The switch game of Anneal Algorithm



Today's mainstream encryption technology is a famous asymmetric public-key encryption technology, it is depending on the of the 1970 s public key encryption system, to make it possible for the safe and efficient Internet transmission. It can say, we now all of the information transmission, Internet depends on the public key encryption technology; Our net silver-colored U aegis, social passwords, confidential E-mail, etc., are all based on the encryption technology, also including headed by the currency in the past two years, high-profile virtual currency is completely based on public key encryption technology, every purse with a public key encryption, and only the owner of the wallet with the private key, can decrypt, attribution credentials as a purse, the decentralized system, the ownership of the private key is fully represents the purse. If there is no password, or password be cracked and the above all security systems will be wiped out, virtual currency will also cease to exist.



In simple terms, the public key encryption algorithm is the product of two large prime Numbers, the product as a public key encryption, and encrypted with prime Numbers. Although it is easy to get the product but want to directly from the product is decomposed into two primes is very, very difficult. Using the existing computer log N do factorization, the operation steps increase with the length of the input index (time). So far are broken down in the experiment on the maximum number of 129, 1994 worldwide use 1600 workstations at the same time spent eight months’ time to successfully complete the decomposition. If use the same computing function to break down a 250 - bit number, want to use in 800000, with 1000 - bit number, will be 10,000,000,000,000,000,000,000,000 years.


Now, however, traditional cryptography system represented by the public key encryption system of is facing a huge challenge, the scientific community recognized, not long after, quantum computers will, quantum computing will no doubt bring enormous technological and social progress, but it will also make traditional password system vulnerable.


Quantum computer using Shor algorithm which can achieve a factor decomposition of 1000 digits within a second, and the operation time only with the third power of the number of input growth. Visible Shor quantum algorithms will be this kind of problem of "hard" into "easily" problem. In front of a quantum computer, existing public key system will not insurable.


Let's see, how does the quantum computer works?

Firstly, let us study the basic knowledge required:

What is quantum: (quantum) is an important concept in modern physics, the basic individual refers to a stop dividing. The first is m. Planck in 1900.He assumes that blackbody radiation of the radiation energy is discontinuous, can only take basic unit energy integer times. Later research showed that not only showed the fractured nature of separation of power, other parameters such as angular momentum, spin, charge, and so on are also showed the discrete quantization phenomenon. For example, "quantum of light" is the smallest unit of light, do not split again.


The principle of quantum state superposition: quantum state is referring to the state in the space of particles, such as energy, spin, sports, games, and so on. Quantum state can be described in the wave function, so the wave function is also known as a state function. Quantum state can be linear superposition, such as double slit interference, interference of light wave function is through the gap of two beams of light wave function of the stack. And such as electron orbitals, etc., can also be explained by the superposition of electronic state. Superposition is there are several kinds of Eigen states of particles in the state, this state is not sure at this moment, only when a "measure" is, will present a is measured to the state, may be it any kind of Eigen states.


Before we understand quantum computing, we need to understand why certain problems, using traditional computer cannot solve. Let's think about such a math problem to draw the outline of this, we call it the light switch.


The light switch game involves in trying to find the best set in a pile of switch. Here's a picture for example to introduce the problem:


Figure 2 Light switch game


Let's imagine that, every light switch has a digital is closely related to it, is to give you alternative (you don't want to change this). We call this number is "deviation". You have to do is: for each lamp switch on or off. In our game, open the said 1, close - 1. We then put all the switch of the deviation value multiplied by the corresponding value of the opening/closing. This will produce a result. This game was meant to set all the switch is closed to ensure minimum value. In mathematics, we define the deviation of each switch for hi, switch setting called Si


Figure 3, play the light switch game, the deviation of each switch value multiplied by their value after aggregation. According to which switch is opened and which switch is closed, we will get different scores. You can try this game. Hope that you can easily find, because it has a simple rule can be successful:



Figure 4, please answer the special "guess" of the switch Settings, we found that if we are set all the belt deviation of the switch is closed, the negative deviation switch, and then together, we will be a minimum value. It is easy, right? I can give you an infinite number of different deviation switch, and you only see the switch can be opened and closed by the rules.


