Related papers: Spatial quantum search in a triangular network
I propose a "quantum annealing" heuristic for the problem of combinatorial search among a frustrated set of states characterized by a cost function to be minimized. The algorithm is probabilistic, with postselection of the measurement…
This paper extends the quantum search class of algorithms to the multiple solution case. It is shown that, like the basic search algorithm, these too can be represented as a rotation in an appropriately defined two dimensional vector space.…
The spatial search problem on regular lattice structures in integer number of dimensions $d\geq2$ has been studied extensively, using both coined and coinless quantum walks. The relativistic Dirac operator has been a crucial ingredient in…
This paper introduces a quantum-classical hybrid algorithm for generalized pattern search (GPS) algorithms. We introduce a quantum search step algorithm using amplitude amplification, which reduces the number of oracle calls needed during…
The running time of a quantum walk search algorithm depends on both the structure of the search space (graph) and the configuration of marked locations. While the first dependence have been studied in a number of papers, the second…
We examine the effect of network heterogeneity on the performance of quantum search algorithms. To this end, we study quantum search on a tree for the oracle Hamiltonian formulation employed by continuous-time quantum walks. We use…
In this paper, we present a novel formulation of traditional sampling-based motion planners as database-oracle structures that can be solved via quantum search algorithms. We consider two complementary scenarios: for simpler sparse…
The quantum SearchRank algorithm is a promising tool for a future quantum search engine based on PageRank quantization. However, this algorithm loses its functionality when the $N/M$ ratio between the network size $N$ and the number of…
We consider a database separated into blocks. Blocks containing target items are called target blocks. Blocks without target items are called non-target blocks. We consider a case, when each target block has the same number of target items.…
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…
Recently, Ambainis gave an O(N^(2/3))-query quantum walk algorithm for element distinctness, and more generally, an O(N^(L/(L+1)))-query algorithm for finding L equal numbers. We point out that this algorithm actually solves a much more…
Quantum computation, in particular Grover's algorithm, has aroused a great deal of interest since it allows for a quadratic speedup to be obtained in search procedures. Classical search procedures for an $N$ element database require at most…
Quantum architecture search (QAS) automates the design of parameterized quantum circuits for variational quantum algorithms. The framework finds a well-suited problem-specific structure of a variational ansatz. Among possible…
Quantum algorithms for several problems in graph theory are considered. Classical algorithms for finding the lowest weight path between two points in a graph and for finding a minimal weight spanning tree involve searching over some space.…
This paper shows how a basic property of unitary transformations can be used for meaningful computations. This approach immediately leads to search-type applications, where it improves the number of steps by a square-root - a simple minded…
We propose a quantum algorithm for closest pattern matching which allows us to search for as many distinct patterns as we wish in a given string (database), requiring a query function per symbol of the pattern alphabet. This represents a…
Continuous-time quantum walks are natural tools for spatial search, where one searches for a marked vertex in a graph. Sometimes, the structure of the graph causes the walker to get trapped, such that the probability of finding the marked…
A discrete time quantum walk is known to be the single-particle sector of a quantum cellular automaton. Searching in this mathematical framework has interested the community since a long time. However, most results consider spatial search…
We study the problem of finding $K$ collision pairs in a random function $f : [N] \rightarrow [N]$ by using a quantum computer. We prove that the number of queries to the function in the quantum random oracle model must increase…
The random k-SAT instances undergo a "phase transition" from being generally satisfiable to unsatisfiable as the clause number m passes a critical threshold, $r_k n$. This causes a drastic reduction in the number of satisfying assignments,…