16-03-2011, 02:09 PM
presented by:
Joseph Stelmach
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Quantum Computing
What is a quantum computer?
A quantum computer is a machine that performs calculations based on the laws of quantum mechanics, which is the behavior of particles at the sub-atomic level.
“I think I can safely say that nobody understands quantum mechanics” - Feynman
1982 - Feynman proposed the idea of creating machines based on the laws of quantum mechanics instead of the laws of classical physics.
1985 - David Deutsch developed the quantum turing machine, showing that quantum circuits are universal.
1994 - Peter Shor came up with a quantum algorithm to factor very large numbers in polynomial time.
1997 - Lov Grover develops a quantum search algorithm with O(√N) complexity
Representation of Data - Qubits
A bit of data is represented by a single atom that is in one of two states denoted by |0> and |1>. A single bit of this form is known as a qubit
A physical implementation of a qubit could use the two energy levels of an atom. An excited state representing |1> and a ground state representing |0>.
Data Retrieval
In general, an n qubit register can represent the numbers 0 through 2^n-1 simultaneously.
Sound too good to be true?…It is!
If we attempt to retrieve the values represented within a superposition, the superposition randomly collapses to represent just one of the original values.
Relationships among data – Entanglement
Entanglement is the ability of quantum systems to exhibit correlations between states within a superposition.
Imagine two qubits, each in the state |0> + |1> (a superposition of the 0 and 1.) We can entangle the two qubits such that the measurement of one qubit is always correlated to the measurement of the other qubit.
Quantum Gates
Quantum Gates are similar to classical gates, but do not have a degenerate output. i.e. their original input state can be derived from their output state, uniquely. They must be reversible.
This means that a deterministic computation can be performed on a quantum computer only if it is reversible. Luckily, it has been shown that any deterministic computation can be made reversible.(Charles Bennet, 1973)
Quantum Gates – Hadamard
Simplest gate involves one qubit and is called a Hadamard Gate (also known as a square-root of NOT gate.) Used to put qubits into superposition