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## Quantum Computers: rapidly rely on the smallest particles

Jan

21

2014

Quantum Computers: rapidly rely on the smallest particles

Quantum computing is a relatively new subject in computer science. The first underlying concepts were introduced thirty years ago by the famous physicist Richard Feynman . In the intervening time, we have learned a lot about programming quantum computers and now we can say sensible things about the theoretical power of it. In the past decade, many universities quantum computing also included as a subject in their curricula.

Despite all these achievements, there is a crucial element in this area that we still have not mastered: actually building a quantum computer. The qubits that the hardware platform should form under these new systems are not yet making sufficient numbers and not long enough shelf life to make larger quantum applications to run on. At this time, approximately a handful usable qubits can be made at the same time and they do not survive more than a few seconds. This is the commitment of the current quantum computers are limited to very specific applications, such as cryptography.

The NSA sees that and has started its own research to make, with a budget of 58 million euros converted. a working quantum computer Quantum computers would, if they exist, many encryption can crack at lightning speed. But what is quantum computing anyway? In this article we will go deeper into this question.

Quantum Computing // (c) CyberHades @ http://www.flickr.com/photos/cyberhades

Bits, qubits and superpositions

Bits

A qubit, short for quantum bit is a building block of a quantum computer similar to ordinary bit, which is the basis of all our current computer technology. Besides the many similarities, there are also crucial differences.

Ordinary bits or binary digits can only have the value 0 or 1. How a bit is then in a computer implemented , is in principle independent of the logical value. For example, digital information is transmitted in computer chips and processed by means of signals from different voltage levels, for example, 0 and 1.2 volts.

In traditional memory and connection cables work with different voltages. Old fashioned hard disks use magnetic polarization contrast for the same digital information store. So you might as well be a computer can just build with pressure and valves, mechanical parts or marbles , taxiways and gates works. The logical principles of the first digital computers were also no different than that of the current machines, were used only in place of the transistors first relay (electromagnetic switch), and later vacuum tubes, the predecessors of the transistor, is used.

In practice, designers for storage, transfer and processing of digital information for each component have chosen an implementation consistent with the application, the required speed and capacity, and the available budget. All these considerations we see for example, in the memory hierarchy of a system.

Qubits

Qubits are fundamentally different from ordinary bits. They have been developed according to quantum mechanics, where units are not only the value 0 or 1 can assume, but also a little one value and at the same time a little different value. A qubit can, for example, one half of the value of 0 and the other half the value 1, or two-thirds the value 0 and one-third the value 1.

“The value of a qubit can be both a bit 0 and bit 1 are”

For those familiar with statistical probability distributions, can be compared with a qubit random variable . Also, it is the value itself is not exactly known, only you know anything about the probability distribution of it. A crucial difference between a random variable and a qubit is that first a probabilistic or statistical concept and the latter a quantum mechanical concept. This means that although the value of a random variable is not precisely known, but it does for each possible value established the probability thereon. While the value of a qubit at the same time a bit may be 0, and a bit 1. In quantum computers, it also does not speak of probability distributions but superpositions.

Superpositions

Superpositions (credits WhiteTimberWolf and Wikipedia) The strength of these superpositions is clearer if we combine several qubits to a series in a similar way as in the traditional deterministic world bits are packed into bytes. For example, we look at a row of three ordinary bits, it could take one of eight different values: 000, 001, 010, 011, 100, 101, 110, 111.

Three bundled qubits simultaneously have a little of each of these eight values. Although the real quantum computer agents would find this sloppy we denote fractions for the eight different values for example as follows: 1/4, 0, 0, 1/4, 0, 1/2, 0, 0. That means that the three qubits for a quarter have a quarter of the value 011 and half the value 101. Value 000

As in the elaboration of wave functions on the next page explains, are random variables and qubits mathematically not equivalent. In a superposition because the fractions can also be negative. Precisely these operations make calculations possible that can be highly probable., not by a conventional machine

Normalized wave functions and amplitudes

Normalized wave functions

Although the individual opportunities just as random variables added a total of 1 should form are random variables and qubits mathematically not equivalent. This first description of a qubit, we also do the underlying quantum mechanics seriously deficient. In reality, we have the state of a qubit ie describe a so-called normalized wavefunction .

For physics interested: wave functions describing the quantum mechanical state of the subatomic particle systems in which quantum computers are built. Think of the electrons and photons that we already know from the atomic model of Bohr , later refined in the Standard Model , which we are now dozens of different flavors of quarks, leptons and bosons see.

The addition of ‘normalized’ to say no more than that the wave equation is scaled so that the total of all opportunities to a specific value, or so the probability mass is indeed equal to 1.

Amplitudes

The wave function specifies for each separate value of a qubit, 0 and 1, is a complex number, the amplitude, from which then the probability of this value can be derived again. Below is the wave function for a single qubit stand.

