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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.
Quantum annealing is used mainly for problems where the search space is discrete (combinatorial optimization problems) with many local minima; such as finding [1] the ground state of a spin glass or solving the traveling salesman problem. The term "quantum annealing" was first proposed in 1988 by B. Apolloni, N. Cesa Bianchi and D. De Falco as ...
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 minimum spanning tree of a weighted planar graph.Finding a minimum spanning tree is a common problem involving combinatorial optimization. Combinatorial optimization is a subfield of mathematical optimization that consists of finding an optimal object from a finite set of objects, [1] where the set of feasible solutions is discrete or can be reduced to a discrete set.
Optimized Markov chain algorithms which use local searching heuristic sub-algorithms can find a route extremely close to the optimal route for 700 to 800 cities. TSP is a touchstone for many general heuristics devised for combinatorial optimization such as genetic algorithms , simulated annealing , tabu search , ant colony optimization , river ...
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 both cases, the models trained by quantum annealing had a similar or better performance in terms of quality. The ultimate question that drives this endeavour is whether there is quantum speedup in sampling applications. Experience with the use of quantum annealers for combinatorial optimization suggests the answer is not straightforward.