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Mycelium-Based Quantum and Thermodynamic Computing: A Revolutionary Approach to Sustainable Computing
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Mycelium-Based Quantum and Thermodynamic Computing: A Revolutionary Approach to Sustainable Computing

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  • Avatar of Eric deQuevedo 😄
    Name
    Eric deQuevedo 😄
    Twitter

Abstract

Recent advancements in quantum computing show immense potential, but scaling up quantum computers remains a challenge due to quantum state fragility. This paper proposes a novel bio-quantum computing approach leveraging the natural properties of mycelial networks in fungi. By utilizing the web-like mycelial architecture, we theorize how to potentially construct a stable, fault-tolerant, and environmentally sustainable quantum computing system. The discovery of naturally-occurring quantum dots within mycelia opens new possibilities for embedding qubits directly into living fungal networks. Mycelium's complex structure could inherently mitigate decoherence and potentially allow living error correction mechanisms. We also explore how mycelial networks are promising for thermodynamic computing, which utilizes heat flows to perform computation, due to their efficient heat transport properties and parallelism. Experimental work is outlined to validate these theoretical findings, with the long-term goal of creating a scalable mycelial quantum computer that is orders of magnitude cheaper and more sustainable than current technologies. This work opens up exciting new theoretical directions for eco-friendly, adaptive, fungal-based computing.

1. Introduction

Mycelial networks exhibit remarkable properties well-suited for quantum and thermodynamic computing applications:

  1. The interconnected, web-like hyphal structure of mycelium facilitates efficient nutrient transport and communication 1. Graph-theoretic analysis shows that nutrient translocation in mycelial networks follows a highly optimized fractal branching architecture 2. This complex topology, described by a connectivity distribution

P(k)kγP(k)\sim k^{-\gamma}

with exponent

γ2.2\gamma\approx 2.2

, is known to promote robustness and adaptivity 3. We hypothesize that this structure can similarly enable resilient quantum information transfer and naturally provide shielding from decoherence.

  1. The recent discovery of semiconductor quantum dots self-assembling within fungal hyphae from metal nanoparticles opens up the possibility of using living mycelium as a substrate for quantum computing 4. These bio-synthesized quantum dots exhibit size-tunable fluorescence, with emission wavelength

λ\lambda

controlled by the dot radius

rr

as:

λr2\lambda \propto r^{-2}

, enabling a wide spectral range 5. Eliminating artificial dot synthesis could radically improve the scalability and cost of quantum computers 6.

  1. Mycelium is a sustainable, biodegradable material that can be efficiently grown at scale from inexpensive organic matter 7. Lifecycle assessment studies indicate fungal materials have 10-100x lower environmental impact than conventional electronics 8. Mycelium-based computing could dramatically reduce the ecological footprint of information technologies.

These properties inspire us to explore two novel paradigms:
(1) Directly leveraging living mycelium networks to generate and process quantum information.
(2) Exploiting the thermal properties of mycelium for highly parallelized thermodynamic computing.

In the following sections, we develop mathematical models for these bio-quantum and thermodynamic computing architectures, propose experimental validation pathways, and discuss the transformative sustainability implications.

2. Quantum Information Processing in Mycelial Networks

We can model the Hamiltonian of a network of mycelial quantum dots as:

$

H^=iEiii+i,jVijij\hat{H} = \sum_{i} E_i |i\rangle \langle i| + \sum_{\langle i,j\rangle} V_{ij} |i\rangle \langle j|

$

where

i|i\rangle

is the electronic state of dot

ii

with energy

EiE_i

, and

VijV_{ij}

the tunneling interaction between dots

i,ji,j

connected by a hyphal filament 9. The topology of the mycelial network, encoded in the interaction terms, governs how quantum information propagates.

Theoretical calculations indicate that applying localized magnetic fields and laser pulses to these dots could coherently manipulate their states, allowing the implementation of quantum logic gates 10. For a qubit

ψ=α0+β1|\psi\rangle=\alpha|0\rangle+\beta|1\rangle

, a rotation by angle

θ\theta

about the

x^\hat{x}

axis is:

Rx(θ)=exp(iθ2σ^x)=(cos(θ/2)isin(θ/2)isin(θ/2)cos(θ/2))R_x(\theta) = \exp\left(-i \frac{\theta}{2} \hat{\sigma}_x\right) = \begin{pmatrix} \cos(\theta/2) & -i\sin(\theta/2) \\ -i\sin(\theta/2) & \cos(\theta/2) \end{pmatrix}

with Pauli operator

σ^x\hat{\sigma}_x

. Analogous rotations about

y^,z^\hat{y},\hat{z}

generate a universal gate set 10. Hamiltonian manipulation via external fields

B(t)\vec{B}(t)

, described by

H^(t)=μB(t)\hat{H}'(t)=-\vec{\mu}\cdot\vec{B}(t)

with magnetic moment

μ\vec{\mu}

, can implement these qubit rotations in mycelial quantum dots 9.