Bit-qubit / (c) Harry Buhrman CWI-Eindhoven Because the amplitudes, alpha and beta, complex numbers, there are several underlying quantum mechanical states, who all have the same probability distribution. A crucial difference to the stochastic world is that the fractions are calculated by squaring the complex amplitudes, and that they should therefore also be able to be negative. Once we try to see (measure), a superposition that takes one of its non-quantum mechanical, deterministic values. We call it the collapse of the superposition. At that time, so quantum mechanics changes in statistics.

Power, distribution and quantum computation

Computing

Superpositions make it possible to count. Values at the same time with a lot of For a two qubit values are: 2 ^ 1, 0 and 1, for three qubits are eight different values: 2 ^ 3, and ten qubits that all 1024 severals values: 2 ^ 10. In mathematical terms, the number of different values that can contain a superposition time is exponential with respect to the number of qubits and that is exactly where the extra power of the quantum computer originated.

The response of a quantum calculation is usually not directly read. Once you are viewing a superposition collapses after all these together into one of the concrete values within that superposition. At this time, the transition of the quantum mechanical to the statistical world created. What specific value by collapse, you can not know in advance. It is true that each bit is the probability that it occurs, corresponds to the size of its squared amplitude, which we called the group on the previous page.

Probability

That means you have to do, then you can deduce from the interrelation of all the different concrete answers that you have measured. Return the value of the last quantum mechanical superposition quantum computation more than once These are indeed consistent with the probability distribution of the superposition. A good quantum algorithm thus leads to a superposition in which the answer is hidden in the probability distribution. This might mean that a particular qubit in a third of cases the value 0 is measured and in two thirds of cases the value 1. The chance that you will find that indeed the correct answer, it is easy to increase by more often to perform. Quantum computation

“Once you are viewing a superposition, return them together”

Quantum Theorists have now developed clever algorithms, which only the correct calculations and unambiguous answers remain. In addition, they make use of, among other things interference. In this way needs to be set up to give the correct answer. To run only once a calculation

Quantum Calculation

Operations on qubits also run very different operations that we know from the deterministic world. Ordinary bits are always logically compared with each other: “If two bits are both set to 1 (AND), at least one of the bits set to 1 (OR), all bits = 0 (NOR)?” and so on. Such logical operations are carried out on electrical signals by transistors which have been laid down in silicon chips and in a specific pattern are connected with each other. For example, logic gates to combine records , units , state machines , and all other digital components which together form a processor, for example.

Calculations by a quantum computer are always performed within the same group of qubits. A superposition can not be copied or rather, is lost when copying the original. An operation thus changing the existing superposition. As for classical digital systems are also quantum computers based operations that all calculations can be performed.

Next page (Modelling and computability – 5/7)

Modelling and computability

Modeling

There are several ways to model. Quantum operations The analytical mathematical theory is based on the wave functions described above: linear combinations of basic values (notation: | 0> and | 1>), with complex coefficients , the amplitudes . Bloch sphere – Credits SmiteMeister and Wikipedia

The Bloch sphere is a geometric representation of a single qubit. At the top and bottom are the values or | 1> |. 0> and A superposition is a point somewhere on the surface of the sphere, wherein the height (the width circle) the ratio of the amplitudes and thus determine the chances of the two base values. That the per se superposition point somewhere on the surface of the sphere around the z-axis must be at a fixed distance from the origin, is the result of the boundary condition that the sum of the probabilities is always 1. Exist in this modeling (simple) quantum operations geometric rotations, displacements of the superposition point about boloppervak.

For techies, it is much more useful to talk in terms of the well-known ports and circuits. Operations on quantum Barenco developed symbols that can be used to capture in diagrams. Operations used Below is an example Controlled NOT’ gate ( CNOT ). The negation operation (| 0> | 1> and vice versa) on the bottom qubit is performed only when the top qubit value | 1> has.

CNOT – Image via Wikipedia While diligently searching for various physical, forms of implementation in order to effectively perform these quantum operations is to support the full range is not necessary. Just as you have enough in the traditional computer science, for example an AND gate and a NOT gate to build all the circuitry for a quantum computer, three gates sufficient.

Computability

Following the centenary of the birth of Alan Turing in mid-2012, we published an extensive story about Turing machines and the theory of computability and complexity of problems and algorithms. To talk, in a similar manner on the power of quantum computers, the physicist David Deutsch Quantum Turing Machine invented. In a similar fashion, there is defined a class of problems to solve those with a quantum computer in a reasonable amount of time on his. That is, in polynomial time in relation to the length of the input.

BQP Complexity — via Wikipedia The figure on the right shows how this class BQP , or Bounded Error Quantum Polynomial Time compares to the traditional complexity classes. At least, as far as we now think to know.

Although not yet proven, as indeed is true of most relationships between the various complexity classes, it seems that quantum computers can solve problems that indeed we can not cope with the current deterministic computers, class P problems. In fact, now there are already several known quantum algorithms for problems for which no one has yet imagined. Deterministic algorithm On the other hand, one has a quantum algorithm found by which also the most difficult problems in the NP Complete, class are soluble in a reasonable time. It is suspected at this time, therefore, that quantum computers are fundamentally more powerful than ordinary computers, but not so powerful that they solve the most difficult problems for us.

