Explore quantum algorithms and their computational advantages across different problem domains, from optimization to cryptography.
The Bernstein-Vazirani algorithm is a quantum algorithm that efficiently determines a secret string of bits encoded within a function, using only a single query, which is exponentially faster than any classical algorithm.
The Deutsch-Jozsa algorithm solves the problem of determining if a black-box function is constant or balanced in a single query, offering an exponential speedup compared to classical deterministic approaches.
Grover's algorithm is a quantum search algorithm that finds a specific entry in an unsorted database in significantly fewer steps than classical algorithms.
The Harrow-Hassidim-Lloyd algorithm is designed to solve systems of linear equations, particularly when the matrices involved are large and sparse, potentially offering exponential speedups in specific applications.
Quantum Amplitude Amplification (QAA) amplifies the probability amplitude of a desired state, quadratically speeding up the search for solutions in problems where a classical algorithm would require a linear search.
Quantum Annealing uses quantum tunnelling to find optimal solutions by gradually evolving a quantum system. This method is especially effective for combinatorial optimization challenges.
A hybrid quantum-classical algorithm that iteratively applies parameterised quantum circuits and optimises the parameters using classical methods to find approximate solutions to combinatorial optimisation problems.
Quantum versions of classical Boltzmann machines, designed to use quantum effects for potentially more efficient training and inference.
QCA efficiently counts solutions to search problems, providing a quadratic speedup over classical methods.
Quantum Error Correction (QEC) techniques protect quantum information from errors like decoherence, essential for fault-tolerant quantum computing.
A fundamental building block in many significant quantum algorithms, enabling them to achieve computational speedups by efficiently manipulating quantum information in the frequency domain.
QGD uses quantum computing to accelerate gradient descent, potentially improving optimization and machine learning. It uses quantum properties for faster gradient calculations and parameter updates.