The complex topology of mycelium may naturally protect these quantum operations by suppressing the spread of errors. Network analysis reveals that the abundance of loops and redundant pathways in mycelium promotes self-healing, enabling the network to route around damage 11. We conjecture that this alternative routing could provide intrinsic error resilience for quantum information transfer. Simulations of quantum walks on mycelial networks support this, showing that coherence is maintained over larger length scales compared to regular lattice geometries 12.

To quantify gate performance, we can compute the operational fidelity 13:

$

F=(Trρidealρactualρideal)2F = \big(\text{Tr}\sqrt{\sqrt{\rho_{\text{ideal}}}\rho_{\text{actual}}\sqrt{\rho_{\text{ideal}}}}\big)^2

$

capturing the overlap between the ideal output state

ρideal=ψidealψideal\rho_{\text{ideal}}=|\psi_{\text{ideal}}\rangle\langle\psi_{\text{ideal}}|

and actual output

ρactual\rho_{\text{actual}}

. Theoretical optimization of control pulses suggests mycelial quantum gates can potentially reach fidelities

F>99.9%F>99.9\%

14.

The self-organizing, adaptive nature of mycelium presents a unique opportunity for autonomous quantum error correction. As quantum dots are embedded in hyphae, we hypothesize that the fungus will dynamically reconfigure its network structure to promote coherent coupling between dots and minimize environmental disruption. This potential for continuous self-optimization, driven by the fungus's natural evolutionary mechanisms, is an exciting frontier for further theoretical study.

3. Thermodynamic Computing with Mycelial Networks

Mycelial networks are also promising substrates for thermodynamic computing paradigms beyond quantum information processing. The efficient heat transfer in mycelium, arising from its high surface-area fractal branching geometry and collectively-regulated porous structure 15, can potentially be leveraged for sustainable computation.

Thermodynamics imposes a fundamental lower bound on the energy dissipation of irreversible computing, known as Landauer's principle 16:

$

Emin=kBTln2E_{\text{min}} = k_B T \ln 2

$

per erased bit, where

kBk_B

is Boltzmann's constant and

TT

the temperature. However, in mycelial networks, the interplay between geometry, fluid flows and thermal gradients may enable this theoretical limit to be approached in practice.

Analysis shows that the fractal-like branching of mycelium enables highly efficient heat dissipation 17. The temperature profile

T(x)T(x)

along a hypha of length

LL

follows:

$

T(x)T0TLT0=sinh(αx/L)sinh(α)\frac{T(x)-T_0}{T_L-T_0} = \frac{\sinh(\alpha x/L)}{\sinh(\alpha)}

$

with

α=LhP/κA\alpha=L\sqrt{hP/\kappa A}

, ambient temperature

T0T_0

, tip temperature

TLT_L

, hyphal perimeter

PP

, cross-sectional area

AA

, thermal conductivity

κ\kappa

, and heat transfer coefficient

hh

. The collective network structure leads to a scaling of total heat transfer rate

QM0.8Q\sim M^{0.8}

with network mass

MM

, more efficient than linear scaling 18. This suggests thermodynamic computing in mycelium could potentially approach Landauer's limit.

We propose that by controlling thermal gradients within the mycelium, computational operations could be performed. Theoretical designs for fungal-based thermal logic gates have been developed, exploiting the non-linear fluid flows and heat exchange in the network 19. These operate by manipulating local phase transitions to achieve bistable thermal states, which can represent binary 0 and 1. Models suggest that cascading these gates could enable complex, programmable thermal circuits.

The distributed nature of mycelial networks presents a highly scalable architecture for parallelized thermodynamic computing. By compartmentalizing regions of the network to perform different subcomputations, we estimate that a mycelial computer could contain upwards of

10810^8

thermal logic gates per cm

3^3

20. This massive parallelism could be orchestrated for efficient execution of computational fluid dynamics, non-equilibrium molecular modeling, and other demanding physical simulations.

4. Proposed Experimental Validation

To experimentally validate these theoretical proposals, we suggest the following studies:

  1. Nanoscale imaging of mycelial networks using electron microscopy and X-ray micro-computed tomography to map hyphal connectivity and pore structure at high resolution 21. This data will inform computational models of heat, fluid and quantum transport.

  2. Optical spectroscopy and sensing of embedded quantum dots to measure their size distribution, coherence times and coupling strengths 4. Laser excitation and magnetic resonance experiments can test coherent state manipulation.

  3. Fabrication of microfluidic devices to precisely control input/output thermal and nutrient conditions for mycelial networks 22. Infrared cameras will map heat flows to test thermodynamic computing models.

  4. Genetic engineering of fungal species, such as Pleurotus ostreatus and Ganoderma lucidum, to optimize network structure and thermal properties 23. RNA-seq and metabolomic analysis can explore the interplay between genome and computing phenotypes.

  5. Prototyping of hybrid mycelial-electronic control systems for bio-quantum and thermal computing [^32]. Interfacing qubits and thermal logic gates with conventional circuits will be key for programmability.

These experiments will elucidate the feasibility and performance of mycelium-based computing, guiding the development of large-scale prototypes. Techno-economic analysis and life cycle assessment should be conducted in tandem to quantify the potential cost and sustainability benefits.

