The expectation that quantum algorithms could lead to efficient solutions of “hard” computational problems proved to be justified.Ī number of “toy problems,” such as the Deutsch problem, provided a first glimpse of hope. There are classically intractable problems, such as the Travelling Salesman Problem, which are proven to belong to the complexity class nondeterministic polynomial time (NP). Recall that a computational problem is considered tractable if an algorithm to solve it in a number of steps and requiring storage space polynomial in the size of the input exists. Once we are convinced that given a function f is able to assemble a quantum circuit capable of evaluating this function, we switch our attention to quantum algorithms. Marinescu, in Classical and Quantum Information, 2012 Quantum Algorithms
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