QUANTUM COMPUTING

A quantum computer is a computer design which uses the principles of quantum physics to increase the computational power beyond what is attainable by a traditional computer. Quantum computers have been built on the small scale and work continues to upgrade them to more practical models.

Entanglement

Entanglement is a term used in quantum theory to describe the way that particles of energy/matter can become correlated to predictably interact with each other regardless of how far apart they are.

Particles, such as photons, electrons, or qubits that have interacted with each other retain a type of connection and can be entangled with each other in pairs, in the process known as correlation. Knowing the spin state of one entangled particle - whether the direction of the spin is up or down - allows one to know that the spin of its mate is in the opposite direction. Even more amazing is the knowledge that, due to the phenomenon of superposition, the measured particle has no single spin direction before being measured, but is simultaneously in both a spin-up and spin-down state. The spin state of the particle being measured is decided at the time of measurement and communicated to the correlated particle, which simultaneously assumes the opposite spin direction to that of the measured particle. Quantum entanglement allows qubits that are separated by incredible distances to interact with each other immediately, in a communication that is not limited to the speed of light. No matter how great the distance between the correlated particles, they will remain entangled as long as they are isolated.
Entanglement is a real phenomenon (Einstein called it "spooky action at a distance"), which has been demonstrated repeatedly through experimentation. The mechanism behind it cannot, as yet, be fully explained by any theory. One proposed theory suggests that all particles on earth were once compacted tightly together and, as a consequence, maintain a connectedness. Much current research is focusing on how to harness the potential of entanglement in developing systems for quantum cryptography and quantum computing.

Operations on pure qubit states
There are various kinds of physical operations that can be performed on pure qubit states

1.            A quantum logic gate can operate on a qubit: mathematically speaking, the qubit undergoes a unitary transformation. Unitary transformations correspond to rotations of the qubit vector in the Bloch sphere.

2.            Standard basis measurement is an operation in which information is gained about the state of the qubit. The result of the measurement will be either ,with probability , or , with probability . Measurement of the state of the qubit alters the values of α and β. For instance, if the result of the measurement is , α is changed to 1 (up to phase) and β is changed to 0. Note that a measurement of a qubit state entangled with another quantum system transforms a pure state into a mixed state.

Quantum Gate

Quantum computing and specifically the quantum circuit model of computation, a quantum gate (or quantum logic gate) is a basic quantum circuit operating on a small number of qubits. They are the building blocks of quantum circuits, like classical logic gates are for conventional digital circuits.

Shor's algorithm

Named after mathematician Peter Shor, is a quantum algorithm (an algorithm that runs on a quantum computer) for integer factorization formulated in 1994. Informally it solves the following problem: Given an integer N, find its prime factors.
On a quantum computer, to factor an integer N, Shor's algorithm runs in polynomial time (the time taken is polynomial in log N, which is the size of the input). Specifically it takes time O((log N)3), demonstrating that the integer factorization problem can be efficiently solved on a quantum computer and is thus in the complexity class BQP. This is substantially faster than the most efficient known classical factoring algorithm, the general number field sieve, which works in sub-exponential time — aboutO(e1.9 (log N)1/3 (log log N)2/3). The efficiency of Shor's algorithm is due to the efficiency of the quantum Fourier transform, and modular exponentiation by repeated squaring