COMP SCI 4413, 4813, 7413 Introduction to Quantum Computing
Assignment 2
Author: Yasir Latif
Submit on MyUni before 11:59pm 11-Sept-2019
Instructions
• 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.
Submission Instructions
The submission will consists of code (assignment2.zip) and a report (assignment2.pdf)
via MyUni. Each question contains a section that needs to be addressed in the report (marked R)
and in the code submission (marked C). You will be evaluated on both the code as well as the
report.
Question 1 Quantum Simulator 10 marks
In the programming language of your choice, design a quantum simulator. The simulator will take
as input a file containing information about the number of qubit, the circuit, and inputs and will
generate another file with the intermediate states as output. The input file will be formatted as
follow:
• N: The first line will contain the number of qubit that we want to simulate, followed by N
lines, all of the same length, describing each wire in the circuit.
• Each wire in the circuit will consists of one of either of the these gates X,Y,Z,H or special
symbols: o describing “control” for a controlled gate and “-” corresponds to no-operation.
Control acts on all the gates that are in the same column as the control symbol.
• M: The number of inputs to the simulator, followed by M lines, each containing N characters
representing inputs. Inputs will be combination one of |0i,|1i,|+i,|−i
Sample Input file:
which is a circuit on N = 2 qubits (the first line). The first wire (least significant) consists of -Xand the second -o-. Thus implementing a controlled-NOT gate where the second bit is the control
bit. The next line contains the number of inputs (M = 5) followed by M N-bit strings representing
the inputs that we want to run through the circuit.
The output file generated will contain:
• For each input, the quantum state of size 2
N after each step (one per line) in the circuit
for which a valid operation has been applied to either of the qubits. We ignore the step on
which all lines have a no-op (“-”). An empty line indicates that the current input has been
completely processed.
Sample output file:
[1 0 0 0]
[0 1 0 0]
[0 0 0 1]
[0 0 1 0]
[0.5 0.5 0.5 0.5]
The output will contain M × (S + 1) , where S is the number of valid steps in the circuit and there
is a blank line to indicate the end of current output.
• R Give details about your implementation and the assumptions that have been made while
implementing the simulator. Also highlight any limitations that you think the simulator has.
• C: Submit the code for the simulator, with the main file titled main.cpp (if for example
your code is in C++). The executable should be able to take the input file as a command line
argument and generate a file named out.txt containing the output.
Question 2 Creating EPR Pairs - 5 Marks
Design a circuit to create an entangled EPR pair. This circuit takes as input |00i and produces
(|00i + |11i).
• R: Comment on what happens if the input is something different from |00i. Are the states
still entangled by this circuit?
• C: Submit the input file (question2.txt) for this circuit along with your code.
Question 3 Dense Coding - 5 Marks
Using your simulator, implement a circuits to perform dense coding described in Section. 5.3.1
of [RP]. The circuit takes |00i as input, creates an entangled pair (Question 1) and then perform
encoding. The second part of the circuit decodes the incoming bits to extract two classical bits.
• R: Discuss how critical is the choice of input to this circuit. Does the scheme fail is input
changes to let’s say |11i?
• C: Submit the circuit input file (question3.txt) simulates Alice’s encoding of the 10
state and the decoded result by Bob.
Question 4 Cat state - 5 Marks
An n-qubit cat state is the state √
12(|00 . . . 0i + |11 . . . 1i). Design a circuit that, upon input of
|00 . . . 0i, constructs a cat state.
• R: Describe the circuit components needed to extend a n-qubit cat state to an n+1-qubit cat
state.
• C: Submit the input file (question4.txt) for the circuit.
Question 5 Permutation - 5 Marks
Design a circuit that permutes the values of three qubits in that it sends |φi |ψi |ηi to |ψi |ηi |φi for
all single qubit states |φi, |ψi, and |ηi in the standard basis.
• R: Discuss how this circuit can be reused to implement a circuit that sends |φi |ψi |ηi to
|ηi |φi |ψi.
• C: Submit the input file (question5.txt) for the original circuit, showing all the possible
combination of the standard basis states as inputs.
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