Quantum
computing is the area of study focused on developing computer technology based
on the principles of quantum theory, which explains the nature and behavior of
energy and matter on the quantum (atomic and subatomic) level. Development of a
quantum computer, if practical, would mark a leap forward in computing
capability far greater than that from the abacus to a modern day supercomputer,
with performance gains in the billion-fold realm and beyond. The quantum
computer, following the laws of quantum physics, would gain enormous processing
power through the ability to be in multiple states, and to perform tasks using
all possible permutations simultaneously. Current centers of research in
quantum computing include MIT, IBM, Oxford University, and the Los Alamos
National Laboratory.
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. This leads to
correlations between observable physical properties of the systems. For
example, it is possible to prepare two particles in a single quantum state such
that when one is observed to be spin-up, the other one will always be observed
to be spin-down and vice versa, this despite the fact that it is impossible to
predict, according to quantum mechanics, which set of measurements will be
observed. As a result, measurements performed on one system seem to be
instantaneously influencing other systems entangled with it. But quantum
entanglement does not enable the transmission of classical information faster
than the speed of light. Quantum entanglement has applications in the emerging
technologies of quantum computing and quantum cryptography, and has been used
to realize quantum teleportation experimentally.
A qubit is
a quantum bit , the counterpart in quantum computing to the binary digit or bit
of classical computing. Just as a bit is the basic unit of information in a
classical computer, a qubit is the basic unit of information in a quantum
computer .In a quantum computer, a number of elemental particles such as
electrons or photons can be used (in practice, success has also been achieved
with ions), with either their charge or polarization acting as a representation
of 0 and/or 1. Each of these particles is known as a qubit; the nature and
behavior of these particles (as expressed in quantum theory ) form the basis of
quantum computing. The two most relevant aspects of quantum physics are the
principles of superposition and entanglement .
A quantum
gate or quantum logic gate is a rudimentary quantum circuit operating on a
small number of qubits. They are the analogues for quantum computers to
classical logic gates for conventional digital computers. Quantum logic gates
are reversible, unlike many classical logic gates. Some universal classical
logic gates, such as the Toffoli gate, provide reversibility and can be
directly mapped onto quantum logic gates. Quantum logic gates are represented
by unitary matrices. The most common quantum gates operate on spaces of one or
two qubits. This means that as matrices, quantum gates can be described by 2 x
2 or 4 x 4 matrices with orthonormal rows.
Shor's
algorithm is a quantum algorithm for factoring a number N in O((log N)3) time
and O(log N) space, named after Peter Shor. The algorithm is significant
because it implies that RSA, a popular public-key cryptography method, might be
easily broken, given a sufficiently large quantum computer. RSA uses a public
key N which is the product of two large prime numbers, One way to crack RSA
encryption is by factoring N, but with classical algorithms, factoring becomes
increasingly time-consuming as N grows large; more specifically. no classical
algorithm is known that can factor in polynomial time. But Shor's algorithm can
crack RSA in polynomial time. Like many
quantum computer algorithms, Shor's algorithm is probabilistic and It gives the
correct answer with high probability, and the probability of failure can be
decreased by repeating the algorithm. Shor's algorithm was discovered in 1994
by Peter Shor, but the classical part was known before. it is credited to G. L.
Miller. Seven years later, in 2001. it was demonstrated by a group at IBM,
which factored 15 into 3 and 5, using a quantum computer with 7 qubits.
