Quantum 101

A short, opinionated glossary of terms that come up constantly in quantum computing. The goal is one or two sentences in plain English — enough to follow a conversation or a paper abstract, not a textbook treatment.

If a definition here is wrong or unclear, please email me — I would rather fix it than leave it confusing.

Foundations

Qubit. The quantum analogue of a classical bit. Unlike a bit, which is either 0 or 1, a qubit can be in a superposition of both until measured.

Superposition. A quantum state that is a weighted combination of multiple basis states. Measurement collapses the superposition to one of those basis states with a probability set by the weights.

Entanglement. A correlation between two or more qubits that cannot be explained by any local description of each qubit individually. Measuring one instantly constrains the outcomes of the others.

Bloch sphere. A geometric picture of a single qubit’s state as a point on the surface of a unit sphere. Useful for visualizing single-qubit gates as rotations.

Decoherence. The process by which a qubit loses its quantum information to the environment. The main reason near-term quantum computers are noisy.

Hardware regimes

NISQ. “Noisy intermediate-scale quantum” — Preskill’s term for the current era of quantum computers: tens to hundreds of physical qubits, significant noise, no full error correction.

Gate model. The mainstream model of quantum computing: discrete unitary gates applied to qubits, then measurement. What IBM, Google, IonQ, and most others build.

Adiabatic quantum computing / quantum annealing. A different model where the answer is encoded in the ground state of a slowly-changing Hamiltonian. D-Wave is the best-known example.

Algorithms

Shor’s algorithm. A quantum algorithm that factors integers in polynomial time. The reason post-quantum cryptography exists.

Grover’s algorithm. A quantum algorithm that searches an unsorted database of $N$ items in roughly $\sqrt{N}$ steps — a quadratic speedup over classical.

HHL. The Harrow–Hassidim–Lloyd algorithm for solving linear systems. Often invoked as a quantum primitive for machine learning, but with many caveats about input/output access.

QFT. The quantum Fourier transform — the workhorse subroutine inside Shor and many phase-estimation algorithms.

Quantum walk. Quantum analogue of a random walk; a building block for search and graph algorithms.

Hamiltonian simulation. Using a quantum computer to simulate the time evolution of another quantum system. The original motivating use case.

Variational and hybrid

VQE. Variational quantum eigensolver — a hybrid algorithm that uses a classical optimizer to tune a parameterized quantum circuit to find a Hamiltonian’s ground-state energy.

QAOA. Quantum approximate optimization algorithm — a related hybrid approach for combinatorial optimization problems like Max-Cut.

Error correction

QEC. Quantum error correction — encoding one logical qubit across many physical qubits so that errors can be detected and reversed without collapsing the state.

Surface code. The leading practical QEC scheme, well-suited to nearest-neighbor 2D qubit layouts.

Magic state. A specific resource state that, combined with Clifford gates, enables universal fault-tolerant computation. Producing them is expensive, which is why “magic-state distillation” is a major topic.

Milestones

Quantum advantage / supremacy. A demonstration that a quantum computer solves a particular task faster than any known classical algorithm running on the best available hardware. The benchmark task matters as much as the result.