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Quantum Computing: A Complete Learning Path

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Malcolm Low

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QUANTUM SERIES 2026
The complete learning path, from a single qubit to Grover’s algorithm.

This is the index to the Techucation Quantum Series: a sequence of hands-on posts that build quantum computing from the ground up. Each one stands on its own, but together they form a single arc, from what a qubit actually is, through the rules that make quantum mechanics strange, to the algorithms that turn those rules into a real speedup. The order below is a learning path from first principles to algorithms, not the order the posts were written.

New to the topic? Read top to bottom. Already comfortable with qubits and gates? Skip ahead to the algorithms in Section 4.
Foundational Pre-reading: The Math Behind the Phase
0
Euler’s Formula: Why eiφ Is Just Shorthand for a Circle
Optional warm-up before the qubit posts: the complex plane, i as a 90° rotation, and why the phase factor eiφ traces a circle.
1  ·  Start Here: Qubits and Superposition
1
Quantum Computing From First Principles: Qubits, Hadamard Gates & Why H² = I
First principles: what a qubit is, how the Hadamard gate builds superposition, and why tensor products scale the state space.
2  ·  The Hadamard Toolkit
2
The Quantum Fourier Transform of a Single Qubit is the Hadamard Transform
The one-qubit QFT turns out to be exactly the Hadamard gate, a small result that anchors the bigger picture.
3
The Walsh-Hadamard Matrix: Backbone of Grover’s Diffusion Operator
How the Hadamard sign table generalises to n qubits and powers Grover’s diffusion step.
3  ·  The Rules of the Quantum World
4
Reversible Computation in Quantum Computing
Why every quantum gate must be reversible, and how ancilla bits turn irreversible logic into unitary logic.
5
The Cost of Garbage in Quantum Computing
Leftover junk qubits destroy interference; uncomputation cleans them up to protect the speedup.
6
The No-Cloning Theorem: Why You Cannot Copy a Qubit
A short proof that an unknown quantum state cannot be duplicated, and what that impossibility makes possible.
7
Quantum Teleportation, and Why It Is Not Cloning
Moving an unknown qubit from one place to another without ever copying it, using entanglement and two classical bits.
4  ·  Algorithms
8
Understanding Phase Kickback
The mechanism where the target qubit flips the control’s phase, the trick underneath Deutsch’s, Grover’s, and Shor’s.
9
Deutsch’s Algorithm: The Four Cases
The four one-bit Boolean functions, the reversible oracle, and the single query that beats the classical two.
10
Deutsch Revisited: Quantum vs Classical in Qiskit
The same algorithm in running Qiskit code: two classical queries against one quantum query.
11
Grover’s Algorithm: Inversion About the Mean
A full three-qubit walkthrough of the oracle and the amplitude amplification that surfaces the marked item.
5  ·  Entanglement and Bell’s Inequality
12
The CHSH Game Simulator and Bell’s Inequality
An interactive game where quantum entanglement beats the classical 75 percent ceiling and violates Bell’s inequality.

Quantum Series 2026  ·  Built with Qiskit 1.x

✦ This article was generated with the assistance of Claude by Anthropic ✦

Continue the Quantum Series
← Quantum teleportation
View the complete Quantum Computing learning path
→ Start with qubits and Hadamard gates

Comments

13 responses to “Quantum Computing: A Complete Learning Path”

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  9. Deutsch’s Algorithm in Quantum Computing: The 4 Cases – Techucation Avatar
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  13. Euler’s Formula: Why e^(iφ) Is Just Shorthand for a Circle – Malcolm Low | Practical AI, Simulation & Quantum Computing Avatar
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