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Ø Introduction
Every so often a new technology surfaces that enables the bounds of computer performance to be pushed further forward. From the introduction of valve technology through to the continuing development of VLSI designs, the pace of technological advancement has remained relentless. Lately, the key to improving computer performance has been the reduction of size in the transistors used in modern processors. This continual reduction however, cannot continue for much longer. If the transistors become much smaller, the strange effects of quantum mechanics will begin to hinder their performance. It would therefore seem that these effects present a fundamental limit to our computer technology, or do they?
In 1982, the Nobel prize-winning physicist (Late) Richard Feynman thought up the idea of a 'quantum computer', a computer that uses the effects of quantum mechanics to its advantage.
In the classical model of a computer, the most fundamental building block, the bit, can only exist in one of two distinct states, a 0 or a 1. In a quantum computer the rules are changed. Not only can a 'quantum bit', usually referred to as a 'qubit', exist in the classical 0 and 1 states, it can also be in a coherent superposition of both. When a qubit is in this state it can be thought of as existing in two universes, as a 0 in one universe and as a 1 in the other. An operation on such a qubit effectively acts on both values at the same time. The significant point being that by performing the single operation on the qubit, we have performed the operation on two different values. Likewise, a two-qubit system would perform the operation on 4 values, and a three-qubit system on eight. Increasing the number of qubits therefore exponentially increases the 'quantum parallelism' we can obtain with the system. With the correct type of algorithm it is possible to use this parallelism to solve certain problems in a fraction of the time taken by a classical computer.
The very thing that makes quantum computing so powerful, its reliance on the bizarre subatomic goings-on governed by the rules of quantum mechanics, also makes it very fragile and difficult to control. For example, consider a qubit that is in the coherent state. As soon as it measurable interacts with the environment it will decohere and fall into one of the two classical states. This is the problem of decoherence and is a stumbling block for quantum computers as the potential power of quantum computers depends on the quantum parallelism brought about by the coherent state. This problem is compounded by the fact that even looking at a qubit can cause it to decohere, making the process of obtaining a solution from a quantum computer just as difficult as performing the calculation itself.
A quantum computer is nothing like a classical computer in design; you can't for instance build one from transistors and diodes. In order to build one, a new type of technology is needed, a technology that enables 'qubits' to exist as coherent superpositions of 0 and 1 states. The best method of achieving this goal is still unknown, but many methods are being experimented with and are proving to have varying degrees of success.
An example of an implementation of the qubit is the 'quantum dot' which is basically a single electron trapped inside a cage of atoms. When the dot is exposed to a pulse of laser light of precisely the right wavelength and duration, the electron is raised to an excited state: a second burst of laser light causes the electron to fall back to its ground state. The ground and excited states of the electron can be thought of as the 0 and 1 states of the qubit and the application of the laser light can be regarded as a controlled NOT function as it knocks the qubit from 0 to 1 or from ' to 0.
If the pulse of laser light is only half the duration of that required for the NOT function, the electron is placed in a superposition of both ground and excited states simultaneously, this being the equivalent of the coherent state of the qubit. More complex logic functions can be modelled using quantum dots arranged in pairs. It would therefore seem that quantum dots are a suitable candidate for building a quantum computer.
Unfortunately there are a number of practical problems that are preventing this from happening:
The electron only remains in its excited state for about a microsecond before it falls to the ground state. Bearing in mind that the required duration of each laser pulse is around 1 nanosecond, there is a limit to the number of computational steps that can be made before information is lost.
Constructing quantum dots is a very difficult process because they are so small. A typical quantum dot measures just 10 atoms (1 nanometer) across. The technology needed to build a computer from these dots doesn't yet exist.
To avoid cramming thousands of lasers into a tiny space, quantum dots could be manufactured so that they respond to different frequencies of light. A laser that could reliably retune itself would thus selectively target different groups of quantum dots with different frequencies of light. This again, is another technology that doesn't yet exist.
This latest development in quantum computing takes a radical new approach. It drops the assumption that the quantum medium has to be tiny and isolated from its surroundings and instead uses a sea of molecules to store the information. When held in a magnetic field, each nucleus within a molecule spins in a certain direction, which can be used to describe its state; spinning upwards can signify a 1 and spinning down, a 0. Nuclear Magnetic Resonance (NMR) techniques can be used to detect these spin states and bursts of specific radio waves can flip the nuclei from spinning up (1) to spinning down (0) and vice-versa.
