Tuesday, February 26, 2008

Quantum Computers

Quantum Computer:
It is any device for computation that makes direct use of distinctively quantum mechanical phenomena, such as superposition and entanglement, to perform operations on data. The word “quantum” came from the Latin word which means "how much". In quantum mechanics, it refers to a discrete unit that quantum theory assigns to certain physical quantities, such as the energy of an atom. Let's have some notes:
  1. Quantum entanglement is a quantum mechanical phenomenon in which the quantum states of two or more objects have to be described with reference to each other, even though the individual objects may be spatially separated.
  2. A quantum state is a mathematical object that fully describes a quantum system. Quantum states can be statistically mixed, corresponding to an experiment involving a random change of the parameters. When performing a certain measurement on a quantum state, the result is in general described by a probability distribution.
  3. Quantum superposition is the fundamental law of quantum kinematics. It defines the allowed state space of a quantum mechanical system. For example, if a particle can be in position A and position B, it can also be in a state where it is an amount "3i/5" in position A and an amount "4/5" in position B. To write this, people usually say:
    W) = 3/5 i A) + 4/5 B)
  4. Bits vs. QuBits: Consider first a classical computer that operates on a 3-bit register. At any given time, the bits in the register are in a definite state, such as 101. In a quantum computer, however, the qubits can be in a superposition of all the classically allowed states. In fact, the register is described by a wave function:
    W) = a 000) + b 001) + .........+ h 111)
    Where the coefficients a, b, c... h are complex numbers whose amplitudes squared are the probabilities to measure the qubits in each state. For example, is the probability to measure the register in the state 010.

Power of Quantum Computers

Quantum Computers can solve any problem of these four properties:

1. The only way to solve it is to guess answers repeatedly and check them,

2. There are n possible answers to check,

3. Every possible answer takes the same amount of time to check, and

4. There are no clues about which answers might be better: generating possibilities randomly is just as good as checking them in some special order.

As an example, Integer Factorization is believed to be computationally infeasible with an ordinary computer for large integers that are the product of only a few prime numbers. A quantum computer could solve this problem more efficiently than a classical computer using Shor's algorithm to find its factors. So a lot of military agents provide massive funds for the experiments on that field of science.

For now, it is still a field of research and we don’t yet have a really effective & practical model of a quantum computer.


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