2025-09 Australian Mathematical Sciences Institute Winter School

Tutorial on Quantum Optimization

This document outlines the steps to set up the development environment for the project. Due to dependencies such as CPLEX, which currently supports up to Python 3.10, it is essential to use Python 3.10 or earlier.

(or you can use uv)

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✅ Prerequisites

Ensure that Python 3.10 is installed on your system.

To verify your Python version, run:

python --version
# or
python3 --version

If Python 3.10 is not installed, follow the instructions below based on your operating system:

• Windows: Download from python.org
• macOS: Use brew install python@3.10 (if available)
• Linux (Debian/Ubuntu): Install via apt (see troubleshooting section)

⚠️ Note: Avoid using Python versions newer than 3.10 to ensure compatibility with CPLEX and other dependencies.

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🛠️ Setup Instructions

1. Clone the Repository

Begin by cloning the project repository:

git clone https://github.com/SMU-Quantum/AMSI_Winter_School_Quantum_Tutorial.git
cd AMSI_Winter_School_Quantum_Tutorial

2. Create and Activate a Virtual Environment

Using a virtual environment is strongly recommended to isolate project dependencies.

Create the virtual environment:

python3.10 -m venv venv

On Windows, if python3.10 is not recognized, use:

py -3.10 -m venv venv

Activate the virtual environment:

OS	Activation Command
Windows	venv\Scripts\activate
macOS	source venv/bin/activate
Linux	source venv/bin/activate

After activation, you should see (venv) prefixed in your shell prompt.

3. Verify Python Version

Confirm that the correct Python interpreter is being used:

python --version

Expected output:

Python 3.10.x

4. Install Project Dependencies

Install all required packages from the requirements.txt file:

pip install -r requirements.txt

Ensure the virtual environment is active before running this command.

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⚠️ Troubleshooting

❌ python3.10 command not found

Ubuntu/Debian Linux

Install Python 3.10 and required components:

sudo apt update
sudo apt install python3.10 python3.10-venv python3.10-dev

Then create the virtual environment:

python3.10 -m venv venv

macOS (with Homebrew)

Install Python 3.10 using Homebrew:

brew install python@3.10

Due to Homebrew's path structure, you may need to use the full path:

# Intel Mac
/usr/local/bin/python3.10 -m venv venv

# Apple Silicon (M1/M2/M3)
/opt/homebrew/bin/python3.10 -m venv venv

Windows

Use the Python Launcher for Windows:

py -3.10 -m venv venv

This method reliably targets Python 3.10 even when multiple versions are installed.

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Quantum Computers Can Evaluate All Possible Solutions at the Same Time...

"Quantum Computers can evaluate all possible solutions at the same time..."

→ A common misunderstanding, particularly for combinatorial optimization!

Explanation

Suppose the equal superposition state:

$$|+\rangle_n = H^{\otimes n}|0\rangle_n = \frac{1}{\sqrt{2^n}} \sum_{x=0}^{2^n-1} |x\rangle_n $$

Furthermore, suppose a function $f: {0, \dots, 2^n - 1} \to \mathbb{R}$ and a corresponding quantum operation:

$$ F: |x\rangle_n |0\rangle_m \mapsto |x\rangle_n |f(x)\rangle_m $$

Thus, we get:

$$F|+\rangle_n = \frac{1}{\sqrt{2^n}} \sum_{x=0}^{2^n-1} |x\rangle_n |f(x)\rangle_m$$

And the quantum computer evaluates the exponential number of solutions in parallel!

Doesn't it?

Unfortunately:

• It remains an exponential number of possible solutions.
• The quantum computer does NOT tell us which one achieves the optimum.
• If we measure the qubits in the state above, we just sample every possible solution with the same probability of $\frac{1}{2^n}$, as we could easily do classically.

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Key Takeaway

→ To get a quantum computer to tell us the optimal solution of a combinatorial optimization problem with probability higher than $\frac{1}{2^n}$, we have to work a bit harder...