Quantum magic into life

D-Wave Adiabatic Computer

The article concludes the cycle of publications devoted to the critical analysis of quantum magic: geektimes.ru/post/285378 and geektimes.ru/post/285490 . This term for some reason strongly annoys some adherents of the new religion. But I did not invent it, but borrowed it from one of its priests, or at least initiated, who tried to publish a magazine and wrote a book with the title royallib.com/book/doronin_sergey/kvantovaya_magiya.html . In addition, the name of the American company MagicQ, engaged in quantum coding systems, contains part of the title of this article before the hyphen. Here I tried to speculate about the technologies existing in the real world, which are commonly associated with quantum entanglement in the sense of the EPR paradox.
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What is the adiabatic algorithm?

It is known that full-fledged quantum computers operating registers with entangled qubits do not yet exist. There are only experimental installations that can do something with the number of qubits read. For example, they say that back in 2001, IBM was able to decompose the number 15 into two simple factors using the Shor algorithm using 7 qubits. But I did not meet the information that some other numbers succumbed to this device. Maybe he was looking badly, but it seems to me that it would be more correct to call him not a computer, but a unique, physical experiment.

First we will clarify what a “full-fledged quantum computer” means. This is a device that implements quantum, parallel computing (see the paragraph “Computer of God” in geektimes.ru/post/285490 ). If not, then talking about a quantum computer means fooling people's heads. In terms of progress and the prospects for quantum technologies, journalists and even many scientists have been very successful in this. It should be noted that quantum technologies, generally speaking, have been used for 60 years already - since the creation of the first maser, and then the laser. Today there are computers using quantum effects.

Examples of such a computer are D-Wave products www.3dnews.ru/822671 . It is known that processors with registers of 128, 512, 1024 and even 2048 qubits, which D-Wave presents effectively, do not form entangled states. Although groups of 8 qubits (qubits) are said to be entangled within themselves and there is still confusion between separate (few) qubits. Little is known about the black box, which literally is the D-Wave computer.

However, it is known that it implements a so-called. adiabatic algorithms. They use the effect of energy redistribution between SQUIDs (“qubits”), during which the register relaxes to a state of thermodynamic equilibrium. In this case, it is possible to solve a very narrow class of problems related to integer optimization. However, it is claimed that among them there is the traveling salesman problem, which is solved faster than on any supercomputer. It certainly makes an impression! Obviously, we are talking about local optimization, i.e., about step-by-step improvement of an arbitrary route in the class of those routes that are close enough to it. However, from a practical point of view, local optimization algorithms, as a rule, work efficiently.

What is the adiabatic algorithm? I will try to explain this with an example that I invented myself. Maybe the algorithms in D-Wave do not work at all. But I can not imagine how otherwise to use the process of redistribution of energy in the qubit system. Judge for yourself how true this looks. In any case, as an optimization algorithm should be interesting. Technically quite feasible!

In this regard, the term "qubit" is not quite suitable, because it is desirable to have more states. There is a suitable word “quudit”. In principle, this is the same qubit, only it has not 2, but an arbitrary number. $$$d$ base states. In the case of a qubit ( $$$d = 2$ ) adiabatically can also be considered, but still assume that D-Wave uses Qudit for some $$$d \ geq 2$ . And let's go even further, arguing that the superposition of the base states is not needed in this case. To implement an adiabatic algorithm, it is sufficient to have data elements, each of which can be in one of $$$d$ energy (stationary) states and move from one to another when interacting with elements close enough to it. The register consists of $$$n$ such “kudits” (we will call them in the following).

Suppose you need to find the maximum function $$$z_1 + z_2 + \ ldots + z_n$ under conditions

$$

$$\ sum_ {j = 1} ^ n m_j \ cdot z_j = K \ qquad z_j \ geq 0 \ qquad z_j \ in {\ mathbb Z}$$

Coefficients $$$m_j$ and $$$K$ are integer, non-negative numbers. It is necessary to find (integer) solution of this optimization problem. Below is an example of how it can occur.

Transform it by introducing new variables. $$$x_j = z_j / M$ where $$$M = LCM (m_1, m_2, \ ldots, m_n)$ . Denoting $$$Q = K / M$ we obtain an equivalent problem: find the maximum $$$x_1 + x_2 + \ ldots + x_n$ under conditions

$$

$$\ sum_ {j = 1} ^ n m_j \ cdot x_j = Q \ qquad x_j \ geq 0 \ qquad \ qquad (1)$$

We assume that energy levels are equidistant at $$$\ Delta E$ . To run the algorithm follows for all $$$j$ set kudit number $$$j$ in a state with energy $$$m_j \ Delta E$ i.e. transfer it to $$$m_j$ - th energy level (starting from zero).

Let the current value of the variable $$$x_j$ determined from the equation $$$E_j = m_j \ Delta E \ cdot x_j$ where $$$E_j$ - energy $$$j$ - go kudita. Then all the initial values $$$x_j = 1$ . In the process of redistribution of energy between the Qudit values $$$E_j$ change that emulates changes in values $$$x_j = E_j / (m_j \ Delta E)$ .

