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What is quantum query complexity?
Query complexity is a model of computation in which we have to compute a function f(x_1, \ldots, x_N) of variables x_i which can be accessed via queries. The complexity of an algorithm is measured by the number of queries that it makes. Query complexity is widely used for studying quantum algorithms, for two reasons.
What do you mean by annealing?
Annealing is a heat treatment process that changes the physical and sometimes also the chemical properties of a material to increase ductility and reduce the hardness to make it more workable.
Is BQP a NP?
The relation between BQP and NP is not known, though we do know that NP is not contained in BQP. In May 2018, computer scientists Ran Raz of Princeton University and Avishay Tal of Stanford University published a paper which showed that, relative to an oracle, BQP was not contained in PH.
When is quantum annealing used in combinatorial optimization?
Quantum annealing is used mainly for problems where the search space is discrete ( combinatorial optimization problems) with many local minima; such as finding the ground state of a spin glass or the traveling salesman problem. Quantum annealing was first proposed in 1988 by B. Apolloni, N. Cesa Bianchi and D. De Falco.
Which is more accurate quantum annealing or AQC?
While quantum annealing (QA) provides a more accurate model for the behavior of actual quantum physical systems, the possibility of non-adiabatic effects obscures a clear separation with conventional computing complexity. A series of technological advances in the control of quantum physical systems have enabled experimental AQC and QA.
How is the adiabatic condition captured in quantum annealing?
A relaxation of the adiabatic condition is captured in the complementary computational heuristic of quantum annealing, which accommodates physical systems operating at finite temperature and in open environments.
In quantum annealing, the strength of transverse field determines the quantum-mechanical probability to change the amplitudes of all states in parallel. Analytical and numerical evidence suggests that quantum annealing outperforms simulated annealing under certain conditions (see for a careful analysis).