The quantum computer in this technique is the molecule itself and its qubits are the nuclei within the molecule. This technique does not however use a single molecule to perform the computations; it instead uses a whole 'mug' of liquid molecules. The advantage of this is that even though the molecules of the liquid bump into one another, the spin states of the nuclei within each molecule remain unchanged. Decoherence is still a problem, but the time before the decoherence sets in is much longer than in any other technique so far. Researchers believe a few thousand primitive logic operations should be possible within time it takes the qubits to decohere.
Some potential Applications of quantum computers
The theories of quantum computation have some interesting implications in the world of artificial intelligence. The debate about whether a computer will ever be able to be truly artificially intelligent has been going on for years and has been largely based on philosophical arguments.
To implement AI (Artificial Intelligence) through quantum computing, one has to consider the Church-Turing principle.
The Church-Turing principle - "There exists or can be built a universal computer that can be programmed to perform any computational task that can be performed by any physical object".
The thing to note is that every physical object, from a rock to the universe as a whole, can be regarded as a quantum computer and that any detectable physical process can be considered a computation. Under these criteria, the brain can be regarded as a computer and consciousness as a computation. The next stage of the argument is based in the Church-Turing principle and states that since every computer is functionally equivalent and that any given computer can simulate any other, therefore, it must be possible to simulate conscious rational thought using a quantum computer.
Exponential rate of processing
In order for a quantum computer to show its superiority over conventional computers, it needs to use algorithms that exploit its power of quantum parallelism (Coherence). Such algorithms are difficult to formulate, to date the most significant theorised being Shor's algorithm and Grover's algorithm. By using good these algorithms a quantum computer will be able to outperform classical computers by a significant margin.
Shor's algorithm
This algorithm, invented by Peter Shor in 1995, allows extremely quick factoring of large numbers, a classical computer can be estimated at taking 10 million billion billion years to factor a 1000 digit number, where as a quantum computer would take around 20 minutes. If it is ever implemented it will have a profound effect on cryptography, as it would compromise the security provided by public key encryption (such as RSA).
Grover's algorithm
Lov Grover has written an algorithm that uses quantum computers to search an unsorted database faster than a conventional computer. Normally it would take N/2 number of searches to find a specific entry in a database with N entries. Grover's algorithm makes it possible to perform the same search in root N searches. The speed up that this algorithm provides is a result of quantum parallelism. The database is effectively distributed over a multitude of universes, allowing a single search to locate the required entry. A further number of operations (proportional to root N) are required in order to produce a readable result.
Grover's algorithm has a useful application in the field of cryptography. It is theoretically possibly to use this algorithm to crack the Data Encryption Standard (DES), a standard which is used to protect, amongst other things, financial transactions between banks. The standard relies on a 56-bit number that both participants must know in advance, the number is used as a key to encrypt/decrypt data.
If an encrypted document and its source can be obtained, it is possible to attempt to find the 56-bit key. An exhaustive search by conventional means would make it necessary to search 2 to the power 55 keys before hitting the correct one. This would take more than a year even if one billion keys were tried every second, by comparison, Grover's algorithm could find the key after only 185 searches. For conventional DES, a method to stop modern computers from cracking the code (i.e. if they got faster) would be simply to add extra digits to the key, which would increase the number of searches needed exponentially. However, the effect that this would have on the speed of the quantum algorithm is negligible.
Quantum Communications
Quantum communications makes use of the fact that information can be encoded as the polarisation of photons (i.e. the orientation of a photon's oscillation). An oscillation in one direction can be thought of as 0 and in another as a 1. Two sets of polarisations are commonly used, rectilinear and diagonal.
The property that quantum communication exploits is that in order to receive the correct information, photons have to be measured using the correct filter polarisation e.g. the same polarisation that the information was transmitted with. If a receiver is in rectilinear polarisation, and a diagonally polarised photon is sent, then a completely random result will appear at the receiver. Using this, property information can be sent in such a way as to make it impossible for an eavesdropper to listen undetected.
Conclusion
With classical computers gradually approaching their limit, the quantum computer promises to deliver a new level of computational power. With them comes a whole new theory of computation that incorporates the strange effects of quantum mechanics and considers every physical object to be some kind of quantum computer. A quantum computer thus has the theoretical capability of simulating any finite physical system and may even hold the key to creating an artificially intelligent computer.
The quantum computers power to perform calculations across a multitude of parallel universes gives it the ability to quickly perform tasks that classical computers will never be able to practically achieve. This power can only be unleashed with the correct type of algorithm, a type of algorithm that is extremely difficult to formulate. Some algorithms have already been invented; they are proving to have huge implications on the world of cryptography. This is because they enable the most commonly used cryptography techniques to be broken in a matter of seconds. Ironically, a spin off of quantum computing, quantum communication allows information to be sent without eavesdroppers listening undetected.
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