Now let the register be able to independently come to a state of thermodynamic equilibrium. In the process, the Qudites with greater energy will transmit it to the Qudites close to them with lower energy in multiple portions $$$\ Delta E$ . Consider pair interaction when energy $$$k \ Delta E$ moves from the element with energy $$$E_p$ to the element with energy $$$E_q$ . Then new variable values $$$x_p$ and $$$x_q$ given by the expressions:

$$

$$x_p '= x_p- \ frac {k} {m_p} \ qquad x_q' = x_q + \ frac {k} {m_q} \ qquad \ qquad (2)$$

Obviously, for such “transactions” in most cases $$$m_p> m_q$ i.e. initial energy $$$p$ - kudit more than $$$q$ - go Then from (2) it follows that $$$x_p '+ x_q'> x_p + x_q$ i.e., the value of the objective function has increased from $$$\ sum_j x_j$ before $$$\ sum_j x'_j$ . Wherein $$$z'_p = Mx'_p = M \ left (x_p- \ frac {k} {m_p} \ right) = z_p-k \ frac {M} {m_p}$ is an integer if the integer was $$$z_p$ .

Since the process is adiabatic, the total energy of the system does not change. Consequently

$$

$$\ sum_ {j = 1} ^ n m_j \ cdot x_j '\ cdot \ Delta E = \ sum_ {j = 1} ^ n E'_j = \ sum_ {j = 1} ^ n E_j = \ sum_ {j = 1} ^ n m_j \ cdot x_j \ cdot \ Delta E = Q \ Delta E$$

where you can see that new values $$$x'_j$ satisfy the constraint (1).

After the thermodynamic equilibrium is established in the system (this happens very quickly), it remains to read the values ​​of the Qudit energy $$$E_j$ , divide them into $$$m_j \ Delta E$ and multiply by $$$M$ . The solution to the original problem is obtained. $$$z_1, z_2, \ ldots, z_n$ . Note that at each step of the algorithm the numbers $$$z_j = Mx_j$ are integers, i.e., the integer optimization problem is solved. Note also that the solution obtained will be locally optimal, but, perhaps, in practice this will suit us.

The real example of the considered task is the following (invented offhand). Suppose you want to serve the largest number of customers in $$$n$ points, each of which should be invited $$$z_j$ person. At the same time, the company has a sum of money. $$$K$ , which should be spent on this operation according to the budget, and the cost of servicing one client in paragraph $$$j$ are equal $$$m_j$ .

Apparently, approximately in this way, D-Wave computers solve a very narrow class of optimization problems, which, however, are of practical interest. For example, craftsmen from Google, using adiabatic algorithms, taught D-Wave to recognize the image of a car in a photo. And yet the products of this company, although they are of great interest, are infinitely far from any kind of universal, truly quantum computer.

Quantum radar from China

Extremely curious information that China allegedly successfully tested a radar using a pair of entangled photons, operating at a distance of up to 100 km and capable of making useless radar technology - invisibility sputniknews.com/military/20161004/1045974842/china-quantum-radar-stealth. html . This media resource is strongly pro-Chinese and less pro-Russian. Brave such agitprop))

As you can see, China is already bluffing with might and main by the fact that it has mastered intricate technologies and uses them in satellite communications, as well as in radar. The idea of ​​such a radar is quite obvious, if you believe in quantum magic. One of the two EPR - entangled in polarizations of photons caught in an optical resonator in the form of a standing wave, and the second went to a meeting with a goal (B2 Spirit). As soon as it was reflected from the surface of the object, then immediately, due to partial refraction, with a probability greater than 0.5, it acquired polarization perpendicular to the plane of incidence-reflection. This means that the polarization state of one of the two photons of the pair has changed. According to the EPR — the paradigm (also known as quantum magic), the polarization of the second photon — that which is bored in the resonator — has also changed. Since this happened not with one photon pair, but with many, a change in the polarization of the field in the resonator can be detected. Got you, Spirit? Now we will knock out the spirit of you in the name of Mao's bright ideas! ))

It is important to note that the target is detected not when the reflected photon has returned to the transmission, but immediately, as soon as it has reflected from the object. It is easy to understand that this roughly contradicts the SRT. In fact, let the laser beam with photons entering entangled pairs shine in a fixed direction. As soon as the ill-fated B2 hit the beam, at the same instant, the PLA warriors determined the azimuth and elevation angle of the target. They knew these angles in advance when they fixed the direction of the beam, but the American reported about his meeting with the beam before it could be seen in this place! If this is not exceeding the maximum permissible signaling rate $$$c = 299,792,458$ m / s, then what?

Adherents and fans of quantum magic this fact does not bother. It has long been customary to explain strange effects by saying that the laws of physics are written in classical space, and quantum physics goes far beyond its limits, where other rules apply (something like how piercing a curved space with a black hole dramatically reduces the distances between stars). I do not undertake to accurately reproduce philosophical explanations based on belief in quantum miracles. But based on the physics, which is confirmed by experiments, this can not happen.

