### CSCI 4612/6612: Quantum Computation

Contact: E. Rodney Canfield, **erc at cs dot uga dot edu**

**Pre-req:** at least one of CSCI 2670, or a 3000-level MATH class,
or a 3000-level PHYS class. You may contact Dr. Canfield if you feel that
you are prepared to take this class despite lacking the prerequisite.

### Background:

In recent years, computer scientists and physicists have begun to discuss the possibility of a

computer whose hardware utilizes quantum phenomena. There has developed a notion of a quantum

algorithm, and examples are known of computational problems whose solution can be carried out

in significantly less time by a quantum algorithm than by the currently best known traditional

algorithm. In this course, students learn what constitutes a quantum algorithm. We proceed

from single qubits, to multiple-qubit registers, and finally to higher level constructions such

as the Quantum Fourier transform. The lecture part of the course culminates in the complete

description and analysis of Schor's factoring algorithm. During the latter part of the class,

each student makes an individual presentation.

Standard topics:

1. Remarks about quantum mechanics.

2. The qubit.

3. The Complex Numbers.

4. Quantum Not.

5. Other single qubit operations.

6. The Controlled Not Operation.

7. The Hypercube.

9. Circuit Diagrams.

10. The Quantum Fourier transform

11. The Toffoli Gate.

12. The Unitary Operator $U_f$.

Sample presentation topics:

1. Grover's Algorithm

2. Intro to Quantumn Mechanics

3. Quantumn teleportation

4. The EPR Paradox and Bell's inequality

5. Quantumn decoherence (2)

6. Entanglement and separability

7. Quantumn encryption

8. Current working implementations

9. Quantumn computation and complexity classes BQP, NP, PSPACE

10. Physical implementation of qubits

###