01-08-2012, 01:40 PM
QUANTUM COMPUTERS
QUANTUM COMPUTERS.docx (Size: 477.26 KB / Downloads: 50)
ABSTRACT
In a quantum computer any superposition of inputs evolves unitarily into the corresponding superposition of outputs. It has been recently demonstrated that such computers can dramatically speed up the task of finding factors of large numbers -- a problem of great practical significance because of its cryptographic applications. Instead of the nearly exponential ($\sim \exp L^{1/3}$, for a number with $L$ digits) time required by the fastest classical algorithm, the quantum algorithm gives factors in a time polynomial in $L$ ($\sim L^2$). This enormous speed-up is possible in principle because quantum computation can simultaneously follow all of the paths corresponding to the distinct classical inputs, obtaining the solution as a result of coherent quantum interference between the alternatives. Hence, a quantum computer is sophisticated interference device, and it is essential for its quantum state to remain coherent in the course of the operation. In this report we investigate the effect of decoherence on the quantum factorization algorithm and establish an upper bound on a ``quantum factorizable'' $L$ based on the decoherence suffered per operational step.
Introduction to Quantum Computers
Around 2030 computers might not have any transistors and chips. Think of a computer that is much faster than a common classical silicon computer. This might be a quantum computer. Theoretically it can run without energy consumption and billion times faster than today’s PIII computers. Scientists already think about a quantum computer, as a next generation of classical computers.
Gershenfeld says that if making transistors smaller and smaller is continued with the same rate as in the past years, then by the year of 2020, the width of a wire in a computer chip will be no more than a size of a single atom. These are sizes for which rules of classical physics no longer apply. Computers designed on today's chip technology will not continue to get cheaper and better. Because of its great power, quantum computer is an attractive next step in computer technology. (Manay, 1998, p. 5).
A technology of quantum computers is also very different. For operation, quantum computer uses quantum bits (qubits). Qubit has a quaternary nature. Quantum mechanic’s laws are completely different from the laws of a classical physics. A qubit can exist not only in the states corresponding to the logical values 0 or 1 as in the case of a classical bit, but also in a superposition state.
History of Quantum Computers
In 1982 R.Feynman presented an interesting idea how the quantum system can be used for computation reasons. He also gave an explanation how effects of quantum physics could be simulated by such quantum computer. This was very interesting idea which can be used for future research of quantum effects. Every experiment investigating the effects and laws of quantum physics is complicated and expensive. Quantum computer would be a system performing such experiments permanently. Later in 1985, it was proved that a quantum computer would be much more powerful than a classical one. (West, 2000, p. 3)
The Major Difference between Quantum and Classical Computers
The memory of a classical computer is a string of 0s and 1s, and it can perform calculations on only one set of numbers simultaneously. The memory of a quantum computer is a quantum state that can be a superposition of different numbers. A quantum computer can do an arbitrary reversible classical computation on all the numbers simultaneously. Performing a computation on many different numbers at the same time and then interfering all the results to get a single answer, makes a quantum computer much powerful than a classical one. (West, 2000)
The Potential and Power of Quantum Computing
Quantum computer with 500 qubits gives 2500 superposition states. Each state would be classically equivalent to a single list of 500 1's and 0's. Such computer could operate on 2500 states simultaneously. Eventually, observing the system would cause it to collapse into a single quantum state corresponding to a single answer, a single list of 500 1's and 0's, as dictated by the measurement axiom of quantum mechanics. This kind of computer is equivalent to a classical computer with approximately 10150 processors. (West, 2000, p. 3)
Conclusion
It is important that making a practical quantum computing is still far in the future. Programming style for a quantum computer will also be quite different. Development of quantum computer needs a lot of money. Even the best scientists can’t answer a lot of questions about quantum physics. Quantum computer is based on theoretical physics and some experiments are already made. Building a practical quantum
computer is just a matter of time. Quantum computers easily solve applications that can’t be done with help of today’s computers. This will be one of the biggest steps in science and will undoubtedly revolutionize the practical computing world.
