Physical and electronic basys of quantum computers

Physical and electronic basys of quantum computers Already Feynman perceived, that the computation wasn’t only a mathematic discipline, but also physics, beginning the complex discussion on entanglement. As mathematical basys have calculation simulations of the classic physics, for this in electronic engeneering find to build physical systems and computational of level, producing information in entrance. In despite of systems based on algorithms, the superimposition principle in the quantum mechanics represents the computational basys, which is associated the probability wave, studied by Max Born. The superimposition principle for the microscopic objects, for which, it is possible that different states relatives to a determinated entity, and that can fairly live together in a non-definition state, as understanding at linear combination of different state in which it can be find, regarding especially the problem of how a quantum computer can physically build, and then regarding the linear algorithms, is computable though the exclusion principle of Pauli in physics, derivating some fundamental principle of the indetermination principle of Heisenberg. In a superimposition, in the light phenomena, is true that one of the mechanisms ineherents to the superimposition principle, in the quantum mechanics, in other words, can’t affirm that an entity will find really in a state or in another, that aren’t known, in difference of a physical mixture, and the superimposition contains, instead, all the possible uses but doesn’t is equivalent to some of these, but it can be true or false the fact that to every particle can be associated a wave, and every wave is a manifestation of a particle (1). Max Born perceived for the first the nature of the wave-particle dualism; the wave associated to a particle is a “probability” wave, in the sense that it indicate which will be the possible evolution for that particle. The state of a possible particle can’t be more that classical state (position in the space and in the time and relative speed), for that state of a particle is done by the superimposition of all his possible futures states, measurable though a probability.

The EPR paradox (Einstein- Podolsky-Rosen) is important for the distinction done today between problems that can be solved in polynomial time (P), that are considerate tractable, and these that can’t be resolved, instead, in polynomial time and that they are generally considered intractable and that can take part, in his turn, of different classes. Between these lasts, we find the NP class. The problems of NP-type can’t be, in general, resolved by deterministic algorithms of polynomial type, and they are, then, in line of principle, intractable. The NP-problem involves non deterministic polynomial time, in which have to dimostrate that the non-linear time will be composed of deterministic equations of the mathematics and computational informatics.

The algorithms can be classified as: -

P: polynomial (for exemple, the multiplication)

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NP-polynomial non-deterministic (for exemple, the factorization for which the electromagnetism problem results static or dynamics in equivalent sense)

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NP-complete: sub-classes of NP in such a way that if one of the class is tractable they are all so (for exemple, the problem of commercial traveller)

Can be concluded that when the electron will be not in a defined state, but in a superimposition of state 0 and 1, if on assign to the state 0 the binaire worth “0”and to the state 1 the binaire worth “1”, on have to affirm that the electron system find himself in a state that represents the superimposition of “0”and “1” in indefinite way, and this phenomenon is binded to the nondeterministic polynomial algorithms. The spin is a conservative quantity, used whether in physics and in quantum informatics: taking in consideration a quantum system constituted of two protons, between there very near locally and with total spin void the system is based on the

invariance of the localization of the spin. In fact, this situation corresponds to have the spins of two protons, measured along an opposite direction, oriented in opposite way, in other words, if a proton has spin +1/2 along a direction, the other will have necessarily spin -1/2 along the same direction. If now on imagine that the two protons will remove themselves indefinitively the one from the other, until to overtake enormous reciprocal distances (even astronomical distances), oughn’t admit, for the conservatives quantities, that the anti-parallelism relation of the spins will remain preserved. For this, where on effect the measurement of a spin component of one of two particles along an assigned direction, assigning it to a determinate state, also the far particle necessarily will be forced immediately in a determined state of his angular moment in way to preserve, along the same direction, the anti-parallelism direction of departure. This phenomenon is noted as entanglement, because is based on probability (also joined probabilities) that the electron will find in the same direction of the electron in the assigned direction. On the contrary, the quantization principle of Dirac is connected to the phenomenons of generalization of possible equations, above all for the non-deterministic NP-polynomial problems and NPcomplete problems.

A qubit is a “superimposition” of 0 and 1 and can be defined from the mathematic notation a I0>+bI1>, presupposing that, if measured, it could be worth 0 with probability a and 1 with probability b, being a e b complex numbers. The mathematic nature of state represented from the symbol I> represents a linear time or a polynomial time, that often represents a vector, for his nature oriented. In fact, the state I1>+I0> is different from the state I0>+I1>.

