In the beginning there was classical mechanics propounding the corpuscular theory of matter and describing the motion of bodies under the influence of a system of forces. But this classical mechanics fails to describe the motion of sub-atomic particles and then Quantum Mechanics was born. Quantum Mechanics deals with mechanics of sub-atomic particles.

### Moore’s Law and Quantum Computing

According to Moore’s law the number of transistors in a dense integrated circuit doubles every two years. This in-turn means that at some point of time the size of transistors will be equal to atomic size. When that happens, the laws governing modern day computers which are based on classical mechanics will not apply any more since classical mechanics do not deal with sub-atomic particles. At this point of time, what we would need is Quantum computers which are based on laws of quantum mechanics.

### Bit and Qubit – Meaow

Schrodinger’s Cat is a thought experiment which simultaneously describes a cat as being dead or alive. If we put a cat in a box and somehow inject a poison in the box, we can not say with surety that the cat is alive or dead. At that moment the cat could be alive or dead. However, when we open the box we will find the cat in any one state – either alive or dead. This experiment shows that until a measurement is done there are multiple states possible (because the states do not get disturbed) and when the measurement is done all the states gets (disturbed) and superimposed into any one of the possible states.

A modern day computer is based on binary number system comprising of two states – 0 or 1. At any point of time any one of these states can be possible and we can easily find out which state it is. However, a quantum computer is based on Qubit or quantum bit. The laws of quantum mechanics allows a qubit to be in a state other than |0) and |1) (pronounced as ket 0 and ket 1, respectively). It can in-fact be a superimposition of both the states at the same time.

|Psi) = alpha|0) + beta|1)

(pronounced as ket psi = alpha ket 0 + beta ket 1)

This is also known as two-state quantum system.

Like there are logic gates in binary computers, there are quantum gates in the quantum computers. A description of all these gates will be beyond the scope of this post.

### Quantum System Modelling

The Quantum and Nano Computing Virtual Centre at Dayalbagh Educational Institute has published various research papers with the International Journal of General Systems on this subject. In a paper published in 2011 on **Graph-Theoretic Quantum System Modelling For Information / Computation Processing Circuits** (GTQSM), the researchers have been able to generalized the graph-theoretic system modelling framework, which was until now used for classical (deterministic) systems, to quantum random systems. Further in the paper the researchers present various applications of GTQSM for quantum information/computation processing circuits. Among other applications of GTQSM presented in this paper, one of the interesting application which caught my attention was a substantive case of 3-port, 5-stage circuit for **Quantum Teleportation**. Quantum teleportation is a process by which quantum information can be transmitted (exactly, in principal) from one location to another.

### GTQSM Linked With Microtubules in Brain – Is our brain a quantum computer?

Microtubules are intracellular structures that are responsible for various kinds of movements on all eukaryotic cells. Eukaryotic cells have a membrane bound nucleus, number of membrane bound organelles (such as mitochondria, chloroplasts, the endoplasmic reticulum, the Golgi apparatus, and lysosomes) and linear chromosomes. These microtubules are filamentous in nature and further made up of tubulin. These microtubules are formed by the polymerization of a dimer of two globular proteins, alpha and beta tubulin. *(Side Note – Microtubules function in many essential cellular processes, including mitosis. Tubulin-binding drugs kill cancerous cells by inhibiting microtubule dynamics, which are required for DNA segregation and therefore cell division.)*

Another research paper written in 2013 by the researchers at Quantum and Nano Computing Virtual Centre at Dayalbagh Educational Institute on Graph-theoretic quantum system modelling for neuronal microtubules as hierarchical clustered quantum Hopfield networks was published in the International Journal of General Systems in March 2014 . This paper presents an insight, otherwise difficult to gain, for the complex system of systems represented by clustered quantum Hopfield network, hQHN, through the application of GTQSM construct. This paper applies GTQSM in continuum of protein heterodimer tubulin molecules of self-assembling polymers, viz. **microtubules in the brain as a holistic system** of interacting components representing hierarchical clustered quantum Hopfield network, hQHN, of networks.

