Related papers: Time and Query Optimal Quantum Algorithms Based on…
A quantum computer encodes information in quantum states and runs quantum algorithms to surpass the classical counterparts by exploiting quantum superposition and quantum correlation. Grover's quantum search algorithm is a typical quantum…
The quantum query complexity of subgraph-containment problems, which ask whether a given subgraph $H$ is present in an input graph $G$, has been the subject of considerable study. However, even for relatively simple subgraphs, such as paths…
Quantum computers can potentially solve problems that are computationally intractable on a classical computer in polynomial time using quantum-mechanical effects such as superposition and entanglement. The N-Queens Problem is a notable…
The query model offers a concrete setting where quantum algorithms are provably superior to randomized algorithms. Beautiful results by Bernstein-Vazirani, Simon, Aaronson, and others presented partial Boolean functions that can be computed…
We present new quantum algorithms for Triangle Finding improving its best previously known quantum query complexities for both dense and spare instances.For dense graphs on $n$ vertices, we get a query complexity of $O(n^{5/4})$ without any…
One of the most important algorithmic applications of quantum walks is to solve spatial search problems. A widely used quantum algorithm for this problem, introduced by Childs and Goldstone [Phys. Rev. A 70, 022314 (2004)], finds a marked…
We study the unsorted database search problem with items $N$ from the viewpoint of unitary discrimination. Instead of considering the famous $O(\sqrt{N})$ Grover's the bounded-error algorithm for the original problem, we seek for the…
A previously developed quantum search algorithm for solving 1-SAT problems in a single step is generalized to apply to a range of highly constrained k-SAT problems. We identify a bound on the number of clauses in satisfiability problems for…
We study the problem of estimating frequency response functions of systems of coupled, classical harmonic oscillators using a quantum computer. The functional form of these response functions can be mapped to a corresponding eigenproblem of…
Many computational problems are subject to a quantum speed-up: one might find that a problem having an O(n^3)-time or O(n^2)-time classic algorithm can be solved by a known O(n^1.5)-time or O(n)-time quantum algorithm. The question…
Quantum Random Access Memory (QRAM) is a crucial architectural component for querying classical or quantum data in superposition, enabling algorithms with wide-ranging applications in quantum arithmetic, quantum chemistry, machine learning,…
We present a quantum algorithmic routine that extends the realm of Grover-based heuristics for tackling combinatorial optimization problems with arbitrary efficiently computable objective and constraint functions. Building on previously…
To investigate the performance of quantum information tasks on networks whose topology changes in time, we study the spatial search algorithm by continuous time quantum walk to find a marked node on a random temporal network. We consider a…
This paper shows that a quantum mechanical algorithm that can query information relating to multiple items of the database, can search a database in a single query (a query is defined as any question to the database to which the database…
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…
This paper presents a parallel solution based on the coarse-grained multicomputer (CGM) model using the four-splitting technique to solve the optimal binary search tree problem. The well-known sequential algorithm of Knuth solves this…
This paper shows that, if we could examine the entire history of a hidden variable, then we could efficiently solve problems that are believed to be intractable even for quantum computers. In particular, under any hidden-variable theory…
Quantum algorithms and circuits can, in principle, outperform the best non-quantum (classical) techniques for some hard computational problems. However, this does not necessarily lead to useful applications. To gauge the practical…
The maximum/minimum bisection problems are, given an edge-weighted graph, to find a bipartition of the vertex set into two sets whose sizes differ by at most one, such that the total weight of edges between the two sets is…
This paper considers the projection-free sparse convex optimization problem for the vector domain and the matrix domain, which covers a large number of important applications in machine learning and data science. For the vector domain…