016), pp. 127-142.

Cited by

[1] G. Alvarado Barrios, J. C. Retamal, E. Solano, and M. Sanz, "Analog simulator of integro-differential equations with classical memristors", Scientific Reports 9 1, 12928 (2019).

[2] Lucas Lamata, "Quantum machine learning and quantum biomimetics: A perspective", Machine Learning: Science and Technology 1 3, 033002 (2020).

[3] Lasse Bjørn Kristensen, Matthias Degroote, Peter Wittek, Alán Aspuru-Guzik, and Nikolaj T. Zinner, "An artificial spiking quantum neuron", npj Quantum Information 7 1, 59 (2021).

[4] Lee Smolin, "Natural and bionic neuronal membranes: possible sites for quantum biology", arXiv:2001.08522.

The above citations are from Crossref's cited-by service (last updated successfully 2021-07-31 18:30:33) and SAO/NASA ADS (last updated successfully 2021-07-31 18:30:34). The list may be incomplete as not all publishers provide suitable and complete citation data.