COMP SCI 4413, 4813, 7413 Introduction to Quantum Computing

Assignment 3

Author: Michele Sasdelli

Submit on MyUni before 11:59pm Tue 8 Oct

Intructions

• Answer all questions. Remember to show your workings in your solutions.

• If necessary, refer to Rieffel and Polak [RP] to help you with the questions.

Question 1 - 5 marks

Construct a reversible operator that implements the unary gate 0-operator (an operator that acts on

one bit and returns 0 independently of the input.). How many bits are necessary?

Question 2 - 5 marks

Show that it is impossible to implement a reversible OR operator with less than three bits.

Question 3 - 5 marks

Implement a reversible OR operator with a Fredkin gate (controlled swap).

Question 4 - 5 marks

Show that there is no reversible quantum operation f that transforms any input state |xi in a state

orthogonal to it (i.e. hf(x)i x = 0 for any |xi).

Question 5 - 3 marks

Write explicitly the (8x8) matrix form of the Toffoli gate and of the Fredkin gate (Control-swap).

Question 6 - 7 marks

Build a circuit that implements the Fredkin gate using one Toffoli gate and some other one or two

bits gates. If you want, write a small code to check the result.

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