Shor’s algorithm

One of the most interesting quantum algorithms that we know today, the Shor algorithm based on quantum Fourier transforms . Thus the prime factors of an integer can be calculated. This factorization can be deployed to a large part of the asymmetric (public-key) cryptography we now use the Internet to crack. Most striking is the TLS / SSL security, which is used. At https and starttls However, the same is also true for ssh and all protocols that are tunneled through this encrypted connections and electronic signature.

As soon as the first truly usable quantum computer sees the light, all these protections in one fell swoop worthless. The current public-key technology is in fact based on the difficulty to decompose. The product of two large prime factors in its Although quantum computer that does not already exist, it is therefore crucial to all work on the mathematical theory for these machines now. For example, to find a new form of public-key cryptography, which is resistant to quantum squatters. Quantum-proof algorithms

Entanglement

Had you been baffled superpositions which is also a bit of one value and a little take the other value, then doing entanglement, entanglement , there even further. Once they are entangled, do not have to be to still continue to behave. Itself as a superposition close together qubits Changes on one qubit have direct consequences for the other qubit. In fact, a measurement to determine when a collapse faster than light, the value of the other, in contrast to the electromagnetic and gravitational fields in classical mechanics, expanding at the speed of light.

Next page (Quantum Security with a Dutch twist – 6/7)

Quantum Security with a Dutch twist

Quantum computers also create new secure communication methods. Quantum mechanical entanglement can be used for example to set up. Absolutely safe communication channels Information on the road can not be intercepted by a man-in-the-middle, without that this is seen at the ends of the connection.

“It Majoranadeeltje would be a suitable building block for the qubits can be”

For this purpose, first divided between the two sides, a series of pairs of entangled qubits quantum key distribution , in order to collapse to their final value. subsequently Both parties now have the same, or more accurately, the opposite key. They can do that by comparing the check. One part of the bits obtained in this way with each other Do these bits are indeed convergent, then the parties are sure that no one else has that key. A man-in-the-middle, the value of an entangled qubit route does not figure to collapse without it. In this way, the symmetric keys for distribution problem is solved. That’s what asymmetric cryptography is often used: the safe exchange of a symmetric session key.

Important caveat is that such quantum systems could be used to exchange keys, but not to interact. Faster than light Indeed, the collapse of two sides going faster than light, but because the actual outcome is determined by chance may include any information transmitted.

Scientific research

In recent years, built the first quantum networks scattered at universities and other research institutions that entangled communication channels and teleportation of quantum states are possible. So let researchers from Cambridge UK last year shows that it is possible to entangled photons through a regular fiber network spread .

In the Netherlands, a theoretical study of quantum algorithms and complexity performed by the CWI . There, a group led by running Harry Buhrman join the world in this field. Other important research groups are located in Zurich ( ETH ), Oxford and Cambridge in the UK, Cambridge in the U.S. ( MIT ), Berkeley , Waterloo (Canada), Singapore and Beijing .

Majoranadeeltjes

Also what the underlying hardware is concerned, the Netherlands is a major player. A year ago acquired the Delft research of Leo Kouwenhoven world fame with the discovery of the Majoranadeeltje . Except for the Standard Model particle that has particular value for developers of quantum systems. It would well be a suitable building block for the qubits can be.

Elsewhere in the world happening. Tweakers brings regular news on technical and scientific breakthroughs in this field. In these messages, we can read how scientists can become more and more stable qubits create, store and transport. In addition, the Canadian company seems D-Wave now indeed the first commercial quantum computer to offer.

Next page (The 1 bit quantum computer – 7/7) The 1bit quantum computer

Whoever wants to buy all his own, affordable quantum computer can turn to the Swiss company ID Quantique . That sells, among other things, a random-number generator in the form of a box with USB connection or a PCI (e) plug-in card. The only thing that their Quantis system does is always a qubit in superposition (1/2, 1/2) in order to bring to collapse into a 0 or a 1. Then In this way, at a rate of 4 Mbit / s and 16Mbit / s a random stream of ones and zeros is generated.

Make no mistake, this 1 bit quantum computer has a very important function. For traditional computers is deterministic and thus generate a true random series namely an almost impossible task. Thus RAND Corporation, a well-known American military research in the fifties a book published and republished in 2001 containing a million random numbers. It served for decades as a standard, especially in cryptography and statistics. Special hardware nowadays usually is used to generate, store and use of cryptographic key material for serious and large-scale applications, think of dnssec .

Wearables

How long it will be before usable kw antumcomputers actually available, we dare not say. Depending on scientific breakthroughs in this area that could be a few years or a few decades, but they are coming out for sure. This is a fundamentally different than computer technology available.

If the history of deterministic computer is a good predictor, then we are entering a new era of faster and smaller systems. Who knows makes a quantum computer in twenty years a standard part of our smartphone or other portable computer.

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