Quantum_ckts

QGSS'25

Qiskit Global Summer School 2025: Completed Coursework 🎓

This repository contains my completed programming exercises from the Qiskit Global Summer School 2025. The coursework provides a comprehensive, hands-on journey through quantum computing, covering the spectrum from foundational principles to advanced topics in quantum error correction.

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Core Concepts & Technical Implementations 🚀

This curriculum is structured to build a strong theoretical and practical foundation in quantum computing using Qiskit. The key technical areas covered are detailed below.

I. Quantum Fundamentals & Circuit Design ⚛️

This section covers the foundational principles of creating, simulating, and executing quantum circuits.

• Circuit Construction: Building multi-qubit quantum circuits using QuantumCircuit.
• Quantum Gates: Applying fundamental single-qubit (H, X, Z) and multi-qubit (CNOT) gates to manipulate qubit states.
• Entanglement: Generating and verifying canonical entangled states, including 2-qubit Bell states and multi-qubit GHZ states.
• Simulation & Measurement: Executing circuits on the AerSimulator and interpreting measurement outcomes from probability histograms.

II. Quantum Algorithm Implementation 🔎

This section focuses on the practical implementation of a cornerstone quantum algorithm.

• Grover's Search Algorithm: Executing an end-to-end implementation of Grover's algorithm. This involved:
  • Oracle Construction: Designing a problem-specific quantum oracle to recognize and phase-shift a "marked" state.
  • Amplitude Amplification: Building the diffuser operator to selectively amplify the amplitude of the marked state, making it measurable.

III. Hardware-Level Noise & Error Management 🛡️

This section provides hands-on experience with running circuits on real IBM Quantum hardware and implementing state-of-the-art techniques to manage noise.

• Noise Characterization: Quantifying the primary sources of noise in a quantum processor by experimentally measuring qubit T1 (relaxation) and T2 (dephasing) times.
• Error Suppression: Actively suppressing errors during computation by applying Dynamical Decoupling pulse sequences (specifically, the Hahn echo) to extend qubit coherence.
• Error Mitigation: Improving the accuracy of final results by using Zero-Noise Extrapolation (ZNE) via the T-REx library. This involves running experiments at scaled noise levels to infer the ideal, zero-noise outcome.

IV. Quantum Error Correction (QEC) ✅

The final section is a deep dive into the theory and implementation of quantum error correction codes.

• Stabilizer Formalism: Working with stabilizer generators and performing syndrome measurements to detect the presence of errors without disturbing the encoded logical state.
• Code Implementation & Decoding:
  • Steane Code: Building a lookup-table based decoder for the [[7,1,3]] Steane code to correct any single-qubit error.
• Advanced Surface Codes:
  • Parity Check Matrices: Programmatically generating the complete Hx and Hz parity check matrices for a 12x6 lattice.
  • Toric Code: Implementing the nearest-neighbor toric code, a foundational surface code.
  • Gross Code: Constructing the Gross code, an advanced code featuring non-local, long-range stabilizer connections.
• Code Analysis: Calculating the number of encoded logical qubits ($k$) for the implemented codes using the formula k = n - rank(Hx) - rank(Hz), demonstrating a complete understanding of a code's properties.

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Repository Structure 📁

• lab0.ipynb: Introduction to Python and the Qiskit environment.
• lab1.ipynb: Quantum Circuits, Gates, and Entanglement.
• lab2.ipynb: Implementation of Grover's Search Algorithm.
• lab3.ipynb: Hardware Noise Characterization, Suppression, and Mitigation.
• lab4.ipynb: Quantum Error Correction: Steane, Toric, and Gross Codes.

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How to Run ⚙️

1. Clone the repository:

   git clone https://github.com/elpantherd/Quantum_ckts.git

2. Navigate to the directory and set up a Python virtual environment.
3. Install the required dependencies:

   pip install qiskit qiskit-ibm-provider numpy matplotlib notebook

4. Launch Jupyter Notebook:

   jupyter notebook

5. Open any of the .ipynb files to view the code and results.

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Acknowledgments

This coursework was developed by the IBM Quantum team for the Qiskit Global Summer School 2025.