Quantum Computing: Grover's Algorithm — Inversion About the Mean
Malcolm Low's article on DEV Community provides a step-by-step, hand-verifiable walkthrough of Grover's algorithm for the 3-qubit case (N=8). It tracks exact amplitudes of all basis states through each gate operation, targeting state |101⟩. The Grover operator G consists of an oracle Uf that phase-flips the target state and a diffusion operator D = H⊗n(2|0⟩⟨0| − I)H⊗n that reflects amplitudes about their mean. For N=8, the optimal number of iterations is ⌊π/4 × √8⌋ = 2, after which the probability of measuring the target state peaks. The article explains that the oracle introduces destructive interference at the target, which the diffusion operator converts into constructive interference, rotating the state vector by 2θ each iteration where sin(θ) = 1/√N. The walkthrough begins with applying H⊗3 to |000⟩ to create a uniform superposition. All arithmetic is shown explicitly, making it suitable for verification by hand. Originally published on malcolmlow.net, the article is aimed at developers and quantum computing enthusiasts seeking a detailed, pedagogical explanation of Grover's algorithm.
Provides a clear, verifiable example of Grover's algorithm for developers learning quantum computing.