Quantum versions of k-CSP algorithms

Abstract

In data processing, we input the results xi of measuring easy-to-measure quantities xi and use these results to find estimates y = f (x1, . . ., xn) for difficult-to-measure quantities y which are related to xi by a known relation y = f(x1, . . ., xn). Due to measurement inaccuracy, the measured values xi are, in general, different from the (unknown) actual values xi of the measured quantities, hence the result y of data processing is different from the actual value of the quantity y.In many practical situations, we only know the bounds Δi on the measurement errors Δxi [EQUATION] xi - xi. In such situations, we only know that the actual value xi belongs to the interval [xi - Δi, xi + Δi], and we want to know the range of possible values of y. The corresponding problems of interval computations are NP-hard, so solving these problems may take an unrealistically long time. One way to speed up computations is to use quantum computing, and quantum versions of interval computations algorithms have indeed been developed.In many practical situations, we also know some constraints on the possible values of the directly measured quantities x1, . . ., xn. In such situations, we must combine interval techniques with constraint satisfaction techniques. It is therefore desirable to extend quantum interval algorithms to such combinations. As a first step towards this combination, in this paper, we consider quantum algorithms for discrete constraint satisfaction problems.