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European Journal of Applied Sciences – Vol. 9, No. 5

Publication Date: October 25, 2021

DOI:10.14738/aivp.95.10690. Puccini, A. (2021). Next Quantum Computers and their Speeds. European Journal of Applied Sciences, 9(5). 15-29.

Services for Science and Education – United Kingdom

Next Quantum Computers and their Speeds

Antonio PUCCINI

Neurophysiologist at Health Ministry, Naples – Italy

ABSTRACT

As known, the Quantum Computer represents the most coveted and promising tool

for transmitting information in the near future. Thus, with the next use of Quantum

Computers (QCs), instead of current computers, the means of transmitting

information will be replaced: in fact we will pass from electrons and bit, to photons

and quantum bit. So the main element, that is the essential and indispensable tool

to make the next QCs, will be represented by the photon, that is by the

electromagnetic signal. These signals, as we know, are not all the same, but they

differ in a wide range, based on their wavelength, on their energy, or even on their

momentum (p). In short, the main task of our work is to ascertain whether, in this

context, the photons with different frequencies transmit the information at the

same speed, or not!

Keywords: Quantum Computers(QCs); momentum (p); Electro-magnetic(EM); kinetic

energy(KE).

INTRODUCTION

As we all know the Quantum Computer (QC) represents the most coveted and promising tool

for transmitting information in the near future. To this purpose, as Boncinelli reminds us, "The

Information is a measurable quantity, like the Matter and the Energy. These 3 quantities are the

basis of the material universe. The information has been defined and baptized recently (50

years ago). One aspect of this magnitude is related to Quantum Computers (QCs). Behind all this

lies a strong thought: science does not care so much to understand how things are, but how we

can get to know it. As to say that knowledge is intrinsically a matter of information; we are at it

from bit. Reality takes shape and body through information"[1].

Up until now the methods of information transmission are those described by Shannon

Equations, they concern both the quantity and the quality of information in common cable

transmission systems and in common computers work electrons [2]. In this respect, we read

from Shannon:“The fundamental problem of communication is that of reproducing at one point

either exactly or approximately a message selected at another point. Frequently the messages

have meaning; that is they refer to or are correlated according to some system with certain

physical or conceptual entities. These semantic aspects of communication are irrelevant to the

engineering problem. The significant aspect is that the actual message is one selected from a

set of possible messages. The system must be designed to operate for each possible selection,

not just the one which will actually be chosen since this is unknown at the time of design.

If the number of messages in the set is finite then this number or any monotonic function of this

number can be regarded as a measure of the information produced when one message is chosen

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European Journal of Applied Sciences (EJAS) Vol. 9, Issue 5, October-2021

Services for Science and Education – United Kingdom

from the set, all choices being equally likely. As Hartley pointed out the most natural choice is

the logarithmic function. Although this definition must be generalized considerably when we

consider the influence of the statistics of the message and when we have a continuous range of

messages, we will in all cases use an essentially logarithmic measure.

The logarithmic measure is more convenient for various reasons:

1. It is practically more useful. Parameters of engineering importance such as time,

bandwidth, number of relays, etc., tend to vary linearly with the logarithm of the number

of possibilities.

2. It is nearer to our intuitive feeling as to the proper measure, since we intuitively measure

entities by linear comparison with common standards.

3. It is mathematically more suitable. Many of the limiting operations are simple in terms

of the logarithm but would require clumsy restatement in terms of the number of

possibilities.

The choice of a logarithmic base corresponds to the choice of a unit for measuring information.

If the base 2 is used, the resulting units may be called binary digits, or more briefly bits, a word

suggested by J. W. Tukey. A device with two stable positions, such as a relay or a flip-flop circuit,

can store one bit of information”[3].

In reference to this context, Lloyd writes: “Merely by existing, all physical systems register

information. And by evolving dynamically in time, they transform and process that information.

The laws of physics determine the amount of information that a physical system can register

(number of bits) and the number of elementary logic operations that a system can perform

(number of operations)”[4].

Therefore, the quantity of information is conveyed in bit/sec.

At this point, let’s take a look at the equations of Shannon. As is well-known, the first Shannon’s

equation describes the quantity of information, (I), held in a message:

I = ̶ p ���! p (1)

where p is the so-called surprise contained in the message, that is the most or least probability

to convey a news. In this regard, in fact, Aleksander states: “The less probable an event is, the

more surprising it is and the more information it conveys”[5].

Therefore, as can be easily seen from the Eq.(1), it indicates the quantity of information

conveyed (in bit/sec).

Now, let’s to analyse the second Shannon equation:

C = W ���! (1+ #

$) (2)

where W is the band-width of the channel, S is the signal strength and N the noise strength [6].

As it is clear from Eq.(2), unlike Eq.(1), the second Shannon equation indicates the quality, (C),

of the transmission mean. In reference to this context, in fact, Faris specifies: “The second

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Puccini, A. (2021). Next Quantum Computers and their Speeds. European Journal of Applied Sciences, 9(5). 15-29.

URL: http://dx.doi.org/10.14738/aivp.95.10690

equation is Shannon’s formula for channel capacity (C). This gives the rate at which information

can be transmitted in the presence of noise”[7].

In this regard, in its turn, Aleksander points out: “Shannon's equations are not about nature,

they are about systems that engineers have designed and developed. Shannon's contribution

lies in making engineering sense of a medium through which we communicate. He shares the

same niche as other great innovators such as his boyhood hero Thomas Edison (who turned

out to be a distant relative, much to Shannon's delight) and Johann Gutenberg"[5].

DISCUSSION

Well, so far we have only considered physical systems represented by atoms or electrons.

Let’s try now to analyse, in similar circumstances, the behaviour of electromagnetic waves and

photons, since they are used in Quantum Computers (QCs) [8].

As we all know, photons are real particles and have a their own energy and momentum [9], so

they are considered proper physical systems [10].

The Momentum

To this purpose, in fact, Fermi states: “The light’s quantum is a corpuscle and has an its own

momentum (p)” [11]. Famously, the momentum was introduced in order to calculate how much

a body in motion weighs. Newton was the first one to fully deal with this subject. He wrote: the

momentum (p) is a measure in itself, since it depends on both the speed (v) and the quantity of

matter (m) [12].

Therefore, as it is clear, the sole mass or speed do not describe what happens in real cases [2].

Newton then referred to what we call momentum(p): something that originates jointly from the

speed(v) and quantity of matter(m). Thus, He defined this vector magnitude in the following

way:

�⃗= � ∙ �⃗ (3)

Eq.(3) describes the quantity of motion (p) of a body having a mass m and moving at a speed v.

Well, the momentum of a particle is the product of two quantities: the particle's mass and its

velocity. Hence, the momentum is a vector quantity: it has both magnitude and direction, and

direction and line coincide with those of v. In fact, the vector p has the same direction and the

same line of the speed(v) and its module is the mass(m) times the speed module. We therefore

find it of particular value, as well as rich in meaning and potential, to point out that the

momentum module of a particle is directly proportional to the mass of the object, and to its

speed too [13].

In short, the greater p the greater the velocity of the considered particle, just in a directly

proportional rate!, just as can be seen from the Newtonian formula, clearly illustrated by Eq.(3).

Since momentum has a direction, it can be used to predict the resulting direction and speed of

motion of particles after they collide.

Thus, in Newtonian Mechanics p is represented by the formula �⃗= � ∙ �⃗; in Quantum

Mechanics, in its turn, p is described by the de Broglie formula: