Complete Quantum Computing Roadmap

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[ ] Phase 0: Foundational Prerequisites

No gaps—master the math, physics, and tools before quantum hits.

• Linear Algebra

  • Vectors, matrices, determinants, eigenvalues, eigenvectors, tensor products, Hermitian matrices, unitary matrices, complex numbers, inner/outer products.
  • Why: Quantum states, operators, and gates live here.
  • Resources:
    • Khan Academy: Linear Algebra.
    • 3Blue1Brown: "Essence of Linear Algebra" (YouTube).
    • "Linear Algebra Done Right" by Axler (find legally).
  • Tasks:
    • Compute a 3x3 determinant.
    • Diagonalize a matrix.
    • Tensor two 2D vectors.

• Probability and Statistics

  • Discrete/continuous distributions, Bayes’ theorem, expectation, variance, covariance, central limit theorem.
  • Why: Quantum measurements are probabilistic.
  • Resources:
    • MIT OpenCourseWare: Probability and Statistics.
    • Khan Academy: Statistics.
  • Tasks:
    • Solve a Bayes’ problem.
    • Compute variance of a dice roll.

• Calculus

  • Derivatives, integrals, partial derivatives, differential equations.
  • Why: Schrödinger equation and dynamics need this.
  • Resources:
    • Khan Academy: Calculus.
    • MIT OpenCourseWare: Single Variable Calculus.
  • Tasks:
    • Solve a basic ODE (e.g., exponential decay).

• Classical Physics

  • Mechanics (Newton’s laws, momentum, energy), electromagnetism (fields, waves, Maxwell’s equations), thermodynamics (entropy, heat).
  • Why: Quantum contrasts and builds on classical rules.
  • Resources:
    • Khan Academy: Physics.
    • "University Physics" by Young & Freedman (find legally).
  • Tasks:
    • Calculate interference pattern.
    • Derive E = mc² intuition.

• Programming Tools

  • Python (NumPy, SciPy), Qiskit, Jupyter, Git, basic C++ (optional for hardware).
  • Why: Your quantum coding backbone.
  • Resources:
    • Qiskit.org: Setup guide.
    • Python.org: NumPy/SciPy docs.
  • Tasks:
    • Run a NumPy matrix operation.
    • Commit a Qiskit “Hello World” to GitHub.

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[ ] Phase 1: Quantum Physics – Every Concept and Law

Every quantum physics topic, no exceptions—your crush deserves it all.

• Quantum Foundations

  • Planck’s quantization (E = hν), photoelectric effect, Compton scattering, de Broglie waves (λ = h/p).
  • Why: Birth of quantum theory.
  • Resources:
    • "Quantum Mechanics" by Griffiths (Ch. 1).
    • Feynman Lectures Vol III (free online).
  • Tasks:
    • Calculate photon energy.
    • Sketch a matter wave.

• Superposition

  • Linear combinations, basis states, coherence.
  • Why: Qubits can be 0 and 1 simultaneously.
  • Resources:
    • Qiskit Textbook: Qubits.
    • YouTube: "Superposition Explained".
  • Tasks:
    • Write a superposition state (e.g., ψ = α|0⟩ + β|1⟩).

• Wave-Particle Duality

  • Double-slit experiment, diffraction, wavefunctions (ψ).
  • Why: Particles act like waves until measured.
  • Resources:
    • Griffiths: Ch. 1.
    • MIT OpenCourseWare: Quantum Physics I.
  • Tasks:
    • Simulate a double-slit pattern (conceptually or in Python).

• Heisenberg Uncertainty Principle

  • ΔxΔp ≥ ħ/2, position-momentum, time-energy uncertainty.
  • Why: Limits precision in quantum systems.
  • Resources:
    • Griffiths: Ch. 1.
    • "Uncertainty" by Heisenberg (if available).
  • Tasks:
    • Derive uncertainty for a Gaussian wavepacket.

• Measurement and Collapse

  • Born rule (|ψ|²), projective measurement, observer effect.
  • Why: Defines quantum outcomes.
  • Resources:
    • Qiskit Textbook: Measurement.
    • Nielsen & Chuang: Ch. 2.
  • Tasks:
    • Code a qubit collapse in Qiskit.

• Entanglement

  • Bell states, EPR paradox, non-locality, Bell’s inequality, no-cloning theorem.
  • Why: Quantum correlations beat classical limits.
  • Resources:
    • Qiskit Tutorials: Bell States.
    • "Spooky Subatomic World" (YouTube).
  • Tasks:
    • Generate and measure a Bell state.

• Schrödinger Equation

  • Time-dependent (iħ ∂ψ/∂t = Hψ), time-independent (Hψ = Eψ), stationary states.
  • Why: Governs quantum evolution.
  • Resources:
    • Griffiths: Ch. 2.
    • MIT Quantum Physics I.
  • Tasks:
    • Solve for a particle in a 1D box.

• Operators and Observables

  • Hermitian operators, Pauli matrices (X, Y, Z), momentum operator (-iħ∇), commutators ([A,B]).
  • Why: Observables are operators in quantum mechanics.
  • Resources:
    • Qiskit Textbook: Operators.
    • Griffiths: Ch. 3.
  • Tasks:
    • Compute [x,p] commutator.
    • Apply Pauli-Z to |0⟩.

• Quantum Tunneling

  • Barrier penetration, tunneling probability.
  • Why: Relevant to quantum hardware.
  • Resources:
    • Griffiths: Ch. 2.
    • YouTube: "Quantum Tunneling Animation".
  • Tasks:
    • Calculate tunneling odds for a simple barrier.

• Spin and Angular Momentum

  • Spin-1/2 particles, Stern-Gerlach experiment, orbital angular momentum (L).
  • Why: Qubits often use spin states.
  • Resources:
    • Griffiths: Ch. 4.
    • Qiskit Textbook: Spin.
  • Tasks:
    • Simulate a spin measurement.

• Pauli Exclusion Principle

  • Fermions, antisymmetric wavefunctions.
  • Why: Impacts multi-particle quantum systems.
  • Resources:
    • Griffiths: Ch. 5.
  • Tasks:
    • Write a 2-electron antisymmetric state.

• Quantum Statistics

  • Bose-Einstein (bosons), Fermi-Dirac (fermions).
  • Why: Particle behavior in quantum systems.
  • Resources:
    • Griffiths: Ch. 5.
  • Tasks:
    • Compare boson vs. fermion distributions.

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[ ] Phase 2: Quantum Computing – Every Detail

From qubits to algorithms—everything CS-related.

• Qubits

  • Bloch sphere, pure vs. mixed states, density matrices.
  • Why: Full qubit representation.
  • Resources:
    • Qiskit Textbook: Qubits.
    • Nielsen & Chuang: Ch. 2.
  • Tasks:
    • Plot a qubit on the Bloch sphere (Qiskit).

• Quantum Gates

  • Single-qubit (H, X, Y, Z, S, T, Rx, Ry, Rz), multi-qubit (CNOT, CZ, SWAP, Toffoli, Fredkin).
  • Why: Quantum logic operations.
  • Resources:
    • Qiskit Tutorials: Gates.
    • Nielsen & Chuang: Ch. 4.
  • Tasks:
    • Build a circuit with H, CNOT, and T gates.

• Quantum Circuits

  • Unitary evolution, gate decomposition, circuit optimization.
  • Why: Programs for quantum machines.
  • Resources:
    • Qiskit Textbook: Circuits.
    • IBM Quantum Lab.
  • Tasks:
    • Optimize a 4-gate circuit.

• Quantum Algorithms

  • Deutsch-Jozsa, Bernstein-Vazirani, Grover’s, Shor’s, Simon’s, phase estimation, HHL (linear systems).
  • Why: Quantum advantages over classical.
  • Resources:
    • Qiskit Tutorials: Algorithms.
    • Nielsen & Chuang: Ch. 5-6.
  • Tasks:
    • Implement Bernstein-Vazirani for 3 qubits.

• Quantum Fourier Transform (QFT)

  • QFT circuit, inverse QFT, applications (Shor’s, phase estimation).
  • Why: Key to quantum speedups.
  • Resources:
    • Qiskit Textbook: QFT.
  • Tasks:
    • Code a 4-qubit QFT.

• Quantum Teleportation

  • Protocol, entanglement swapping.
  • Why: Quantum info transfer.
  • Resources:
    • Qiskit Tutorials: Teleportation.
  • Tasks:
    • Simulate teleporting a qubit state.

• Superdense Coding

  • 2 classical bits via 1 qubit.
  • Why: Quantum communication trick.
  • Resources:
    • Qiskit Tutorials: Superdense Coding.
  • Tasks:
    • Code a superdense protocol.

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[ ] Phase 3: Advanced Quantum Computing

Industry-level depth—hardware, errors, and cutting-edge methods.

• Quantum Error Correction

  • Noise models (bit-flip, phase-flip, depolarizing), Shor code, surface code, stabilizer codes.
  • Why: Practical quantum computing needs this.
  • Resources:
    • Qiskit Tutorials: Error Correction.
    • Nielsen & Chuang: Ch. 10.
  • Tasks:
    • Implement a 3-qubit bit-flip code.