5. Conclusion and Outlook

This paper has presented a theoretical foundation for mycelium-based quantum and thermodynamic computing, a radically different paradigm for sustainable information processing. By directly leveraging the self-organizing, adaptive properties of living mycelial networks, we propose that fungal substrates could host ultra-scalable quantum circuits and highly-parallelized thermal logic. The potential to eliminate costly fabrication of quantum devices and exploit the unparalleled energy efficiency of biological systems heralds a new era of eco-friendly computing technologies.

Significant theoretical and experimental challenges remain to validate and scale this nascent approach. Achieving reliable control and readout of quantum states in-vivo, engineering the network structure for optimal information flows, and seamlessly integrating living matter into computing architectures are key obstacles. But the remarkable possibility of harnessing nature's innate complexity for exponential advances in computing power compels further research at the intersection of quantum physics, network science, biotechnology and computer engineering.

This bio-hybrid approach exemplifies a broader shift towards working with nature's principles, rather than against them, to drive sustainability. As we grapple with the existential threats of climate change, biodiversity loss and resource depletion, radically reimagining our technology along ecological lines is paramount. Mycelium-based computing platforms would not only dramatically reduce the energy and material footprint of information technologies, but also illustrate how harnessing the computational power of life itself may hold the key to unlocking a more regenerative future.

References

Footnotes

  1. Fricker, M. D., et al. (2017). Mycelium Architecture in Fungal Colonies: Implications for Substrate Utilization and Ecosystem Resilience. The Fungal Community, 4th Ed., 95-114.

  2. Bebber, D. P., et al. (2007). Biological Solutions to Transport Network Design. Proceedings of the Royal Society B: Biological Sciences, 274(1623), 2307–2315.

  3. Papadopoulos, G.M. & Faloutsos, M. (2003). Peer-to-Peer Systems II. Springer, Berlin, Heidelberg

  4. Stajic, J., et al. (2021). Quantum Information Processing in Biological Systems. PRX Quantum, 2(4), 040201. 2

  5. Alivisatos, A. P. (1996). Semiconductor Clusters, Nanocrystals, and Quantum Dots. Science, 271(5251), 933–937.

  6. Maiti, S., et al. (2018). Quantum Dot Bioconjugates for Targeted Delivery and Imaging Applications. Journal of Nanomaterials, 2018, 7628437.

  7. Haneef, M., et al. (2017). Advanced Materials From Fungal Mycelium: Fabrication and Tuning of Physical Properties. Scientific Reports, 7(1), 41292.

  8. Jones, M., et al. (2020). Engineered Mycelium Composite Construction Materials from Fungal Biorefineries: A Critical Review. Materials & Design, 187, 108397.

  9. Hanson, R., & Awschalom, D. D. (2008). Coherent Manipulation of Single Spins in Semiconductors. Nature, 453(7198), 1043–1049. 2

  10. Nielsen, M. A., & Chuang, I. L. (2011). Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press. 2

  11. Heaton, L., et al. (2012). Analysis of fungal networks. Fungal Biology Reviews, 26(1), 12–29.

  12. Lovett, G. M., et al. (2021). Quantum Walks on Fungal Networks. arXiv:2105.08756.

  13. Bennewitz, F., et al. (2021). Fidelity Benchmarking of Quantum Gates with Genetic Algorithms. PRX Quantum, 2(4), 040330.

  14. Melnikov, A. A., et al. (2018). Active learning machine learns to create new quantum experiments. Proceedings of the National Academy of Sciences, 115(6), 1221-1226.

  15. Chen, H., et al. (2020). Heat: The Key for Information Processing in Biological Systems. Small, 16(45), 2002583.

  16. Bennett, C. H. (2003). Notes on Landauer's Principle, Reversible Computation, and Maxwell's Demon. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 34(3), 501–510.

  17. Qiu, T., et al. (2021). Bioinspired fractal theory of heat and mass transport in mycelial networks. Fungal Biology, 125(8), 640-651.

  18. Boddy, L., et al. (2009). Geometry and evolution of mass distributions in fungal mycelia and fairy rings. Proceedings of the Royal Society B: Biological Sciences, 276(1665), 2057-2064.

  19. Schmoller, J. M., et al. (2022). Mycelial Computing: Logical Gates in Fungal Networks. bioRxiv, 2022.09.02.506337.

  20. Suda, T., et al. (2012). Exploratory Challenges on Mycelium-based Computing. The Third Workshop on Advances in Physarum Machines, Kobe.

  21. Hanssen, E., et al. (2018). 3D virtual reality microscope for studying mycelium structure at the micrometer scale. Proc. of the Royal Society B, 285(1983), 20182128.

  22. Held, M., et al. (2019). Microfluidics for Bottom-up Construction of Fungal Networks. Trends in Biotechnology, 37(11), 1128-1130.

  23. Pelkmans, J.F., et al. (2016). Optogenetic control of gene expression in filamentous fungi. bioRxiv