Quantum ComputingBy Joseph Szatkowski and Cody

Borgschulte

What is a Quantum Computer?● Uses phenomenon associated with quantum

mechanics instead of electrical circuitry● Quantum mechanics explains how particles

interact on an individual level.● Superposition● Entanglement

Qubits● Uses qubits instead of bits● Unlike bits, qubits can be on, off, or a

superposition of both.● 2 qubits can hold 00, 01, 10, 11, or any

superposition of these values.● This allows a quantum computer to perform

multiple calculations simultaneously.

Physical representation● A qubit can be represented by a single

electron.● Electrons have a property called spin, which

determines how they act in a magnetic field.● Up spin and down spin representing 1 and 0

Superposition●Quantum particles have the ability to exist partially in different states.●When measured the superposition collapses into a single state.●A superposition can be represented by a complex number, with coefficients representing how much of each state there is.

Entanglement● Entanglement allows two particle to interact

directly with each other, allowing operations to be performed.

● Necessary because particles cannot be observed during calculations as this would collapse the superposition.

History● First theorized by Paul Benioff in 1981● In 1998 the scientists at Los Alamos created an extremely

simple prototype using 1 qubit.● In 2000 a 7 qubit computer was created.● This computer was programmed using radio frequency

pulses.● In 2001 Shor's algorithm was successfully demonstrated.● In 2007 D-Wave used a 16 qubit computer to solve a

Sudoku puzzle.

Limitations● To create a quantum computer you must be able to

control and measure particles.● Lasers, superconductors, etc.● Super expensive● It is unlikely quantum computers will be publicly

available any time soon.● Cannot measure while calculating.● Individual operations are slower.

Applications● Quantum computer can perform algorithms which

transistor computers can't.● Shor's algorithm can be used to factor large

numbers in polynomial time (O((log N)^3)).● Can be used to break RSA codes● Can simulate quantum mechanics.● Study cures, analyze large networks, solve other

“unsolvable” problems.

More Applications! NAS Ames Research Center Exascale Computing (10^18 floating

point operations per second) Grover’s algorithm (N^(1/2))

Questions?