Zero to Quantum

From curiosity to writing your own quantum algorithms

I started this series knowing nothing about quantum computing. No physics degree. No quantum mechanics background. Just curiosity and a willingness to work through the math.

The goal is ambitious: by the end of this series, you should understand quantum algorithms deeply enough to design new ones. Not just run tutorials — actually understand why each algorithm works, what makes it faster than classical, and how to think about new problems quantumly.

Every concept is explained from first principles. Every equation is derived step by step. Every algorithm comes with working code you can run in a browser.

The Reader Journey

Phase 1 (Foundations): "What even is a qubit?" → "I just ran Grover's search on my laptop"
Phase 2 (Core Algorithms): "How does Shor break encryption?" → "I can build quantum circuits for real problems"
Phase 3 (Modern Algorithms): "What are variational algorithms?" → "I can design hybrid quantum-classical solutions"
Phase 4 (Frontier): "What's quantum error correction?" → "I understand the full stack from physics to algorithms"

Phase 1: Foundations — Your First Quantum Speedup

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Part 1: Zero to Grover's Search

From "what is a qubit" to cracking a cipher on real IBM quantum hardware. Qubits as vectors, gates as matrices, the full verifier oracle, and your first quadratic speedup. With Colab notebooks and IBM QPU results.

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Part 2: Entanglement and Multi-Qubit Systems

Tensor products, Bell states, CNOT gates, and why entanglement is a resource — not just a curiosity. The math behind "spooky action at a distance" and why it matters for algorithms.

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Part 3: The Quantum Fourier Transform

The classical DFT, then the quantum version — gate by gate. Why QFT is exponentially faster and how it becomes the backbone of Shor's algorithm and phase estimation.

Phase 2: Core Algorithms — The Ones That Changed Everything

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Part 4: Quantum Phase Estimation

The workhorse subroutine behind Shor's algorithm, quantum chemistry, and more. How to extract eigenvalues from a unitary operator using QFT and controlled rotations.

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Part 5: Shor's Algorithm — Breaking RSA

The algorithm that put quantum computing on the map. Period finding, modular exponentiation, and why factoring large numbers becomes easy with a quantum computer. Full circuit, full math, full code.

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Part 6: Quantum Walks and Beyond Grover

Quantum walks on graphs, amplitude estimation, and how Grover's idea generalizes to solve optimization and counting problems.

Phase 3: Modern Algorithms — What People Actually Run Today

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Part 7: Variational Circuits and the NISQ Era

Parameterized quantum circuits, the variational principle, and why hybrid quantum-classical loops are the dominant paradigm on today's noisy hardware.

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Part 8: VQE — Quantum Chemistry from Scratch

The Variational Quantum Eigensolver: finding ground state energies of molecules. Ansatz design, cost landscapes, barren plateaus, and running VQE on a real QPU.

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Part 9: QAOA — Quantum Optimization

The Quantum Approximate Optimization Algorithm for combinatorial problems. MaxCut, graph coloring, and how QAOA bridges quantum annealing and gate-based computing.

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Part 10: Quantum Machine Learning

Quantum kernels, quantum neural networks, data encoding strategies, and an honest assessment of where QML actually provides advantage over classical ML.

Phase 4: The Full Stack — From Physics to Production

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Part 11: Noise, Decoherence, and Why Quantum is Hard

What goes wrong on real hardware. T1/T2 times, gate fidelity, readout errors, and why 1000 logical qubits might need millions of physical qubits.

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Part 12: Quantum Error Correction

The surface code, stabilizer formalism, logical qubits, and the overhead of fault tolerance. Why error correction is the biggest engineering challenge in quantum computing.

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Part 13: Running on Real Quantum Hardware

IBM, Google, IonQ, Quantinuum — the hardware landscape. Transpilation, qubit connectivity, noise mitigation, and getting meaningful results from today's machines.

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Part 14: Designing Your Own Quantum Algorithm

Putting it all together. Problem decomposition, oracle construction, choosing the right subroutines, complexity analysis, and the mindset shift from classical to quantum algorithm design.

Cite this series

@misc{fofadiya2026zerotoquantum,
  author       = {Darshan Fofadiya},
  title        = {Zero to Quantum: From Curiosity to Writing Your Own Quantum Algorithms},
  year         = {2026},
  url          = {https://darshanfofadiya.com/zero-to-quantum/}
}