Related papers: Spatial quantum search in a triangular network
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…
Tensor network algorithms seek to minimize correlations to compress the classical data representing quantum states. Tensor network algorithms and similar tools---called tensor network methods---form the backbone of modern numerical methods…
We present an algorithm for the generalized search problem (searching $k$ marked items among $N$ items) based on a continuous Hamiltonian and exploiting resonance. This resonant algorithm has the same time complexity $O(\sqrt{N/k})$ as the…
Local search is a powerful heuristic in optimization and computer science, the complexity of which has been studied in the white box and black box models. In the black box model, we are given a graph $G = (V,E)$ and oracle access to a…
This paper presents a quantum search approach to combinatorial constraint satisfaction problems, demonstrated through the generation of magic squares. We reformulate magic square construction as a quantum search problem in which a…
This paper aims at enlarging the problem of Neural Architecture Search (NAS) from Single-Path and Multi-Path Search to automated Mixed-Path Search. In particular, we model the NAS problem as a sparse supernet using a new continuous…
We consider the quantum time complexity of the all pairs shortest paths (APSP) problem and some of its variants. The trivial classical algorithm for APSP and most all pairs path problems runs in $O(n^3)$ time, while the trivial algorithm in…
Given an item and a list of values of size $N$. It is required to decide if such item exists in the list. Classical computer can search for the item in O(N). The best known quantum algorithm can do the job in $O(\sqrt{N})$. In this paper, a…
We present a framework wherein the trajectory optimization problem (or a problem involving calculus of variations) is formulated as a search problem in a discrete space. A distinctive feature of our work is the treatment of discretization…
Unstructured search remains as one of the significant challenges in computer science, as classical search algorithms become increasingly impractical for large-scale systems due to their linear time complexity. Quantum algorithms, notably…
Anytime heuristic search algorithms try to find a (potentially suboptimal) solution as quickly as possible and then work to find better and better solutions until an optimal solution is obtained or time is exhausted. The most widely-known…
In this paper we present a novel quantum algorithm, namely the quantum grid search algorithm, to solve a special search problem. Suppose $ k $ non-empty buckets are given, such that each bucket contains some marked and some unmarked items.…
The driving force in the pursuit for quantum computation is the exciting possibility that quantum algorithms can be more efficient than their classical analogues. Research on the subject has unraveled several aspects of how that can happen.…
We use a Bayesian approach to optimally solve problems in noisy binary search. We deal with two variants: 1. Each comparison can be erroneous with some probability $1 - p$. 2. At each stage $k$ comparisons can be performed in parallel and a…
Executing quantum circuits on currently available quantum computers requires compiling them to a representation that conforms to all restrictions imposed by the targeted architecture. Due to the limited connectivity of the devices' physical…
We propose a new finding $k$-minima algorithm and prove that its query complexity is $\mathcal{O}(\sqrt{kN})$, where $N$ is the number of data indices. Though the complexity is equivalent to that of an existing method, the proposed is…
Quantum computing has made significant progress in recent years, attracting immense interest not only in research laboratories but also in various industries. However, the application of quantum computing to solve real-world problems is…
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…
We consider the quantum query complexity of local search as a function of graph geometry. Given a graph $G = (V,E)$ with $n$ vertices and black box access to a function $f : V \to \mathbb{R}$, the goal is find a vertex $v$ that is a local…
The quantum search problem is an important problem due to the fact that a general NP problem can be solved efficiently by an unsorted quantum search algorithm. Here it has been shown that the quantum search problem could be solved in…