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For combinatorial optimization, the quantum approximate optimization algorithm (QAOA) [6] briefly had a better approximation ratio than any known polynomial time classical algorithm (for a certain problem), [7] until a more effective classical algorithm was proposed. [8] The relative speed-up of the quantum algorithm is an open research question.
The quantum approximate optimization algorithm takes inspiration from quantum annealing, performing a discretized approximation of quantum annealing using a quantum circuit. It can be used to solve problems in graph theory. [50] The algorithm makes use of classical optimization of quantum operations to maximize an "objective function."
In quantum computing, the variational quantum eigensolver (VQE) is a quantum algorithm for quantum chemistry, quantum simulations and optimization problems.It is a hybrid algorithm that uses both classical computers and quantum computers to find the ground state of a given physical system.
In quantum computing, Grover's algorithm, also known as the quantum search algorithm, is a quantum algorithm for unstructured search that finds with high probability the unique input to a black box function that produces a particular output value, using just () evaluations of the function, where is the size of the function's domain.
"A cross-disciplinary introduction to quantum annealing-based algorithms" [37] presents an introduction to combinatorial optimization problems, the general structure of quantum annealing-based algorithms and two examples of this kind of algorithms for solving instances of the max-SAT (maximum satisfiable problem) and Minimum Multicut problems ...
Shor's algorithm is a quantum algorithm for finding the prime factors of an integer. It was developed in 1994 by the American mathematician Peter Shor. [1] [2] It is one of the few known quantum algorithms with compelling potential applications and strong evidence of superpolynomial speedup compared to best known classical (non-quantum ...
Adiabatic quantum computing has been shown to be polynomially equivalent to conventional quantum computing in the circuit model. [6] The time complexity for an adiabatic algorithm is the time taken to complete the adiabatic evolution which is dependent on the gap in the energy eigenvalues (spectral gap) of the Hamiltonian.
Qiskit Optimization is an open-source framework that covers the whole range from high-level modeling of optimization problems, with automatic conversion of problems to different required representations, to a suite of easy-to-use quantum optimization algorithms that are ready to run on classical simulators, as well as on real quantum devices ...