🧭 Grover’s Algorithm — 3-Qubit Quantum Search

This project demonstrates Grover’s Quantum Search Algorithm implemented on IBM Quantum Composer and verified on both simulated and real IBM QPU hardware.

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🧩 Overview

Grover’s algorithm provides a quadratic speed-up for searching an unsorted database.
This 3-qubit circuit searches for the marked state |101⟩ among 8 possible bitstrings, using 2 Grover iterations.

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⚙️ Implementation Details

• Language: OpenQASM 2.0
• Platform: IBM Quantum Composer
• Backend: Aer Simulator / IBM Fez QPU
• Qubits: 3
• Target State: 101
• Iterations: 2

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🧠 Algorithm Steps

1. Initialization: Apply Hadamard gates to all qubits to create a uniform superposition.
2. Oracle: Flip the phase of the target state (|101⟩).
3. Diffuser: Reflect the amplitudes about the average (amplitude amplification).
4. Measurement: The target state’s probability dominates after two iterations.

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📊 Results

| Backend | |101⟩ Probability | Notes | |----------|------------------|-------| | Simulator | ≈ 95–98 % | Nearly perfect amplification | | Real QPU (ibm_fez) | ≈ 75–85 % | Slight noise due to decoherence |

The histogram clearly peaks at 101, confirming correct algorithm behavior.

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🖼️ Circuit Visualization

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📂 Files

File	Description
grover_3qubit.qasm	Full OpenQASM 2.0 code for Grover’s algorithm
grover_circuit.png	Circuit diagram exported from IBM Quantum Composer
README.md	Project documentation

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🧪 How to Run

1. Open the .qasm file in IBM Quantum Composer.
2. Select a simulator or available backend (e.g., ibm_fez).
3. Set shots = 1024, then Run circuit.
4. View the histogram to verify the amplitude peak at 101.

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✨ Author

Matthias Masiero
Santa Clara University • Computer Science, Class of 2028

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📘 Reference

• Lov Grover, “A fast quantum mechanical algorithm for database search,” 1996.
• IBM Quantum Documentation