A comprehensive, progressive learning repository for quantum computing using AWS Braket. Designed for programmers with strong mathematical backgrounds who are new to quantum computing.
- Python 3.9+
- AWS Account with Braket access
- Strong foundation in linear algebra and complex numbers
- Familiarity with probability theory
quantum-fundamentals/
├── shared/ # Shared utilities and visualization tools
├── 01_hello_world/ # Superposition and measurement basics
├── 02_bell_state/ # Quantum entanglement
├── 03_quantum_teleportation/ # Quantum state transfer
├── 04_deutsch_algorithm/ # First quantum speedup
├── 05_bernstein_vazirani/ # Hidden string problem
├── 06_quantum_fourier_transform/ # Foundation for advanced algorithms
├── 07_phase_estimation/ # Eigenvalue extraction
├── 08_grovers_search/ # Quadratic speedup for search
├── 09_quantum_simulation/ # Simulating quantum systems
├── 10_quantum_counting/ # Combining Grover with QPE
├── 11_shors_algorithm/ # Integer factorization
└── 12_quantum_bioinformatics/ # Real-world application
| Project | Concept | Quantum Advantage |
|---|---|---|
| 01 | Superposition & Measurement | Parallel state exploration |
| 02 | Entanglement | Non-classical correlations |
| 03 | Teleportation | Quantum state transfer |
| 04 | Deutsch Algorithm | Exponential query reduction |
| 05 | Bernstein-Vazirani | Linear vs exponential queries |
| Project | Concept | Quantum Advantage |
|---|---|---|
| 06 | Quantum Fourier Transform | O(n²) vs O(n·2ⁿ) classical |
| 07 | Phase Estimation | Eigenvalue extraction |
| 08 | Grover's Search | O(√N) vs O(N) classical |
| 09 | Quantum Simulation | Exponential speedup for physics |
| 10 | Quantum Counting | Amplitude estimation |
| Project | Concept | Quantum Advantage |
|---|---|---|
| 11 | Shor's Algorithm | Exponential speedup for factoring |
| 12 | Bioinformatics | Practical application |
A quantum bit (qubit) lives in a 2-dimensional complex Hilbert space ℂ². The computational basis states are:
A general qubit state is:
Quantum gates are unitary matrices (U†U = I). Key single-qubit gates:
Pauli Gates: $$X = \begin{pmatrix} 0 & 1 \ 1 & 0 \end{pmatrix}, \quad Y = \begin{pmatrix} 0 & -i \ i & 0 \end{pmatrix}, \quad Z = \begin{pmatrix} 1 & 0 \ 0 & -1 \end{pmatrix}$$
Hadamard Gate: $$H = \frac{1}{\sqrt{2}}\begin{pmatrix} 1 & 1 \ 1 & -1 \end{pmatrix}$$
Phase Gates: $$S = \begin{pmatrix} 1 & 0 \ 0 & i \end{pmatrix}, \quad T = \begin{pmatrix} 1 & 0 \ 0 & e^{i\pi/4} \end{pmatrix}$$
Measurement in the computational basis projects onto |0⟩ or |1⟩:
- Probability of measuring |0⟩: |α|²
- Probability of measuring |1⟩: |β|²
pip install -r requirements.txtaws configure
# Enter your AWS Access Key ID, Secret Access Key, and regioncd 01_hello_world
python hello_quantum.pyThis repository uses AWS Braket simulators:
| Simulator | Description | Use Case |
|---|---|---|
braket_sv |
State vector simulator | Small circuits, debugging |
braket_dm |
Density matrix simulator | Noise modeling |
braket_ahs |
Analog Hamiltonian | Quantum simulation |
Cost Note: Local simulators are free. Managed simulators have per-task costs.
| Symbol | Meaning |
|---|---|
| |ψ⟩ | Quantum state (ket) |
| ⟨ψ| | Dual state (bra) |
| ⟨ψ|φ⟩ | Inner product |
| |ψ⟩⊗|φ⟩ | Tensor product |
| U† | Hermitian conjugate |
| [A, B] | Commutator AB - BA |
- Nielsen, M. A., & Chuang, I. L. (2010). Quantum Computation and Quantum Information
- Preskill, J. (2018). Quantum Computing in the NISQ era and beyond
- AWS Braket Documentation: https://docs.aws.amazon.com/braket/
MIT License - See LICENSE file for details.