相关论文: Quantum query complexity of some graph problems
Answering complex logical queries on incomplete knowledge graphs is a challenging task, and has been widely studied. Embedding-based methods require training on complex queries, and cannot generalize well to out-of-distribution query…
The quadratic minimum spanning tree problem and its variations such as the quadratic bottleneck spanning tree problem, the minimum spanning tree problem with conflict pair constraints, and the bottleneck spanning tree problem with conflict…
This work concerns with proving space lower bounds for graph problems in the streaming model. It is known that computing the length of shortest path between two nodes in the streaming model requires $\Omega(n)$ space, where $n$ is the…
We present quantum algorithms to search for marked vertices in structured databases with low connectivity. Adopting a multi-stage search process, we achieve a success probability close to $100\%$ on Cayley trees with large branching…
A continuous-time quantum walk is modelled using a graph. In this short paper, we provide lower bounds on the size of a graph that would allow for some quantum phenomena to occur. Among other things, we show that, in the adjacency matrix…
Branching programs are quite popular for studying time-space lower bounds. Bera et al. recently introduced the model of generalized quantum branching program aka. GQBP that generalized two earlier models of quantum branching programs. In…
The qubit routing problem, also known as the swap minimization problem, is a (classical) combinatorial optimization problem that arises in the design of compilers of quantum programs. We study the qubit routing problem from the viewpoint of…
A new quantum algorithm for a search problem and its computational complexity are discussed. It is shown in the search problem containing 2^n objects that our algorithm runs in polynomial time.
Testing graph completeness is a critical problem in computer science and network theory. Leveraging quantum computation, we present an efficient algorithm using the Szegedy quantum walk and quantum phase estimation (QPE). Our algorithm,…
We establish a lower bound of $\Omega{(\sqrt{n})}$ on the bounded-error quantum query complexity of read-once Boolean functions, providing evidence for the conjecture that $\Omega(\sqrt{D(f)})$ is a lower bound for all Boolean functions.…
A randomly walking quantum particle evolving by Schr\"odinger's equation searches on $d$-dimensional cubic lattices in $O(\sqrt{N})$ time when $d \ge 5$, and with progressively slower runtime as $d$ decreases. This suggests that graph…
In this paper we present a quantum algorithm solving the triangle finding problem in unweighted graphs with query complexity $\tilde O(n^{5/4})$, where $n$ denotes the number of vertices in the graph. This improves the previous upper bound…
In this research we present a quantum circuit for estimating algorithmic complexity using the coding theorem method. This accelerates inferring algorithmic structure in data for discovering causal generative models. The computation model is…
The Minimum Spanning Tree Problem with Conflicts consists in finding the minimum conflict-free spanning tree of a graph, i.e., the spanning tree of minimum cost, including no pairs of edges that are in conflict. In this paper, we solve this…
Quantum network is a set of nodes connected with channels, through which the nodes communicate photons and classical information. Classical structural complexity of a quantum network may be defined through its physical structure, i.e.…
The problem of finding the connected components of a graph is considered. The algorithms addressed to solve the problem are used to solve such problems on graphs as problems of finding points of articulation, bridges, maximin bridge, etc. A…
We develop a general framework to construct quantum algorithms that detect if a $3$-uniform hypergraph given as input contains a sub-hypergraph isomorphic to a prespecified constant-sized hypergraph. This framework is based on the concept…
The symmetry of complex networks is a global property that has recently gained attention since MacArthur et al. 2008 showed that many real-world networks contain a considerable number of symmetries. These authors work with a very strict…
Searching for collisions in random functions is a fundamental computational problem, with many applications in symmetric and asymmetric cryptanalysis. When one searches for a single collision, the known quantum algorithms match the query…
We study the quantum query algorithms for simplex finding, a generalization of triangle finding to hypergraphs. This problem satisfies a rank-reduction property: a quantum query algorithm for finding simplices in rank-$r$ hypergraphs can be…