QUANTUM COMPUTERS.docx (Size: 477.26 KB / Downloads: 50)
ABSTRACT
In a quantum computer any superposition of inputs evolves unitarily into the corresponding superposition of outputs. It has been recently demonstrated that such computers can dramatically speed up the task of finding factors of large numbers -- a problem of great practical significance because of its cryptographic applications. Instead of the nearly exponential ($\sim \exp L^{1/3}$, for a number with $L$ digits) time required by the fastest classical algorithm, the quantum algorithm gives factors in a time polynomial in $L$ ($\sim L^2$). This enormous speed-up is possible in principle because quantum computation can simultaneously follow all of the paths corresponding to the distinct classical inputs, obtaining the solution as a result of coherent quantum interference between the alternatives. Hence, a quantum computer is sophisticated interference device, and it is essential for its quantum state to remain coherent in the course of the operation. In this report we investigate the effect of decoherence on the quantum factorization algorithm and establish an upper bound on a ``quantum factorizable'' $L$ based on the decoherence suffered per operational step.
Introduction to Quantum Computers
Around 2030 computers might not have any transistors and chips. Think of a computer that is much faster than a common classical silicon computer. This might be a quantum computer. Theoretically it can run without energy consumption and billion times faster than today’s PIII computers. Scientists already think about a quantum computer, as a next generation of classical computers.
Gershenfeld says that if making transistors smaller and smaller is continued with the same rate as in the past years, then by the year of 2020, the width of a wire in a computer chip will be no more than a size of a single atom. These are sizes for which rules of classical physics no longer apply. Computers designed on today's chip technology will not continue to get cheaper and better. Because of its great power, quantum computer is an attractive next step in computer technology. (Manay, 1998, p. 5).
A technology of quantum computers is also very different. For operation, quantum computer uses quantum bits (qubits). Qubit has a quaternary nature. Quantum mechanic’s laws are completely different from the laws of a classical physics. A qubit can exist not only in the states corresponding to the logical values 0 or 1 as in the case of a classical bit, but also in a superposition state.
History of Quantum Computers
In 1982 R.Feynman presented an interesting idea how the quantum system can be used for computation reasons. He also gave an explanation how effects of quantum physics could be simulated by such quantum computer. This was very interesting idea which can be used for future research of quantum effects. Every experiment investigating the effects and laws of quantum physics is complicated and expensive. Quantum computer would be a system performing such experiments permanently. Later in 1985, it was proved that a quantum computer would be much more powerful than a classical one. (West, 2000, p. 3)
The Major Difference between Quantum and Classical Computers
The memory of a classical computer is a string of 0s and 1s, and it can perform calculations on only one set of numbers simultaneously. The memory of a quantum computer is a quantum state that can be a superposition of different numbers. A quantum computer can do an arbitrary reversible classical computation on all the numbers simultaneously. Performing a computation on many different numbers at the same time and then interfering all the results to get a single answer, makes a quantum computer much powerful than a classical one. (West, 2000)
The Potential and Power of Quantum Computing
Quantum computer with 500 qubits gives 2500 superposition states. Each state would be classically equivalent to a single list of 500 1's and 0's. Such computer could operate on 2500 states simultaneously. Eventually, observing the system would cause it to collapse into a single quantum state corresponding to a single answer, a single list of 500 1's and 0's, as dictated by the measurement axiom of quantum mechanics. This kind of computer is equivalent to a classical computer with approximately 10150 processors. (West, 2000, p. 3)
Conclusion
It is important that making a practical quantum computing is still far in the future. Programming style for a quantum computer will also be quite different. Development of quantum computer needs a lot of money. Even the best scientists can’t answer a lot of questions about quantum physics. Quantum computer is based on theoretical physics and some experiments are already made. Building a practical quantum
computer is just a matter of time. Quantum computers easily solve applications that can’t be done with help of today’s computers. This will be one of the biggest steps in science and will undoubtedly revolutionize the practical computing world.