So radar on entangled photons is fiction? Yes and no. In the form in which I am jokingly described - definitely YES. But it is possible to speculate the mechanism of operation of this radar, which has a purely quantum nature. So, no tangled pairs arise. Instead, each photon is divided into two modes, one of which remains in the resonator, and the other is sent to the meeting with a goal (see on this subject a quote from Dirac in p. "Aspe Experience" geektimes.ru/post/285378 ). After the return of the reflected mode and the radar absorption of the entire photon, the field in the resonator weakens. With a large number of photons, this can be detected.

Evaluating these arguments it is important to understand that the photon has no idea of ​​Schrodinger. This means that it does not have a location in space. A photon is present wherever there is a field, of which it is a part, roughly speaking. On this occasion, it is useful to read the introduction to the book by Dirac “Principles of Quantum Mechanics”, where he talks about photons. This will take only a few minutes, but it will help get rid of the obsessive image of the photon - the point particle that underlies the false interpretation of Aspe's experiments.

Thus, apparently, the usual location takes place, but photons. It is clear that only a small part of them returns to the radar. However, the reflected photon mode will be a scattered wave, so the probability of its returning to the place of radiation is not so small. All these heuristic considerations, of course, may be erroneous. However, my explanation is based on QM and does not attract such mystical entities as entangled states of infinitely distant particles.

One thing is clear: the Chinese have created a radar on photons, which allows you to detect the aircraft beyond the line of sight. This is the success of wave optics and photonics. It is possible that such a radar will increase the vulnerability of stealth aircraft. But quantum magic is hardly involved in this, although the Chinese themselves faithfully believe in the opposite.



Figure from an article on this topic wonderfulengineering.com/the-chinese-have-allegedly-developed-a-quantum-radar-that-can-detect-american-stealth-planes , which I could not figure out without knowing the abbreviations. This is clearly not related to entangled photons. It looks like a normal photon location.



In this figure from the same article, as far as can be judged, the principle of the Doppler radar.

Cryptography and spontaneous parametric scattering

Quantum cryptography systems have been in use for a decade, if not more. They are constantly mixed with quantum magic, but, apparently, it has nothing to do with such systems. As an example, consider the BB84 secret key generation algorithm described here ru.wikipedia.org/wiki/Quant_Cryptography .

The protection mechanism is based on the fact that if an attacker Eve intercepts a bit carried by a polarized photon, she will thereby translate it into a polarization state, which may differ from the one specified by Alice. During the verification of the transmitted bits between Alice and Bob, this change in polarization will be detected. The quantum effect is used - the photon transitions into its own state of the measured polarization, but the EPR is not involved.

Thus, real-life systems of quantum cryptography play the role of an important argument in favor of quantum magic, but in reality they are not. As for theoretical results in this area, based on EPR - entanglement, their physical feasibility is associated with the same fundamental problems as teleportation and quantum computing geektimes.ru/post/285490 .

The article wonderfulengineering.com/the-chinese-have-allegedly-developed-a-quantum-radar-that-can-detect-american-stealth-planes shows a drawing depicting the spontaneous parametric scattering of a photon as a hypothetical source of entangled pairs for the quantum radar . It is believed that during this process, a photon, passing through a nonlinear crystal, spontaneously splits into two photons entangled in polarizations. This is a well known effect since the late 60s. A pair born as a result is called a biphoton, which theoretically turns out to be confusing.



Spontaneous parametric scattering (spontaneous down conversion)

But really, do two photons appear here, as shown in the figure, or would it be more correct to speak of two modes of one photon at the exit from the crystal? That is about something like double refraction? In some articles on this topic, the authors carefully write that the decay of a photon into two should not be taken too literally. Judging by the fact that this effect is registered through the interference of “photon pairs”, one can confidently assert that a pair does not arise here. The fact is that, in accordance with the CM, a photon can interfere only with itself! In his fundamental book, P.A.M. Dirac directly writes that two different photons never interfere (see the introduction). This circumstance, presumably, will not significantly affect the theory of spontaneous parametric scattering. However, it will knock out an important backup from the myth of entangled photons, which remain so after flying apart at distances of tens and hundreds of kilometers (EPR is entanglement). Of course, this question needs precise research.

The result of three publications, expressing my personal point of view. Quantum magic has no theoretical basis, it is the product of arbitrary speculation with the formalism of QM and, in fact, is not supported by experiments. Fundamental experiments Aspe were mistakenly interpreted on the basis of the classical idea that photons emitted in one cascade have eigenvalues ​​of pulses and angular moments simultaneously (which is impossible due to CM and QED). EPR - the paradigm is not embodied in real, quantum technologies, contrary to what is customary to think under the pressure of journalists and not quite conscientious scientists. The scientific community is sorely lacking a critical assessment of this paradigm, which has actually become a dogma.

PS My articles do not in any way question the actual quantum mechanics. The reverse claims of adherents of quantum magic are evidence of the bad faith described above.