Quantum Algorithms

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 tunneling to find optimal solutions by gradually evolving a quantum system. This method is especially effective for combinatorial optimization challenges.

QAOA is a hybrid quantum-classical algorithm that iteratively applies parameterized quantum circuits and optimizes the parameters using classical methods to find approximate solutions to combinatorial optimization problems.

Quantum Boltzmann Machines (QBMs) are quantum-enhanced probabilistic models that improve upon classical Boltzmann Machines using quantum effects for enhanced learning and sampling.

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.

The Quantum Fourier Transform (QFT) efficiently performs a discrete Fourier transform on quantum states, serving as a key building block for many other quantum algorithms.

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.

Quantum K-Means enhances data clustering, particularly for high-dimensional data, by performing distance and centroid calculations using quantum computation.

Quantum Phase Estimation (QPE) is a quantum algorithm that accurately measures the phase of an eigenvalue associated with an eigenvector of a unitary operator.

Quantum Principal Component Analysis (QPCA) uses quantum computation to speed up PCA, particularly for eigenvalue decomposition and data projection, potentially accelerating dimensionality reduction.

QSVMs use quantum computing to accelerate Support Vector Machine tasks, especially kernel calculations, for faster training and classification.

Quantum Walks use quantum mechanics to create a superposition of possible paths, allowing simultaneous exploration of a graph. They can outperform classical random walks in tasks like search and navigation.

Shor's algorithm uses quantum computation to find the prime factors of a large integer in polynomial time, a task considered computationally infeasible for classical computers.

Simon's algorithm efficiently solves the hidden subgroup problem, demonstrating exponential speedup over classical methods by finding a hidden binary string pattern in a black-box function.

VQE combines classical optimization with quantum circuits to approximate the ground state energy of a quantum system.