Quantum Algorithms Database

Factors large numbers exponentially faster than any known classical algorithm, threatening RSA encryption.

Searches unsorted data in roughly √N steps instead of N, using amplitude amplification.

The first algorithm to prove a quantum computer could solve a problem exponentially faster than any classical deterministic algorithm.

Finds a hidden pattern (period) in a function exponentially faster than classical methods, directly inspiring Shor's Algorithm.

The quantum analog of the discrete Fourier transform, performed exponentially faster than the classical Fast Fourier Transform.

Estimates the eigenvalue (phase) associated with a quantum operation, a critical building block for many other quantum algorithms.

A hybrid quantum-classical algorithm for finding the lowest energy state of a molecule or material, designed to work on noisy near-term hardware.

A hybrid algorithm for finding approximate solutions to combinatorial optimization problems on near-term quantum hardware.

Solves systems of linear equations exponentially faster than classical methods, under specific conditions.

The quantum analog of a classical random walk, used to search graphs and networks faster than classical methods in specific structured cases.

Estimates the number of solutions to a search problem, combining Grover's Algorithm with quantum phase estimation.

Estimates an unknown probability or expected value quadratically faster than classical Monte Carlo sampling.

A protocol for transferring an unknown quantum state from one location to another using entanglement and classical communication.

The first quantum key distribution protocol, allowing two parties to generate a shared secret key with security guaranteed by physics rather than mathematical assumptions.

A quantum key distribution protocol based on entangled particle pairs and Bell inequality tests rather than single-photon polarization.

A computational task used to demonstrate 'quantum supremacy' — sampling outputs from a deliberately complex, randomly generated quantum circuit.

Algorithms and encoding schemes for protecting quantum information from errors by spreading it across multiple physical qubits.

A quantum algorithm for identifying the dominant patterns (principal components) in data, with potential exponential speedup under specific conditions.

A specialized, non-gate-based quantum computing approach that finds low-energy solutions to optimization problems by gradually evolving a quantum system.

A specialized computational task using photons (rather than qubits) believed to be exponentially hard to simulate classically, proposed as a near-term path to demonstrating quantum advantage.

Finds a hidden binary string encoded in a function using just one query, versus many queries classically — a simple but illustrative example of quantum parallelism.

A quantum algorithm for identifying counterfeit (different-weight) coins among genuine ones using a weighing-based query model, faster than the best classical strategies.

Finds two inputs that produce the same output from a function (a 'collision') faster than classical methods, with direct implications for hash function security.

A quantum approach to the gradient descent optimization technique that underlies most classical machine learning training, offering speedups under specific structural assumptions.

A quantum version of the classical support vector machine classification algorithm, offering an exponential speedup under specific idealized conditions.

Quantum approaches to identifying unusual or outlier data points within a larger dataset, relevant to fraud detection and system monitoring.

A proposed architecture for accessing classical data in superposition, theoretically required to realize many quantum machine learning speedups in practice.

A simple but widely used quantum subroutine for estimating how similar two quantum states are, without fully measuring either one.

A quantum version of the classical k-means clustering algorithm, grouping similar data points together using quantum distance estimation techniques.

A general technique for implementing operations that aren't directly unitary by expressing them as a weighted combination of simpler unitary operations.

A unifying mathematical framework for designing highly efficient quantum algorithms by applying polynomial transformations to a quantum operation's eigenvalues.

A technique for approximating the time evolution of a complex quantum system by breaking it into a sequence of simpler, easier-to-implement steps.

Estimates the number of solutions to a search problem approximately, trading some precision for a simpler and often faster quantum circuit than exact quantum counting.

A quantum-walk-based reformulation of the classical PageRank algorithm (originally used by Google to rank web pages), offering different ranking behavior rather than a proven speedup.

A general-purpose model of quantum computation (closely related to quantum annealing) that encodes a problem's answer as the lowest-energy state of a carefully designed quantum system.

Algorithms that exploit the quantum Zeno effect — where frequent measurement can effectively 'freeze' a quantum system's evolution — for tasks like quantum state preparation.

An extension of BB84-style quantum key distribution using six measurement states instead of four, improving security against certain eavesdropping strategies.

A quantum key distribution approach whose security can be guaranteed without trusting the internal workings of the devices used, relying only on observed Bell inequality violations.

A quantum protocol allowing a sender to digitally 'sign' a message such that recipients can verify its authenticity, with security guaranteed by quantum mechanics rather than computational assumptions.

A protocol for splitting a secret among multiple parties using entangled quantum states, such that the secret can only be reconstructed if a sufficient number of parties cooperate.

Quantum walk-based approaches to determining whether two graphs have identical structure, a notoriously difficult classical problem with unclear classical complexity.

Adaptations of QAOA and related quantum optimization algorithms to the classic traveling salesman problem — finding the shortest route visiting a set of locations exactly once.

Quantum approaches to the Max-Cut problem — partitioning a network's nodes into two groups to maximize the number of connections between the groups — the original benchmark problem for QAOA.

A quantum generalization of the classical belief propagation algorithm used for probabilistic inference in graphical models, relevant to both quantum error correction and quantum machine learning.

Quantum approaches to the optimal transport problem — finding the most efficient way to move or transform one distribution of resources into another — relevant to logistics and machine learning.

Applies quantum amplitude estimation specifically to numerical integration problems, offering a quadratic speedup over classical Monte Carlo integration methods.

Quantum algorithms for solving semidefinite programs — a powerful and widely used class of optimization problems — offering polynomial speedups under certain conditions.

A resource-efficient variant of standard quantum phase estimation that uses a single ancilla qubit repeatedly, instead of many qubits at once — better suited to near-term hardware.

A family of techniques for reducing the impact of noise on NISQ-era quantum computations without requiring full quantum error correction's heavy qubit overhead.

An improved optimization technique for training variational quantum algorithms like VQE and QAOA, accounting for the underlying geometry of quantum state space to converge faster.

An alternative to VQE for finding a quantum system's ground state, using a mathematical technique borrowed from statistical mechanics adapted to run on quantum hardware.

A generalization of Grover's Algorithm that boosts the probability of measuring a desired outcome for any quantum algorithm, not just database search.

Finds the minimum value in an unsorted list quadratically faster than classical exhaustive search, using a repeated application of Grover's Algorithm.

A unifying framework that encompasses nearly all known quantum speedups by expressing them as polynomial transformations of singular values of a block-encoded matrix.

A near-term hybrid alternative to HHL for solving linear systems, using variational circuits to avoid HHL's deep circuit requirements.

Uses quantum circuits to compute inner products between quantum feature maps, potentially enabling support vector machines to classify data that is hard to separate classically.

A quantum analog of classical generative adversarial networks, where both generator and discriminator may be quantum circuits, potentially learning quantum state distributions.

Estimates the mean of a function over a probability distribution quadratically faster than classical Monte Carlo sampling.

A quantum generalization of the Boltzmann machine, using quantum effects (tunneling and entanglement) in the hidden units to potentially learn richer probability distributions.

A quantum algorithm for sampling from a target distribution using samples from an easier-to-prepare distribution, generalizing classical rejection sampling.

Prepares the thermal (Gibbs) state of a quantum Hamiltonian — a fundamental task for simulating quantum systems at finite temperature.

Encodes n classical bits into fewer than n qubits, allowing probabilistic recovery of any single bit — demonstrating quantum advantage in communication complexity.

A quantum generalization of the classical Metropolis-Hastings algorithm for sampling from quantum Gibbs states without requiring phase estimation or expensive state preparation.