相关论文: Quantum algorithms for a set of group theoretic pr…
When two spatially separated parties make measurements on an unknown entangled quantum state, what correlations can they achieve? How difficult is it to determine whether a given correlation is a quantum correlation? These questions are…
This note is intended to foster a discussion about the extent to which typical problems arising in quantum information theory are algorithmically decidable (in principle rather than in practice). Various problems in the context of…
In this article we survey recent progress in the algorithmic theory of matrix semigroups. The main objective in this area of study is to construct algorithms that decide various properties of finitely generated subsemigroups of an infinite…
We give efficient quantum algorithms for the problems of Hidden Translation and Hidden Subgroup in a large class of non-abelian solvable groups including solvable groups of constant exponent and of constant length derived series. Our…
Recently developed quantum algorithms suggest that quantum computers can solve certain problems and perform certain tasks more efficiently than conventional computers. Among other reasons, this is due to the possibility of creating…
General key problems in relation to the application of self-organizing structures theory to the analysis of current cooperative phenomena are discussed. Particularly, we present the new results of the analysis of burning problem to form a…
We study the problem of learning an unknown graph provided via an oracle using a quantum algorithm. We consider three query models. In the first model ("OR queries"), the oracle returns whether a given subset of the vertices contains any…
Community detection, also known as graph partitioning, is a well-known NP-hard combinatorial optimization problem with applications in diverse fields such as complex network theory, transportation, and smart power grids. The problem's…
We consider two decision problems in infinite groups. The first problem is Subgroup Intersection: given two finitely generated subgroups $\langle \mathcal{G} \rangle, \langle \mathcal{H} \rangle$ of a group $G$, decide whether the…
In clustering problems, a central decision-maker is given a complete metric graph over vertices and must provide a clustering of vertices that minimizes some objective function. In fair clustering problems, vertices are endowed with a color…
The Quantum Oracle Classification (QOC) problem is to classify a function, given only quantum black box access, into one of several classes without necessarily determining the entire function. Generally, QOC captures a very wide range of…
The solution space of many classical optimization problems breaks up into clusters which are extensively distant from one another in the Hamming metric. Here, we show that an analogous quantum clustering phenomenon takes place in the ground…
Dissipative collective effects are ubiquitous in quantum physics, and their relevance ranges from the study of entanglement in biological systems to noise mitigation in quantum computers. Here, we put forward the first fully quantum…
We present a polynomial-time quantum algorithm for the Hidden Subgroup Problem over $\mathbb{D}_{2^n}$. The usual approach to the Hidden Subgroup Problem relies on harmonic analysis in the domain of the problem, and the best known algorithm…
We propose a technique to design control algorithms for a class of finite dimensional quantum systems so that the control law does not present discontinuities. The class of models considered admits a group of symmetries which allows us to…
We present a number of results related to quantum algorithms with small error probability and quantum algorithms that are zero-error. First, we give a tight analysis of the trade-offs between the number of queries of quantum search…
Noiseless subsystems offer a general and efficient method for protecting quantum information in the presence of noise that has symmetry properties. A paradigmatic class of error models displaying non-trivial symmetries emerges under…
We construct efficient data structures that are resilient against a constant fraction of adversarial noise. Our model requires that the decoder answers most queries correctly with high probability and for the remaining queries, the decoder…
In this article, we advance divide-and-conquer strategies for solving the community detection problem in networks. We propose two algorithms which perform clustering on a number of small subgraphs and finally patches the results into a…
Quantum algorithmics with single spins poses serious technological challenges such as precision fabrication, rapid decoherence, atomic-scale addressing and readout. To circumvent atomic-scale challenges, we examine the case of fully…