Related papers: Toward Minimum Graphic Parity Networks

Let $G$ be an $n$-vertex graph with $m$ edges. When asked a subset $S$ of vertices, a cut query on $G$ returns the number of edges of $G$ that have exactly one endpoint in $S$. We show that there is a bounded-error quantum algorithm that…

The growing variety of quantum hardware technologies, each with unique peculiarities such as connectivity and native gate sets, creates challenges when selecting the best platform for executing a specific quantum circuit. This selection…

Topological quantum computing has recently proven itself to be a very powerful model when considering large- scale, fully error corrected quantum architectures. In addition to its robust nature under hardware errors, it is a software driven…

The vertex connectivity of a graph $G$ is the size of the smallest set of vertices $S$ such that $G \setminus S$ is disconnected. For the class of planar graphs, the problem of vertex connectivity is well-studied, both from structural and…

Given an undirected, unweighted graph with $n$ vertices and $m$ edges, the maximum cut problem is to find a partition of the $n$ vertices into disjoint subsets $V_1$ and $V_2$ such that the number of edges between them is as large as…

This work shows that minimizing the depth of a quantum circuit composed of commuting operations reduces to a vertex coloring problem on an appropriately constructed graph, where gates correspond to vertices and edges encode…

NISQ devices have inherent limitations in terms of connectivity and hardware noise. The synthesis of CNOT circuits considers the physical constraints and transforms quantum algorithms into low-level quantum circuits that can execute on…

We perform optimal-control-theory calculations to determine the minimum number of two-qubit CNOT gates needed to perform quantum state preparation and unitary operator synthesis for few-qubit systems. By considering all possible gate…

We study a variant of the subgraph isomorphism problem that is of high interest to the quantum computing community. Our results give an algorithm to perform pattern matching in quantum circuits for many patterns simultaneously,…

Motivated by the increasing need to understand the algorithmic foundations of distributed large-scale graph computations, we study a number of fundamental graph problems in a message-passing model for distributed computing where $k \geq 2$…

A graph $G=(V,E)$ is a {\it unipolar graph} if there exits a partition $V=V_1 \cup V_2$ such that, $V_1$ is a clique and $V_2$ induces the disjoint union of cliques. The complement-closed class of {\it generalized split graphs} are those…

We study the problem of CNOT-optimal quantum circuit synthesis over gate sets consisting of CNOT and Z-basis rotations of arbitrary angles. We show that the circuit-polynomial correspondence relates such circuits to Fourier expansions of…

We present an algorithm for compiling arbitrary unitaries into a sequence of gates native to a quantum processor. As accurate CNOT gates are hard for the foreseeable Noisy- Intermediate-Scale Quantum devices era, our A* inspired algorithm…

In the paper, we consider quantum circuits for the Quantum Fourier Transform (QFT) algorithm. The QFT algorithm is a very popular technique used in many quantum algorithms. We present a generic method for constructing quantum circuits for…

We present methods for constructing any target coupling graph using limited global controls in an Ising-like quantum spin system. Our approach is motivated by implementing the quantum approximate optimization algorithm (QAOA) on trapped ion…

Distributed graph signal processing algorithms require the network nodes to communicate by exchanging messages in order to achieve a common objective. These messages have a finite precision in realistic networks, which may necessitate to…

We study graph connectivity problem in MPC model. On an undirected graph with $n$ nodes and $m$ edges, $O(\log n)$ round connectivity algorithms have been known for over 35 years. However, no algorithms with better complexity bounds were…

Connectivity (or equivalently, unweighted maximum flow) is an important measure in graph theory and combinatorial optimization. Given a graph $G$ with vertices $s$ and $t$, the connectivity $\lambda(s,t)$ from $s$ to $t$ is defined to be…

Linear Nearest Neighbor (LNN) synthesis in reversible circuits has emerged as an important issue in terms of technological implementation for quantum computation. The objective is to obtain a LNN architecture with minimum gate cost. As…

Many combinatorial optimization problems can be phrased in the language of constraint satisfaction problems. We introduce a graph neural network architecture for solving such optimization problems. The architecture is generic; it works for…