### Look Ma, I found a link between Quantum Physics and Consciousness!

In my previous blog post “On The Origin of The Universe and Consciousness“, I mentioned that – “*In the western perspective the focus is mostly on the outward and in the eastern tradition the focus is on the inwards. As a result of this the western approaches prefer scientific methods.*” If we really wanted a scientific approach towards understanding consciousness then a study of human brain is a must. Quantum theories of consciousness are based on mathematical abstraction. The most promising theory in this area is Penrose-Hameroff Orch-OR (Orchestrated Objective Reduction) theory. The International Journal of General Systems have another research paper published in 2015 by researchers at Quantum and Nano Computing Virtual Centre at Dayalbagh Educational Institute. This paper on Modelling microtubules in the brain as n-qudit quantum Hopfield network and beyond presented the extension Penrose-Hameroff model to **n-dimensional quantum states or n-qudits** thus promising for even higher mathematical abstraction in modelling consciousness systems. This 2015 paper has recently been followed by another paper written in 2016 and published by International Journal of General Systems in April 2017. This paper – From *n*-qubit multi-particle quantum teleportation modelling to *n*-qudit contextuality based quantum teleportation and beyond expands the horizon by arguing for point-sized loops or fine-grained particles of nature, which have been rejected out of hand by string theorists. People familiar with Quantum Physics would know that it is not possible to have any particle smaller than Planck’s length, which is 1.6 x 10^{-35} m. Consequently, this is the length which has any sensible meaning in physics. The argument present in this paper for sizes smaller than Planck’s length is very interesting. Satsangi argues that finer-grained particles than Planck’s length 10^{−35} m may exist, although, they are not matter anymore. Further he says that why stop at degree of freedom of three? Why not pursue quantum odd-prime based units (qudit) with higher degree *n* such as 5, 7, 11, 13, 17 and so on till *n*^{th} degree of freedom even tending to infinity. Satsangi says that it is unscientific to stop at Planck’s dimension, the particles have grown so subtle that we have not devised physical instruments to measure them. Further quoting from the paper (and it is explained in such simple terms that I can not simplify it further) –

“Similarly, on the large side, scientists are not able to consider more than 10

^{10}light years, so they do not know what exists in space beyond 10^{10}light years. So they are limited deliberately on these counts, whereas mathematics which is part of science, shows that particles are there which are subtler, subtler and subtlest ones. They move to infinity, they are most subtle, they become very small or subtle when we are close to zero, infinity is the macrocosm problem. Scientists can neither access infinity, nor zero, but none would say mathematics is not part of science.To make the scientific community see what the reality is, the best way forward seems to make them realize that their own mathematics shows that we have to tackle a problem with zero and infinity, since they are not admitting zero point loops.

….The whole basis is a mathematical construct, but naturally, what keeps them in disbelief and doubt their own discoveries is that they visualize that there will be very high temperatures characteristic of fusion reactor such as is present in the sun, which is part of the milky way galaxy where earth is located (as a planet). But they overlook this point that in that environment, what has to survive are these small particles, not the physical body that we possess, this body has to be given up much earlier. Physical body cannot withstand those temperatures. The spirit force as part of Hilbert vector space over a field of complex numbers, are what Roger Penrose says, why not,

x^{y}where bothxandyare integers, instead of visualizing quantum odd-based prime units, i.e. qudits. These particles possess infinite capabilities mathematically and precisely. So for us, whether we look at it from the angle of modern fashion, or scientific faith or even fantasy, the picture is all very clear that the characterization in scientific space is the Hilbert vector space over a field of complex numbers, or a field of integers, or whatever you want to say in the same vein for that matter. And when you raise the power, the particles under consideration are infinitesimally small and they have infinitely large capabilities, so that is where they possess this characteristic of omniscience along with omnipresence and omnipotence. “

### Conclusion

A very deep research is going on in the field of Quantum and Nano Computing, Quantum Information Systems and Consciousness atQuantum and Nano Computing Virtual Centre . Hopefully, we will eventually be able to reach to fully explain consciousness using scientific methods.

Very well written, Ajitabh! Lucid and easy to understand – for such a notoriously difficult concept.