• Quantum Hardware

  • Superconducting qubits, trapped ions, photonic qubits, topological qubits, coherence times, gate fidelities.
  • Why: Real quantum machines.
  • Resources:
    • IBM Quantum: Hardware docs.
    • arXiv.org: Quantum hardware papers.
  • Tasks:
    • Compare coherence times of two qubit types.

• Near-Term Quantum (NISQ)

  • Variational Quantum Eigensolver (VQE), Quantum Approximate Optimization Algorithm (QAOA), quantum machine learning.
  • Why: Usable on today’s devices.
  • Resources:
    • Qiskit Tutorials: VQE/QAOA.
    • PennyLane Tutorials.
  • Tasks:
    • Run VQE for a 2-qubit Hamiltonian.

• Quantum Cryptography

  • BB84 protocol, quantum key distribution, no-cloning impact.
  • Why: Quantum security edge.
  • Resources:
    • Qiskit Tutorials: BB84.
    • Nielsen & Chuang: Ch. 12.
  • Tasks:
    • Simulate BB84 key exchange.

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[ ] Phase 4: Industry Tools and Projects

Hands-on with real systems and a final-year masterpiece.

• Quantum SDKs

  • Qiskit (IBM), Cirq (Google), PennyLane, PyQuil (Rigetti), Q# (Microsoft).
  • Why: Industry-standard frameworks.
  • Resources:
    • Official docs: Qiskit.org, Cirq.dev, Pennylane.ai, etc.
  • Tasks:
    • Convert a Qiskit circuit to PennyLane.

• Cloud Quantum Platforms

  • IBM Quantum, AWS Braket, Azure Quantum, Google Quantum Engine.
  • Why: Access real hardware remotely.
  • Resources:
    • IBM Quantum Lab (free tier).
    • AWS/Braket tutorials.
  • Tasks:
    • Run a Grover’s search on IBM’s quantum device.

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[ ] Phase 5: Career and Mastery

Stay ahead and secure your future.

• Research

  • Seminal papers (Shor 1994, Grover 1996), arXiv quantum preprints.
  • Why: Grasp the field’s evolution.
  • Resources:
    • arXiv.org
  • Tasks:
    • Write a 1-page summary of a recent paper.

• Communities

  • Qiskit Slack, Quantum Computing Stack Exchange, Reddit (r/quantum), Discord groups.
  • Why: Learn from pros, get feedback.
  • Resources:
    • Qiskit.org/community
  • Tasks:
    • Post a circuit, ask for critique.

• Portfolio

  • GitHub repos (simulator, algorithm implementations), blog posts/videos explaining quantum.
  • Why: Impress employers or grad schools.
  • Resources:
    • GitHub.com
  • Tasks:
    • Record a 5-min video on entanglement, upload it.

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[ ] Every Quantum Physics Law and Concept

• Planck’s Law: E = hν (energy quantization).
• Photoelectric Effect: Photon ejection threshold.
• Compton Scattering: Photon-electron momentum shift.
• de Broglie Hypothesis: λ = h/p (matter waves).
• Heisenberg Uncertainty: ΔxΔp ≥ ħ/2, ΔEΔt ≥ ħ/2.
• Schrödinger Equation: iħ ∂ψ/∂t = Hψ (dynamics).
• Born Rule: P = |ψ|² (probability).
• Superposition Principle: ψ = Σ c_i |ψ_i⟩.
• Entanglement: Non-separable states (e.g., |Φ⁺⟩ = (|00⟩ + |11⟩)/√2).
• Pauli Exclusion: No identical fermions in same state.
• Wave-Particle Duality: Interference and collapse.
• Tunneling: Exponential decay through barriers.
• Spin: Intrinsic angular momentum (ħ/2 for electrons).
• Bose-Einstein/Fermi-Dirac: Particle statistics.
• No-Cloning Theorem: Can’t copy unknown states.

[ ] Every CS Connection

• Qubits: Bits with quantum properties.
• Gates: Unitary ops (e.g., H = 1/√2 [[1,1],[1,-1]]).
• Circuits: Sequences of gates + measurements.
• Algorithms: Quantum parallelism (e.g., Grover’s √N speedup).
• Error Correction: Stabilizers map to classical codes.
• Hardware: Qubit types → CS implementation.
• Simulation: Classical approximation of quantum systems.

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Note: This is your full roadmap—quantum and AI-ready. Start anywhere; check [X] when done. Push to GitHub.com/MuhammadAliyan10 as quantum-roadmap.md. Crush it—one box at a time.