Doubling of qubits, Superconducting States and Law for Quantum Computing!
If we consider the miniaturization era from year 1963 to 2014 then the computing power of classical computer has increased multi-fold and with the increasing growth in the computing power for every two years the cost per chip has dropped exponentially from few million dollar to few dollars, or even less than dollar per chip. The fabrication processes and manufacturing techniques have evolved dramatically in the past few decades. In the classical computer system the data operates on Bit. The computing power has doubled in approximately 24 months according to Moore's law. From year 2014 onward for almost next few decades the computing power of classical computer has to be doubled in almost 36 to 38 months due to the limitation of shrinking. But if we try to perceive the quantum computing using the qubits then as multiple states are processed simultaneously the computing power will rise exponentially in 'N' years.
If we consider ‘n’ dimensional plane with n qubits, and if we try to perceive the behavior of energy at atomic and sub-atomic level the 2^n superconducting states can be processed simultaneously. So the computing system with ‘n’ qubits can be considered as universe. As energy associated with every universe is constant but still transmutation of the energy from one universe to another universe is possible. If we consider the computing system with ‘n’ qubits in one of the universe then all possible states can be transmuted to another universe of ‘n’ qubits and thus exponential improvement in the computing performance by 2 to the power of 2n. The way in which human brain works using the various clusters, where every cluster can be treated as information processing universe, the same concept if we apply to imagine the multiple universe as parallel processing engine then it is possible to imagine the billions of superconducting states at the same time instances and the computation speed similar to the speed of universe.
So according to the theory of multi-universe proposed by respected Stephen Hawking and the basic mathematics the universal law for superconducting states can be stated. If we consider the single object or the atom with ‘n’ states then the object can transmute the ‘n’ states or all possible states to the series or parallel universe. So effectively every series-parallel universe can consists of the unique number of such possible states.
Now consider simple mathematical analysis using the linear approximation. Assumption is power doubles or multi-folds depending on exponential rise of qubits. But depending on all or minimum possible entanglement of n qubits with the other universe.
q1: Number of qubits during year y1
q2: Number of qubits during year y2
Then by using linear approximation theory we can establish relation as following
q2=q1*2 ^ (Δy/N), Where Δy= y2-y1
N= Number of years required to double the qubits
So according to the data availability from previous few years, the number of qubits has doubled in approximately N years.
Observation I: During year 2011: q1=128, during year 2015: q2 is approximately equal to 1024
Therefore q2 = 2^3 * q1 and we will get the mathematical analysis as 2^3 *q1 = q1 * 2 ^ ((2015-2011)/ N)
Therefore 2^3 = 2 ^ (4/N)
Where, N is equal to number of years to double the qubits. Therefore 3= 4/N and N=1.33 years
That is almost around 16 months
Observation II: During year 2005: q1=4, during year 2011: q2 is approximately equal to 128
Therefore q2 = 2^5* q1 and we will get the mathematical analysis as 2^5 *q1 = q1 * 2 ^ ((2011-2005)/ N)
Therefore 2^5 = 2 ^ (6/N)
Where, N is equal to number of years to double the qubits.
Therefore 5= 6/N and N=1.20 years
That is almost around 14 months
Observation III: During year 2002: q1=1, during year 2015: q2 is approximately equal to 1024
Therefore q2 = 2^10 * q1 and we will get the mathematical analysis as 2^10 *q1 = q1 * 1 ^ ((2015-2002)/ N)
Therefore 2^10 = 2 ^ (13/N)
Where, N is equal to number of years to double the qubits
Therefore 10= 13/N and N=1.33 years
That is almost around 16 months
So the law for quantum computing can be stated as: The number of qubits has to be doubled in approximately 14 to 16 months to have exponential rise of computing power which may be multi-fold in comparison with the classical computers.
So if we consider the classical computer versus quantum computing then the data transfer speed in the classical computer is limited due to speed of light. But in case of quantum computing if ‘n’ qubits with the superposition and entanglement with another universe in series or parallel then distance of the universe and speed of light is immaterial or not be considered as limiting factors. But according to my mathematical analysis this may be true till year 2053. Now imagine the ‘n’ superconducting states in the universe entangled with another universe, ‘n’ or all possible states in this universe can communicate without the limitation of speed of light with the another universe. So effectively the quantum superposition and entanglement can create exponential growth in computing power. The 1024 qubit quantum computing machine can act as the supreme super computer where billions of superconducting states at a time to solve the critical problems and optimization in just one step.
But if we consider the up or down spin of electron where the quantum wavelength is the fundamental limit to measure the spin or position of particle. Concept even applicable to photons. If the factor of 2 ^ (Δy/N) is multiplied by Compton Wavelength λc= (2.426*10^ (-12)) then to get the maximum value of 1 using N=1.2 years and y1=2002 we will get y2= 2048.5
If we consider the doubling of qubits in 1.33 years then for N=1.33 years and y1=2002 we will get y2=2053.20.
For classical computer using the transistors the miniaturization limit may reach during 2030 to 2035. As there is limitation for shrinking using the lower process nodes below 10 nan0-meter. By using the spin-up and spin-down state, correlation the universe can communicate with another universe and even it can give the birth to the programmable interconnect using the light as source to transfer and receive the energy. Even as programmable interconnect the photon spin-up and spin-down state can be used to transfer information from one of the qubit to another qubit. But according to this analysis the quantum computing limit can reach during period 2048 to 2053 and we will witness one more technological shift in the form of new evolution in computing.
So as the history always repeats with the cyclic technological shift. And we will witness the similar kind of evolution which we have witnessed using silicon transistors. The similar situation we are witnessing in the present scenario as the cost of quantum computing machine is few million dollars. There will be evolution of the interconnects and pathways from one of the universe to another universe using the atomic and sub-atomic energy. The cost of quantum computing machines will reduce during next decade from million dollars to few thousand dollars and will be available to the mass with hundreds of dollars during year 2030. It is like the super-computing power to the mass.
But the era of super-computing or parallel processing can give us the discrete optimization algorithms, space search, brain programming, multi universe communication etc in the next few decades. The real multi-world, multi-universe concept using the relativity can be proved by using the quantum computing superconducting states. So let us hope for the great era of super-computing!