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In the neural networks of living organisms, transformations are incomparably more difficult than in a quantum computer.

Yuri Magarshak is Professor, Editor-in-Chief of the Journal of New Concepts (New York).
Март 2023



Rice. 1. Scheme illustrating the projective color formation.
Google has been able to revolutionize computing technology. Using quantum computer software called Sycamore ("Pycamore"), Google representatives claimed "quantum superiority" over the most powerful supercomputers in the world. They reported that Sycamore was indeed able to perform a calculation in 200 seconds that would have taken the most powerful supercomputer in the world 10,000 years. Moreover, performing the same experiment on a Google Cloud server would take 50 trillion hours (5.7 billion years).


“This achievement is the result of years of research and the dedication of many people. It is also the beginning of a new journey: figuring out how to make this technology work. We work with the research community and have open source tools that enable others to work with us,” the company said. “As far as we know, this experiment marks the first computation that can only be performed on a quantum processor. Quantum processors have thus achieved quantum supremacy. We expect their computing power to continue to grow at double the exponential rate."

Beats in a square

The advantage of a quantum computer over a traditional one is explained by scientists and journalists in terms understandable even to a primary school student.

Ordinary computers perform calculations using "bits" of information that have two and only two states, in calculations corresponding to the numbers 1 or 0. Quantum computers do not use bits, but "qubits", which can exist in two states at once: in 1 and 0 at the same time , that is, in states (00, 01, 10, or 11) at any given time.

This possibility is a consequence of quantum mechanical equations and is, as stated, the main quality of the superiority of a quantum computer over a conventional one. In the case of a small number of qubits, the difference seems to be small. But if there are, for example, 100 qubits, the information they store is 2100 times more than the corresponding number of bits. That is a thousand billion billion billion times! And this difference in the capabilities of a quantum and conventional computer grows rapidly with an increase in the amount of memory.


Rice. 2. Image of complex numbers flowers. Author's illustrations.
In addition to qubits, quantum computers use a property of quantum mechanical systems known as entanglement. It lies in the fact that if two particles are generated at the same time, their properties are related, even if the particles are separated by a significant distance. Using this property, in principle, allows you to control the operations of calculations in the same way as it happens in ordinary computers. Which was demonstrated by Google when solving the demo problem.


To demonstrate the power of a quantum computer, researchers led by John Martinis of the University of California solved a specially formulated problem. Of course, for now, this is just a specially chosen problem of generating a very long list of random numbers associated with quantum phenomena, and testing their values ​​a million times. However, its solution by a quantum computer demonstrated the advantage of computing using qubits instead of the traditional Boolean algebra of ones and zeros.

A 53-qubit processor was used in the experiment on the Sycamore quantum computer. At the same time, experts emphasized that their new system can only perform one calculation, and the use of quantum computers to solve practical problems is in the distant future.

However, a controversy has already arisen among specialists regarding the adequacy of the assessment of this computer experiment. So, employees of the department of quantum computing at IBM said that Google falsely reported the achievement of quantum superiority. The company claims that a conventional calculator will cope with this task in the worst case in 2.5 days, and at the same time the answer will be more accurate than that of a quantum computer. This conclusion was made based on the results of the theoretical analysis of several optimization methods. The authors of the article also drew attention to the fact that the use of the term "quantum superiority" can confuse anyone who does not specialize in research in this area.

Google CEO Sundar Pichai responded to complaints from IBM. According to him, in this case, the achievement of quantum superiority is a milestone and you should not quibble over terms. To demonstrate quantum supremacy more broadly, Pichai said, one would need to build a fault-tolerant quantum computer with a large number of qubits, which could take several years. However, according to him, a breakthrough has already been made: “If you take an analogy, the Wright brothers. The first plane only flew for 12 seconds, and there was no practical use in that either. But it proved that the plane could fly."

Color vision and complex numbers

A detailed description of the functioning of quantum computers is beyond the scope of this short article. The goal is something else. Namely, a statement of the fact that neural networks in the brain of a person, as well as other living organisms, function like a quantum computer created by different companies. At the same time, many times more perfect!

To explain the phenomenon of color vision - a problem on which work was carried out at the University of the Swedish city of Uppsala in the early 90s - the author of this article discovered one interesting analogy. The formation of the perception of colors, as well as color images, in the human brain occurs similarly to the generation of a field of complex numbers, with an imaginary number i equal, as is known from a school physics course, to the root of -1. (Y. Magarshak, Projective geometry of color vision, generating the field of complex numbers, Biophysics, 41, 3, 734–743 (1996).

This connection explains the fact that electromagnetic waves are characterized by frequency and amplitude (changing from zero to infinity), while colors in human perception form a color wheel. The transformation of frequency into the color wheel is carried out due to the fact that a projective transformation takes place on the retina of the eye and in several layers of neural networks directly adjacent to it (Fig. 1).

From this formalism follows the possibility of representing functions of a complex variable by colors. In this case, the phase corresponds to the color, and the intensity of the color corresponds to the amplitude of the complex number. The corresponding computer program, which associates any functions of a complex variable - either entered into the corresponding window manually or obtained as a result of computer calculations - was created by the author of this article with colleagues in the 90s.

On fig. 2 shows the representation by complex numbers of one of the relatively simple mathematical functions. In principle, in a similar way, with the help of complex numbers in the field of view of a person, any image in human perception can be described, whether it be a person’s face, a landscape, or Raphael’s “Sistine Madonna”.

To describe the formation of color in the human brain, it is necessary to use a matrix, three- or four-dimensional, representation of complex numbers, similar to the representation of quaternions by spinors in Pauli matrices. Which arise when solving the Schrödinger equation, which, in particular, is the basis of quantum computing.

Let us pay attention to one more consequence of the connection between complex numbers and colors. The axis transformation in the complementary algebra that governs the perception of colors in the human brain is extremely reminiscent of the Lorentz transformation in Einstein's theory of relativity. The only difference is that in the denominator, instead of the root of the difference of squares, there is the sum of the corresponding quantities.

The combination of these properties is the basis for the formation of color images in human perception. And this is the root cause of the fact that electromagnetic waves, seemingly chaotically falling on the retina of the eye, are transformed into beautiful images in the human brain!

Quantum supremacy of the brain

Let's go back to the Sycamore experiment. The US National Aeronautics and Space Administration (NASA) first posted a message on its website about achieving quantum supremacy. However, the material was later removed. “Quantum computing is still in its infancy, but this transformative achievement is moving us forward. Our missions to the Moon, Mars and other planets in the coming decades will be fueled by innovations like this,” said Eugene Tu, director of the NASA Ames Research Center.

To make sure quantum supremacy was indeed achieved, NASA and Google turned to the Oak Ridge, Tennessee National Laboratory, home to Summit, the world's most powerful supercomputer. They checked whether the results of a quantum computer coincided with the results of a supercomputer up to the limit of quantum superiority - it turned out that it had been achieved.

And yet, when comparing quantum computing with the perception of color images in the brain, it becomes clear that the transformations in neural networks are incomparably more complex and perfect.

While qubits have four values, in neural networks there are incomparably more of them, and the structures they form are much more diverse than entanglement. Since color vision is just one of the many functions of human thought and perception, the capabilities of neural networks not only cover those of Google's qubits, but have tremendous versatility in generating possible structures in computing, pattern recognition, and other brain functions.

In connection with what has been said, it is clear that modeling the processes occurring in the human brain has not only scientific, but also colossal technological prospects.



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