Related papers: Quantum algorithm for the Boolean hidden shift pro…
We give an algorithm for the hidden subgroup problem for the dihedral group $D_N$, or equivalently the cyclic hidden shift problem, that supersedes our first algorithm and is suggested by Regev's algorithm. It runs in $\exp(O(\sqrt{\log…
We discuss the fundamental role of entanglement as the essential nonclassical feature providing the computational speed-up in the known quantum algorithms. We review the construction of the Fourier transform on an Abelian group and the…
Many quantum algorithms can be analyzed in a query model to compute Boolean functions where input is given by a black box. As in the classical version of decision trees, different kinds of quantum query algorithms are possible: exact,…
We achieve essentially the largest possible separation between quantum and classical query complexities. We do so using a property-testing problem called Forrelation, where one needs to decide whether one Boolean function is highly…
This paper introduces a novel quantum algorithm that is able to classify a hierarchy of classes of imbalanced Boolean functions. The fundamental characteristic of imbalanced Boolean functions is that the proportion of elements in their…
In this paper we describe a quantum algorithm to solve sparse systems of nonlinear differential equations whose nonlinear terms are polynomials. The algorithm is nondeterministic and its expected resource requirements are polylogarithmic in…
We show that several problems that figure prominently in quantum computing, including Hidden Coset, Hidden Shift, and Orbit Coset, are equivalent or reducible to Hidden Subgroup for a large variety of groups. We also show that, over…
Functions are a fundamental object in mathematics, with countless applications to different fields, and are usually classified based on certain properties, given their domains and images. An important property of a real-valued function is…
To address the issue of excessive quantum resource requirements in Kuperberg's algorithm for the dihedral hidden subgroup problem, this paper proposes a distributed algorithm based on the function decomposition. By splitting the original…
In this article we give several new results on the complexity of algorithms that learn Boolean functions from quantum queries and quantum examples. Hunziker et al. conjectured that for any class C of Boolean functions, the number of quantum…
Quantum computers can execute algorithms that sometimes dramatically outperform classical computation. Undoubtedly the best-known example of this is Shor's discovery of an efficient quantum algorithm for factoring integers, whereas the same…
We exploit Grover operator of database search algorithm for weight decision algorithm. In this research, weight decision problem is to find an exact weight w from given two weights as w1 and w2 where w1+w2=1 and 0<w1<w2<1. Firstly, if a…
Computational models typically assume that operations are applied in a fixed sequential order. In recent years several works have looked at relaxing this assumption, considering computations without any fixed causal structure and showing…
We design a quantum method for classical information compression that exploits the hidden subgroup quantum algorithm. We consider sequence data in a database with a priori unknown symmetries of the hidden subgroup type. We prove that data…
This paper studies the important problem of quantum classification of Boolean functions from a entirely novel perspective. Typically, quantum classification algorithms allow us to classify functions with a probability of $1.0$, if we are…
It is well known that quantum computers can efficiently find a hidden subgroup $H$ of a finite Abelian group $G$. This implies that after only a polynomial (in $\log |G|$) number of calls to the oracle function, the states corresponding to…
This paper summarizes a quantum algorithm of [R.D. Somma, et.al., Phys. Rev. Lett. 101, 130504 (2008)] that simulates a classical annealing process for solving discrete optimization problems. The complexity of the quantum algorithm scales…
The problem of learning Boolean linear functions from quantum examples w.r.t. the uniform distribution can be solved on a quantum computer using the Bernstein-Vazirani algorithm. A similar strategy can be applied in the case of noisy…
It has been proved that almost all $n$-bit Boolean functions have exact classical query complexity $n$. However, the situation seemed to be very different when we deal with exact quantum query complexity. In this paper, we prove that almost…
It is believed that there is no efficient classical algorithm to determine the linear structure of Boolean function. We investigate an extension of Simon's period-finding quantum algorithm, and propose an efficient quantum algorithm to…