Well, we let the problem become harder. Please imagine there are a lot of "on" switch have additional rules, the one here is "a" instead of a switch. We add a new deviation J, and after the two switches is multiplied by the value of J multiplication, we use such a rule for each pair of results before and after the switch is the result of the aggregation. Still the same, we need to do is, how to choose the switch state open or close to adapt to the new rules.



Figure 5, increase the difficulty of the additional rules to switch the game depends on the switch "on". But now this is very, very difficult to decide whether to which a switch should be opened or closed, because the neighbors will affect it. Even simplified to former figure only two switches, you still can't use previous rules, is also a negative deviation value is set according to them. In front of a complex network of all switches are neighbors, this all of a sudden to find out the right combination allows you to get the minimum value, becomes very difficult.



Figure 6, the light switch game, with additional rules, produce a light switch network interact with each other, each pair of switch if you try all combinations, there are four possibilities: [on, on], [on and off], [off, on], [off, off]. But as you increase the number of switch more and more, with the number of this possibility will switch quantity increase exponentially:




Figure 7, the index of the problems of the light switch game. You should understand why this game is no longer fun. In fact this problem even for most powerful supercomputers are very difficult. To put so many possible configurations into memory, and sends them to the traditional processor, to calculate our guess is correct, that will cost a very long time. Assuming that 500 switch, all the universe does not have enough time to check all of the configuration.


Then, how does the Quantum computing solve this problem?


Quantum computer basic computing power is derived from an idea, or you can put a bit of information in the superposition state. You can imagine such a situation; quantum bit hasn’t decided it would be for that state. Some people like the superposition as "also has two states". Or you can consider the state of quantum bit is not decided to choose + 1 or -1. This means that if you are using a quantum computer, we will be able to open and close at the same time the light switch.



Figure 8: Quantum mechanism of information bits (Q bits) can exist in a superposition state is known, the superposition and not choose what is + 1 or - 1 (in other words, you can think it is + 1 and 1)


Now take a look at the previous same number of switch group, but now into a quantum computer memory (note that the deviation value has not been added).



Figure 9, a mesh of superposition of quantum bits, the answer is somewhere in here! Because all the light switch is open and then shut down at the same time, we know the correct answer, the correct opening and closing every switch) will play somewhere, it is now also hide us. But also no problem, because of quantum mechanism will give it to us.


Here is how it works:



Figure 10, the computer applied the superposition bit and began to produce. At the end, the traditional normal bit stream appears, and find the answer along the way


You start the aformentioned system under the quantum superposition, and you slowly adjust quantum computer to close quantum superposition effect. At the same time, you slowly raised all the deviation. When the operation performed, all switches will slowly out of their superposition and select a state whether open or closed. When you add them, internal using quantum mechanism of computer help switch is set to the correct state to obtain the minimum value. Although N switches may produce 2 N a possibility of configuration, it can also be found at the end of the minimum value, won the light switch.


Isn't it amazing? Completely don't need us to calculate, we only need to do some simple manipulation, the objective laws of quantum can solve a problem! This is called a quantum annealing algorithm, we only need to configure good the parameters and evaluation function, we need all the rest of the hands of the nature, we wait and see the results, and we know that the calculation results of nature is always right. Although in our cognitive now, we still can't understand why the transaction was infinite computation, by quantum it only takes a few seconds to complete, the massive computing is through the quantum through to the other parallel to complete in the universe?


However, we must keep in mind what engineering can do is to significantly amplify a natural phenomenon, even though it can’t be understood. Bernoulli's law points out that movement of the curved surface is smaller than the movement of the flat surface air pressure, although scientists are still not fully resolved about Bernoulli's law on how to make a lift of the wing of the math problems, engineering has accepted the subtle fact and focuses to create the prosperity of today of the aviation industry.