...nd also any value in beteen. To understand the idea of a quantum object being in 2 states at once here is a very simple experiment. Fig1 AFig1 B Fig1 CFig 1 CThis conclusion, in more technical terms, could be rephrased as fallo the photon is in a coherent superposition of being in the transmitted beam and the reflected beam. In the same sort of manner, the atom can be prepared in a superposition of to different electronic states. Such a quantum system ith to states is called a quantum bit, or a qubit and it can be prepared in superposition of its 2 logical states 0 and 1. i2sIf e take a very simple example. Lets say e have 3 bits. ith the classical computation methods, e can store in these 3 bits one of all 3 digit numbers in base 2 at a time. For example 001, 010, 011 and so on. In total there are 23 8 possible numbers hich can be stored in this 3 bit register. But a similar quantum 3 bit register ould be able to store all these 8 numbers at the same time. So, a N bit quantum register ould be able to store numbers 2N numbers at the same time. And the best thing about this is that operations can be performed on all of them at the same time. One ay in hich e could do this, is by taking quabits as atoms and then ith tuned laser pulses e ould be able to affect the atomic electronic states. In this ay, e ould be able to operate on all of them at the same time. During the operation all the numbers in the superposition are affected. This is a parallel computation. In this ay it ould be able to perform in one computational step 2N classical operations. To get the same result ith a classic computer, it ould have to do the computations 2N or one ould have to use 2N processors hich are orking in parallel at the same time. i1sThe parallelism comes for free ith quantum computing. The output of the algorithm ould be the constructive interference beteen the parallel computations. i4sComparison beteen the to computational systemsAll this may not seem very exciting. All it is saying is that the classic computer ould have to ork more and faster in order to catch up ith the quantum computer. But the main idea is that the quantum computer is exponentially faster than the classic computer. Lets take an example. Lets assume that e have a set ith N elements and e ant to generate all the subsets of the given set. The smallest important step of a classic algorithm hich ould have to solve the problem, ould be to generate one subset. Because there are 2N subsets of a set ith N elements, the complexity of such an algorithm ould be O2N . So it ould take 2N steps to solve the problem. Lets say that N is 100. Then the total number of operations ould be 2100 steps. A modern computer does apx. 3 million basic operations per second and about 1 million complex operations per second. Lets do some calculations to see ho long it ould take for a normal computer to solve the problemThe number of steps required to solve the problem is2N 1267650600228229401496703205376 stepsIf, a computer can perform 1 million complex operations per second, then it ould take2N 1000000 1267650600228229401496703 secondsThat ould take2N 1000000 60 60 24 7 365 5742419548761639 yearsHaving this its easy to see that it ould take more than 5 million billion years to complete all the operations. But, using a quantum computer ith a N bit register, all these steps 2N steps can be done in one go. So there is the extremely big advantage of quantum computers. Several billion years reduced to a single second. Or, rather better, to a single computational step.Applications RSA codingAnother major application of quantum algorithms could be used in cryptography RSA. Noadays the bases of the internet security relies upon the idea that verylarge numbers cannot be factorized very easily. Lets take an example If e ere to solve thisX Y Z T 2001Not using a calculator, therefore, only using pen and paper, it ould probably take someone an hour to find the unique integer solution of the problem.But, on the other hand2 11 7 13 The reverse problem ould take only a couple of minutes to solve. And that is not because ere better at solving this problem rather than the first one, but because e dont kno algorithms fast and efficient enough. In other ords if e ere to solve the second problem ith 30 digit numbers, then, using the same pen and paper technique, it ould require little extra-ork. But in order to factorize a 30 digit number using trial and error algorithms, the extra time required ould be huge. i2s In classical computation there arent any algorithms able to factorize numbers in polynomial time. The best knon algorithm ith input the number N, has complexity Oe649 13 ln N 13 ln ln N 23s In this case, log10N is the size of the input or in other ords the number of digits of number N. As you can see, the complexity of the algorithm varies exponentially ith the size of the input. As N gros, the time required to solve the problem gros exponentially. So, for a 1000 digit number, the time required to solve the problem ould be 1025 years. This is considerably longer than the age of the universe. In 1994, an army of mathematicians and computer engineers factorized a 129 digit number. This has taken over 8 months.On the other hand, a quantum algorithm as produced. It has complexity OlogN2k here k is small. So, its roughly quadratic. So, factorizing a 1000 digit number ould take only a fe million steps hich is a fe seconds. i4sApplications AI So far all the ne ideas about Artificial Intelligence ere just improvements of the old ones and all the advances made are ithin the Turing model. But the quantum computation opens ne stages and levels of development. The dynamics of an isolated quantum system are governed by the Schrodner equation. The systems future state can be obtained by multiplication by a unitary matrix. The implementation of the algorithm should be focused on trying to find the matrix for the given problem and then map the matrix into a sequential product of smaller matrices. This can be implemented relatively easy. All its saying is that a quantum register can store 2N simultaneously, as said before. One of the main issues of this type of algorithm is to be able to separate the good solutions from the bad ones, this algorithm generates all the possible solutions. This must be done ithout actually looking and checking the solutions because this ay, the interaction ith the content of the register ill make the superposition state to collapse.Basic algorithms able to do this have been already developed, but of course they are in the earliest stages. One of the most important ideas concerning artificial intelligence is that the quantum processes are the basis of biological information processing. One can look at this from 3 perspectivesPhilosofical at the deepest level of description, nature is quantum mechanical. Neurophysiological some researchers have argued that the microtubules inside the cytos...
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