🖥️ Introduction to Quantum Computing

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🌐 EN | 🇯🇵 JP | Last sync: 2026-08-16

🎯 Series Overview

Quantum computing has moved from a theoretical curiosity to a field with working hardware, real algorithms, and a great deal of hype surrounding both. This series is written for learners coming from materials science, chemistry, and machine learning who want to understand what quantum computers actually do — and what they do not yet do — without first completing a physics degree.

We build the subject from the ground up. Starting from why classical computers struggle with certain problems, we introduce the qubit, superposition, and entanglement as concrete linear algebra rather than as slogans. We then assemble gates into circuits, walk through the landmark algorithms, and finish in the noisy hardware of today, where variational methods such as VQE connect quantum computing to the electronic structure problems at the heart of materials research. Every chapter pairs the theory with NumPy code you can run immediately: a state vector is just a complex array, and a gate is just a matrix multiplication. No quantum computing SDK is required.

Above all, this series aims to leave you calibrated. You will be able to read a quantum computing announcement and tell which claims are established, which are plausible, and which are marketing.

Learning Path

flowchart LR A["Chapter 1
Why Quantum Computing?"] B["Chapter 2
Qubits & Entanglement"] C["Chapter 3
Gates & Circuits"] D["Chapter 4
Quantum Algorithms"] E["Chapter 5
NISQ & Applications"] A --> B --> C --> D --> E style A fill:#667eea,stroke:#764ba2,stroke-width:2px,color:#fff style B fill:#667eea,stroke:#764ba2,stroke-width:2px,color:#fff style C fill:#667eea,stroke:#764ba2,stroke-width:2px,color:#fff style D fill:#667eea,stroke:#764ba2,stroke-width:2px,color:#fff style E fill:#667eea,stroke:#764ba2,stroke-width:2px,color:#fff

📋 Learning Objectives

Explain why certain problems are hard for classical computers, and what kind of structure a quantum computer can exploit
Represent qubits, superposition, and entanglement as vectors and matrices, and compute measurement probabilities from them
Build quantum circuits from elementary gates and simulate them from scratch with NumPy
Describe how the landmark quantum algorithms achieve their speedups, and state honestly where those speedups do and do not apply
Assess NISQ-era hardware and variational algorithms, and connect quantum simulation to problems in chemistry and materials science

📖 Prerequisites

Basic linear algebra is the one real requirement: vectors, matrices, matrix multiplication, eigenvalues, and complex numbers. Familiarity with Python and NumPy is needed for the hands-on sections, though every code example is short and fully explained.

No prior quantum mechanics is assumed — the physics is introduced as it becomes necessary. If you would like deeper background on the underlying physics, the Introduction to Quantum Mechanics series in the Fundamentals of Mathematics Dojo is an excellent optional companion, but this series is self-contained without it.

Chapter 1

Why Quantum Computing?

Understand the motivation behind the field: which problems resist classical computers, what the exponential scaling of quantum states means, and where the honest boundaries of quantum advantage lie. Learn the history from Feynman's proposal to today's devices, and set expectations that survive contact with the literature.

Motivation Computational Complexity Exponential Scaling History Quantum Advantage