Related papers: The dihedral hidden subgroup problem
We study the problem of finding a subgroup of a given order in a finite group, where the group is represented by its Cayley table. We analyze the complexity of the problem in the special case of abelian groups and present an optimal…
Every semigroup which is a finite disjoint union of copies of the free mono- genic semigroup (natural numbers under addition) has soluble word prob- lem and soluble membership problem. Efficient algorithms are given for both problems.
Searching and sorting used as a subroutine in many important algorithms. Quantum algorithm can find a target item in a database faster than any classical algorithm. One can trade accuracy for speed and find a part of the database (a block)…
We consider the problem of deterministically cloning quantum channels with respect to the best attainable rate and the highest quality, so-called optimal cloning. We demonstrate that cloning quantum states is, in-fact, equivalent to cloning…
A new type of algorithms is presented that combine the advantages of quantum and classical ones. Those combined advantages along with aspects of Geometric Algebra that open possibilities unavailable to both of these computations are…
Learning with Errors (LWE) problems are the foundations for numerous applications in lattice-based cryptography and are provably as hard as approximate lattice problems in the worst case. Here we present a reduction from LWE problem to…
We consider a generalized version of the correlation clustering problem, defined as follows. Given a complete graph $G$ whose edges are labeled with $+$ or $-$, we wish to partition the graph into clusters while trying to avoid errors: $+$…
Biclustering is a problem in machine learning and data mining that seeks to group together rows and columns of a dataset according to certain criteria. In this work, we highlight the natural relation that quantum computing models like boson…
We obtain the strongest separation between quantum and classical query complexity known to date -- specifically, we define a black-box problem that requires exponentially many queries in the classical bounded-error case, but can be solved…
We consider quantum algorithms for the unique sink orientation problem on cubes. This problem is widely considered to be of intermediate computational complexity. This is because there no known polynomial algorithm (classical or quantum)…
Quantum algorithms based on quantum kernel methods have been investigated previously [1]. A quantum advantage is derived from the fact that it is possible to construct a family of datasets for which, only quantum processing can recognise…
The problem of when a given digraph contains a subdivision of a fixed digraph $F$ is considered. Bang-Jensen et al. laid out foundations for approaching this problem from the algorithmic point of view. In this paper we give further support…
The Dihedral Coset Problem (DCP) in $Z_N$ has been extensively studied in quantum computing and post-quantum cryptography, as for instance, the Learning with Errors problem reduces to it. While the Ettinger-Hoyer algorithm is known to solve…
In classical computation, a problem can be solved in multiple steps where calculated results of each step can be copied and used repeatedly. While in quantum computation, it is difficult to realize a similar multi-step computation process…
Finding a hidden partition in a random environment is a general and important problem, which contains as subproblems many famous questions, such as finding a hidden clique, finding a hidden coloring, finding a hidden bipartition etc. In…
We consider the reverse problem to the distinguishability of two quantum channels, which we call the disguising problem. Given two quantum channels, the goal here is to make the two channels identical by mixing with some other channels with…
The quantum algorithm with polynomial time for discrete logarithm problem proposed by Shor is one of the most significant quantum algorithms, but a large number of qubits may be required in the Noisy Intermediate-scale Quantum (NISQ) era.…
We revisit the finite Abelian hidden subgroup problem (AHSP) from a mathematical perspective and make the following contributions. First, by employing amplitude amplification, we present an exact quantum algorithm for the finite AHSP, our…
This is a survey of algorithmic problems in group theory, old and new, motivated by applications to cryptography.
Clustering is a fundamental problem in data analysis. In differentially private clustering, the goal is to identify $k$ cluster centers without disclosing information on individual data points. Despite significant research progress, the…