quantum computing full report

[seminar class]

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