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