Quantum Computing: the final presentation

1. Quantum Computing:the final presentation Presented by: The guy with the beard, (Lee Ballard) The guy without the beard, (Hey, I do have a beard.) And (Sort of.) The girl who doesn’t present. (Amanda Denton)

2. Logic Gates Basic Logic Gates Not And Or NAnd NOr XOr

3. Quantum Logic Gates Quantum gates are very similar to classical logic gates. Quantum gates must be reversible due to the nature of quantum computing. Most classical logic gates are not reversible. Only the “Not” gate can return to the original input.

4. Other gates are not reversible The “And” Gate: If output = 1: input = 1 and 1 If output = 0: input could be 1 and 0 0 and 1 0 and 0 We don’t know what the input was, therefore it isn’t reversible

5. Creating a reversible gate: The value of x = the value of a If a = 0, then the value of y = the value of b If a = 1, the the value of y = the value of NOTb

6. The Toffoli Gate: x = a b = y If a = 1 and b = 1, then z = NOTc Else, z = c

7. Applying logic gates to QC • As shown in an article on the Nature web site, scientists have performed a simple NOT operation using photons as qubits rather than the charge on electrons. This is of interest here because of our use of reversible logic. http://www.nature.com/nsu/021021/021021-4.html

8. Building a quantum adder • To construct a quantum adder, we use our two reversible gates (CNOT and the Toffoli gate) to add up a couple of bits into a total. • In the examples given by Glassner, three separate 1-bit registers are added into two 1-bit register, so the 3 inputs can be 0 or 1 and the output can be from 0 to 3 (0 to 11)

9. Quantum adder • In Glassner’s five register example, the logic is fairly simple – two Toffoli gates and a CNOT gate affect the second register or “10’s” place, and the next three CNOT gates set the 1’s place.

10. Quantum adder

11. The Quantum Adder