The Hidden Subgroup Problem and Why It Matters
The hidden subgroup problem unifies Simon’s and Shor’s algorithms. Its formulation, the role of the quantum Fourier transform and open research questions.
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Quantum Algorithms
Shor, Grover, QAOA, VQE and the rest — what each quantum algorithm does, the problem it targets and where the promised speedup really comes from.
85 articles
Quantum Phase Kickback: The Trick Behind Many Speedups
Phase kickback moves a phase from a target qubit to a control qubit. Why this simple effect underlies Deutsch-Jozsa, phase estimation and Shor’s algorithm.
The Quantum Random Walk Algorithm, Explained
How quantum random walks work: the coin operator, interference, implementation on quantum hardware, search algorithms and experiments.
Quantum Metropolis Sampling: Monte Carlo, Quantised
Quantum Metropolis sampling adapts the Metropolis-Hastings Monte Carlo method to quantum systems. Its theory, relation to annealing and potential uses.
Quantum Simulation Algorithms and What They Model
Quantum simulation algorithms model molecules and materials that classical computers struggle with. Uses in chemistry, drug discovery and materials science.
Amplitude Amplification: Grover’s Idea, Generalised
Amplitude amplification generalizes Grover’s search: it raises the probability of target states step by step. How the iteration works and where it is used.
Simon’s Algorithm: The Problem That Started Shor
Simon’s algorithm finds a hidden period of a two-to-one function exponentially faster than classical methods, and it directly inspired Shor’s algorithm.
The Deutsch-Jozsa Algorithm: The First Speedup
The Deutsch-Jozsa algorithm decides whether a black-box function is constant or balanced in one query. Its circuit, steps, complexity and limits.
The HHL Algorithm for Linear Systems of Equations
The HHL algorithm by Harrow, Hassidim and Lloyd solves linear systems on a quantum computer. Its circuit, state preparation, caveats and applications.
The Quantum Counting Algorithm, Explained
The quantum counting algorithm combines Grover’s search with phase estimation to count solutions. How it works, its speedup and its limitations.
Quantum Walks: The Quantum Version of Random Walks
Quantum walks are the quantum version of random walks. How they spread faster than classical walks, run on graphs and feed into algorithm design.
Quantum Annealing: How D-Wave Machines Solve Problems
How quantum annealing uses tunneling and a slowly changing transverse field to find low-energy solutions, how D-Wave machines work and where they help.