In quantum environment, it is possible to reverse content of a qubit according to the simulation of algorithmics models, based on the polynomial time in deterministic system, in other way that will contain a simple probability to find possible Hamiltonians cycles, fundamentals for the calculation machines. The impulse of a light of opportune duration is equivalent in all the effects to an operator NOT. But it is saw also that lighting up the atom for half time (in respect to that necessarely to commute the electron state), on obtain a superimposition of states. A complete impulse of the qubit is equivalent, then, at the operator NOT. Then it exists the square root of NOT, otherwise a calculation principle at he basys of the reduction of algorithms, and of the quantization of artificial machines. At the basys of these calculations it exists the variance for the calculation of the average of quantum vector, at the basys of polynomial time, when speak about infinitesimal analysis and bring near the differential mathematics.

If, presently, proceed to build a register constituted by two electrons, which stable state of spin will be four, corresponding to the four binaire states (00,01,10,11), where the state of the register could not find in a definite state, but in a superimposition of states, will be concluded that the system “electrons couple” (=the register in two electrons), will be find in a state that represents the superimposition of the couple of states 00,01,10,11. In a register in two cells, can happen simultaneous events in the sense that they exist commutative properties and esponential factors of a process named entanglement. The register contain all the four states, according to an adjoining probability between 01 and 11, but it contains also 00. They exist, then, worth containing discret worth (ad not continuos) of n states, in esponential time or in polynomial time. To register, in fact, the four worths indicated in classical form must be necessary four register in two cells, in quantum form the four values indicated are containibles in only one register the auto-values to a limited degree. Then a register in 1 cell can contain 2 1 values, in register in two cells can contain 2₂ values, and so (2). Among the requirements that a quantum computer have to soddisfy, for the calculation speed of bits it is necessary to consider that 1)the qubits can be initialized to an arbitrary value

2)the quantum gate have to be more fast of the decoerence time 3)physically it must be scaling to increase the qubit number 4)the qubit can be easily read 5)they must contain a Turing complete gate set The technologies utilisables have to resolve particular access problems, in which they exist: 1)superconductor-based quantum computers (including SQUID-based quantum computers) 2)cavity quantum elettrodynamics (CQED) – based 3)nuclear magnetic resonance on molecules in solution-based 4)molecular magnet-based 5)quantum dot-on surface-based 6)trapped ion quantum computer 7)the solid state NMR Kane quantum computer 8)fullerene-based ESR quantum computer The quantum parallelism, according to whether can imagine to have, for Deutsch, a function being able to predict the tendency of the share market, is able to cause an adjoining probability wave pf phenomenons apparently different. If it is necessary to value this function for only two worths, 0 and 1, in other words f(0) and f(1), can be imagined that, consisting for the quantum computer in a complex problem, to a classic computer will be necessary 24 hours to calculate the same function, then 48 hours to verificate if f(0)=f(1), then for the quantum parallelism, could be possible to calculate at the same time f(0)=f(1) in the capacity of operator of the quantum calculation, than even in the entanglement is possible to know if is possible to modificate states or auto-values of the system, in fact, could be probably known if f(0)=f(1) in 24 hours, and then if it exist an useful time to invest with success.

In the last analysis, the theoric physics affirm that it is possible to establish quantum worths of discret variability though artificial machines, above all for all that concern the quantum mechanics in the ondulatory and corpuscular phenomenons, and than the quantum computers though molecules tracing In very high level (3). The molecular theory for this mets obstacles in the theory of electromagnetism (4) and the technology NMR, representing in fact a new level of the quantum mechanics.

1)As all the physics systems, the electron prefer to inhabit the energetic states most low in respect of these more high, often at the low temperatures. The energy of a physical system as the electron depends by the state of other electrons. An electron can indicate to the near particules to reverse the direction of spin (rotation) in hourly time to achieve an energetic state more low; another electron can hand on an opposite message, indicating an anti-hourly spin. The energetic state most low for the set of electrons that can do a rotation is that where the general number of clashs between adiacent spins is the most low. In order that the group of electron can register, in the whole, the minimum energetic state, the so-called “fundamental state”, it is necessary to find an agreement to lining up the directions of spin. As a complex computational problem can be resolved dividing it up in many binaire digits, it can be represented in terms of fundamental state of an appropriate physical system”. Article of S. Llloyd, Quamtum computers?

2)Instead, according to the quantum mechanics, the spin can be in a superimposition state, that is in every combination of the two directions, for exemple 30% hourly and 70% anti-hourly. The whole system is, for this, an aggregated very complex of superimpositions of all the possible combination of spin of each particle.

