Quantum Computing

By 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?