Related papers: Quantum Search on Computation Trees
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…
Span program is a linear-algebraic model of computation originally proposed for studying the complexity theory. Recently, it has become a useful tool for designing quantum algorithms. In this paper, we present a time-efficient…
Shenvi, Kempe and Whaley's quantum random-walk search (SKW) algorithm [Phys. Rev. A 67, 052307 (2003)] is known to require $O(\sqrt N)$ number of oracle queries to find the marked element, where $N$ is the size of the search space. The…
We introduce quantized bipartite walks, compute their spectra, generalize the algorithms of Grover \cite{g} and Ambainis \cite{amb03} and interpret them as quantum walks with memory. We compare the performance of walk based classical and…
Recently, Farhi, Goldstone, and Gutmann gave a quantum algorithm for evaluating NAND trees that runs in time O(sqrt(N log N)) in the Hamiltonian query model. In this note, we point out that their algorithm can be converted into an algorithm…
Searching in partially ordered structures has been considered in the context of information retrieval and efficient tree-like indexes, as well as in hierarchy based knowledge representation. In this paper we focus on tree-like partial…
In this paper, we study quantum algorithms for computing the exact value of the treewidth of a graph. Our algorithms are based on the classical algorithm by Fomin and Villanger (Combinatorica 32, 2012) that uses $O(2.616^n)$ time and…
Quantum search algorithms offer a remarkable advantage of quadratic reduction in query complexity using quantum superposition principle. However, how an actual architecture may access and handle the database in a quantum superposed state…
One of the significant breakthroughs in quantum computation is Grover's algorithm for unsorted database search. Recently, the applications of Grover's algorithm to solve global optimization problems have been demonstrated, where unknown…
We recast Grover's generalised search algorithm in a geometric language even when the states are not approximately orthogonal. We provide a possible search algorithm based on an arbitrary unitary transformation which can speed up the steps…
This extended abstract reports on on-going research on quantum algorithmic approaches to the problem of generalised tree search that may exhibit effective quantum speedup, even in the presence of non-constant branching factors. Two…
Quantum search on the two-dimensional lattice with one marked vertex and cyclic boundary conditions is an important problem in the context of quantum algorithms with an interesting unfolding. It avails to test the ability of quantum walk…
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…
We present the first sublinear-in-$n$ round algorithm for sampling an approximately uniform spanning tree of an $n$-vertex graph in the CongestedClique model of distributed computing. In particular, our algorithm requires…
Suppose we have n algorithms, quantum or classical, each computing some bit-value with bounded error probability. We describe a quantum algorithm that uses O(sqrt{n}) repetitions of the base algorithms and with high probability finds the…
Link prediction is one of the fundamental problems in graph theory, critical for understanding and forecasting the evolution of complex systems like social and biological networks. While classical heuristics capture certain aspects of graph…
A modification of Tulsi's quantum search algorithm with intermediate measurements of the control is presented. In order to analyze the effect of measurements in quantum searches, a different choice of the angular parameter is used. The…
We consider the neighborhood tree induced by alternating the use of different neighborhood structures within a local search descent. We investigate the issue of designing a search strategy operating at the neighborhood tree level by…
Spatial search on graphs is one of the most important algorithmic applications of quantum walks. To show that a quantum-walk-based search is more efficient than a random-walk-based search is a difficult problem, which has been addressed in…
Motion planning is challenging when it comes to the case of imperfect state information. Decision should be made based on belief state which evolves according to the noise from the system dynamics and sensor measurement. In this paper, we…