Related papers: Quantum property testing for bounded-degree graphs

We initiate the study of parameterized complexity of $\textsf{QMA}$ problems in terms of the number of non-Clifford gates in the problem description. We show that for the problem of parameterized quantum circuit satisfiability, there exists…

Quantum searching for one of $N$ marked items in an unsorted database of $n$ items is solved in $\mathcal{O}(\sqrt{n/N})$ steps using Grover's algorithm. Using nonlinear quantum dynamics with a Gross-Pitaevskii type quadratic nonlinearity,…

We deal with the problem, initiated in [8], of finding randomized and quantum complexity of initial-value problems. We showed in [8] that a speed-up in both settings over the worst-case deterministic complexity is possible. In the present…

We present a bounded-error quantum algorithm for evaluating Min-Max trees. For a tree of size N our algorithm makes N^{1/2+o(1)} comparison queries, which is close to the optimal complexity for this problem.

Only a few classes of quantum algorithms are known which provide a speed-up over classical algorithms. However, these and any new quantum algorithms provide important motivation for the development of quantum computers. In this article new…

We present two new quantum algorithms that either find a triangle (a copy of $K_{3}$) in an undirected graph $G$ on $n$ nodes, or reject if $G$ is triangle free. The first algorithm uses combinatorial ideas with Grover Search and makes…

Shor's and Grover's famous quantum algorithms for factoring and searching show that quantum computers can solve certain computational problems significantly faster than any classical computer. We discuss here what quantum computers_cannot_…

In this paper we study quantum algorithms for NP-complete problems whose best classical algorithm is an exponential time application of dynamic programming. We introduce the path in the hypercube problem that models many of these dynamic…

This paper explores Quantum Search on the two dimensional spatial grid. Recent exploration into the topic has devised a solution that runs in O(sqrt(n*ln(n))). This paper explores a new algorithm that gives promise for the O(sqrt(n)) result…

We experimentally evaluate the practical state-of-the-art in graph bipartization (Odd Cycle Transversal), motivated by recent advances in near-term quantum computing hardware and the related embedding problems. We assemble a preprocessing…

We examine the number T of queries that a quantum network requires to compute several Boolean functions on {0,1}^N in the black-box model. We show that, in the black-box model, the exponential quantum speed-up obtained for partial functions…

We construct a quantum searching model of a signed edge driven by a quantum walk. The time evolution operator of this quantum walk provides a weighted adjacency matrix induced by the assignment of sign to each edge. This sign can be…

We propose a complete quantum-classical hybrid branch-and-bound algorithm (QCBB) to solve binary linear programs with equality constraints. That includes bound calculation, convergence metrics and optimality guarantee to the quantum…

As a fundamental metric for quantifying quantum advantage in non-local games, the quantum chromatic number reveals the power of entanglement in distributed tasks. In this paper, we investigate this parameter for $q$-ary Hamming graphs and a…

The minimum cut problem in an undirected and weighted graph $G$ is to find the minimum total weight of a set of edges whose removal disconnects $G$. We completely characterize the quantum query and time complexity of the minimum cut problem…

Programmable quantum systems based on Rydberg atom arrays have recently emerged as a promising testbed for combinatorial optimization. Indeed, the Maximum Weighted Independent Set problem on unit-disk graphs can be efficiently mapped to…

Quantum computers show potential for achieving computational advantage over classical computers, with many candidate applications in combinatorial optimisation. We present an application level benchmarking framework for near-term quantum…

Probabilistic graphical models play a crucial role in machine learning and have wide applications in various fields. One pivotal subset is undirected graphical models, also known as Markov random fields. In this work, we investigate the…

We present a quantum algorithm that verifies a product of two n*n matrices over any field with bounded error in worst-case time n^{5/3} and expected time n^{5/3} / min(w,sqrt(n))^{1/3}, where w is the number of wrong entries. This improves…

Grover Search is currently one of the main quantum algorithms leading to hybrid quantum-classical methods that reduce the worst-case time complexity for some combinatorial optimization problems. Specifically, the combination of Quantum…