Quantum Speedup: The Four Kinds Worth Knowing
The main kinds of quantum speedup: exponential, polynomial, provable and heuristic, with Shor’s and Grover’s algorithms as examples.
BasicsAlgorithmsHardwareError CorrectionCryptographyMachine LearningInformation TheoryPhysics & SimulationApplicationsIndustry & Careers
Tagged: Grover's Algorithm
15 articles
Quantum Oracle Query Complexity and Its Bounds
Oracle query complexity counts the queries a quantum algorithm needs. Bounds, amplitude amplification, speedups and practical limitations.
Quantum Walk Search Algorithms and Their Speedups
Search algorithms based on quantum walks: continuous and discrete time walks on graphs, their relation to Grover’s algorithm and their limits.
Quantum Algorithm Design: Patterns That Recur
Recurring patterns in quantum algorithm design: oracles, amplitude amplification, the Fourier transform and error correction constraints.
Quantum Query Complexity: Counting Oracle Calls
Query complexity counts how often an algorithm must query an oracle. How quantum queries give speedups such as Grover’s and where limits lie.
Quantum Algorithms for Optimization Problems
Quantum approaches to optimization compared: quantum annealing, quantum walks and Grover’s algorithm, and industries where they are being tested.
Quantum Algorithms for Matrix Operations
Quantum algorithms for matrix operations: inversion, singular value decomposition and linear systems, with their uses and important caveats.
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.
Grover’s Algorithm: Quantum Search, Explained
How Grover’s algorithm searches an unsorted list in about √N steps using an oracle and amplitude amplification, and its effect on cryptography.
Every Major Quantum Algorithm, Listed
The major quantum algorithms in one place: Grover, Shor, QFT, Simon, phase estimation, QAOA, quantum walks, HHL, VQE and amplitude estimation.
Quantum Algorithms for Graph Theory Problems
Quantum approaches to graph problems: Grover search, quantum walks, QAOA, quantum annealing and algorithms for spanning trees and graph coloring.
Quantum Algorithms for Cryptography Applications
How Shor’s and Grover’s algorithms affect cryptography, and the alternatives: quantum key distribution and lattice, code, multivariate and hash schemes.
