This repository contains my submissions for 2 assignments in the Introduction to Quantum Computing subject at the University of Technology Sydney (UTS) taught by Dr. Christopher Ferrie and Dr. Christina Giarmatzi.
Each assignment is done using IBM Qiskit along with a Google Colab notebook, which includes a detailed implementation and explanation of the quantum concepts involved in a fun and interactive way.
This is an enhanced version of the traditional Tic-Tac-Toe, incorporating elements of quantum mechanics, such as quantum gates, superposition, entanglement, etc., to add depth and complexity to the strategic gameplay.
Here, I demonstrated the game rules, my fair play mechanisms, as well as its measurement and collapse processes. I also provided examples of movement operations, mainly focusing on the quantum aspects, such as entanglement and its associated risk levels.
👉 For more details, check the assignment1_quantum_tictactoe folder.
This is an implementation of the Shor's Algorithm, a Quantum Algorithm for Integer Factorization. It is divided into 2 main parts:
1. Classical Part: This involves reducing the problem of factorizing an integer
2. Quantum Part:
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This involves using a quantum computer to find the period
$r$ efficiently. The algorithm creates a superposition of states to encode information about the period into the quantum state. -
The Quantum Fourier Transform (QFT) is applied to the quantum state to extract the period
$r$ :$$\left| \tilde{x} \right\rangle = QFT_N \vert x \rangle = \frac{1}{\sqrt{N}} \sum_{k=0}^{N-1} e^{2\pi i \frac{xk}{N}} \vert k \rangle$$ $$\text{where N = number of qubits; } \vert k \rangle = \vert k_1 k_2 \cdots k_n \rangle (\text{binary qubit state })$$ -
This is a series of Hadamard and Controlled Phase Rotation gates to the output state of the Modular Exponentiation circuit. This transforms the state into a form where measuring the qubits can yield the period
$r$ (just a change of basis). -
This Modular Exponentiation is crucial for creating the periodic function. It involves applying a series of controlled-U gates, where
$U$ represents modular multiplication.
👉 For more details, check the assignment2_shor_algorithm folder.