The evolution of a similar system, described by a comples probability wave function, is a problem never tractable, even today from every supercomputer. Here, therefore, the idea of Feynman. What will happen if the simulation of the system doesn’t lead over a classic computer but over a computer that could operate, even it, according to the laws of quantum mechanics? The circuits and the memory bits of the last could not be bound to a duality of values 0 and 1 but could operate, even there, in a superimposition of states 0 and 1.

Feynman, in reality, in 1981, didn’t go far of this intuition. But [in the conference] another physics, Paul Benoff, presented a model of the quantum computer based on an ipothetic Turing machine that worked operating a sequence of operations took place according to the laws of the quantum mechanics. […] The basic principle of every classic computer is that each function that can be calculated, can be calculated even by a Turing machine. But now, for Deutsch, it existed an universal computer be able to operate everyone type of calculation, that every physical entity will be able to effect. The computation wasn’t again a branch of the only mathematics but become a manifestation of the laws of he physics”. From classic computer to that quantum: realisability and potential applications, article of E. Hofmann 3)On the basys of Thomson’s works, forcing however to remain more adherent to the geometrical approach of Faraday, Maxwell, in the first part of the article [ On a mechanical representation of electric, magnetic and galvanic forces, publied in 1847], proposes a new analogy: that between the electromagnetic phenomenons and the uncompressible fluid across a weight that operate some resistance. The force lines of Faraday are, for Maxwell, an incomplete geometrical method for the electric and magnetic phenomenons, because they indicate informations of the direction but not on the intensity of forces” . Sheldon Lee Glashow, Maxwell, Electricity, magnetism and light, the library of Repubblica, 2012, pag.53-57 4)The description of the electricity from his model [ the magneto-optic effect of Thomson] permits to him to consider the phenomenons of polarization of dielectrics as a particular case of phenomenons of conduction “It is a fact experimentally noted – write Maxwell- that the electric tension is the same thing observed whether in the static electricity or in the currency, so that an electromotrix force produced by the magnetism can be utilized to charge a bottle of Leida”. When a difference of tension is applied to different parts of a force have two possible effects. If the body is the conductor, the “matter of the electricity” moves doing a rotation over the surfaces of vortixes, so generating the electric currency; the tangential forces impressed form the matter of the cells are the elecromotrix forces and the pressure that the particles operate the one to the others correspond to the electricity potential. If the body is an insulator, the tension difference is stored up in the elastic mean in a type of potential energy though the deformation of the molecular vortixes. These deformations induce a shifting of the particles constituting the “matter of the electricity” from their balance position, , for which a part of the molecule charge positively and the other charge negatively. In difference to what happen in a conductor, nevertheless, the electricity remain tied up to the molecules and doesn’t proceed from a molecule to the other. The effect of this action on the whole dielectric produce a general shifting of he electricity in a specified direction. This shifting –write Maxwell-doesn’t is equivalent to a current, since reached to a certain value it is hold in unchanged way, but it is the beginning of a currency, and his variations take place to currents in positive direction or negative direction, in accordance with the shifting will increase or reduce”. Maxwell, for that, concludes that the distinction between conduction and electric static induction is all similar to the distinction that, in the matter, is done among viscouses processes and elastic processes: the conductor is assimilable to a porous membrane that is impermeable to the fluid but from there tramit the pressure from a part to the other. In this manner, Maxwell obtain two important results. The first consider the fact a variable current in a conductor produces in the surrounding space (whether this an insulating material or simply the space) small changes in the positions of electric particles, that is the effect of a variable currency is that to generate small currents in the weight associed to the “shifting” of the particles. This allows to Maxwell to complete his equations, taking in consideration the effects of that, fairly at the present, are named “shifting currents”. In second place, considerating that the weight is elastic, it is possible to determine the speed whom electromagnetic inconvenience propagate across it. On the basys of calculations performed utilizing his model [the Thomson’s model] Maxwell is arranged to conclude: “The speed of ondulatory movement across the ipothetic conductor, calculed form the electromagnetic experiments of

Kohlraush and Weber, agree in so perfect manner with the light speed, calculed from optics experiments of Fizeau, that will be difficult not infer that the light should consist in the ondulatory mouvements across the same conductor that is the principal cause of electric and magnetic phenomenous”. Sheldon Lee Glashow, Mawxell, Electriciy, magnetism and light, the library of Repubblica, 2012, pag.67-69