Related papers: Preparing graph states forbidding a vertex-minor
In this work, we study the complexity of graph-state preparation. We consider general quantum algorithms consisting of Clifford operations acting on at most two qubits for graph-state preparations. We define the CZ-complexity of a graph…
A set $Z$ of vertices of a graph $G$ is a zero forcing set of $G$ if initially labeling all vertices in $Z$ with $1$ and all remaining vertices of $G$ with $0$, and then, iteratively and as long as possible, changing the label of some…
We start by studying the subgroup structures underlying stabilizer circuits and we use our results to propose a new normal form for stabilizer circuits. This normal form is computed by induction using simple conjugation rules in the…
Stabilizer states form an important class of states in quantum information, and are of central importance in quantum error correction. Here, we provide an algorithm for deciding whether one stabilizer (target) state can be obtained from…
We show how to prepare any graph state of up to 12 qubits with: (a) the minimum number of controlled-Z gates, and (b) the minimum preparation depth. We assume only one-qubit and controlled-Z gates. The method exploits the fact that any…
Let $G$ be a connected graph of order $n$.The Wiener index $W(G)$ of $G$ is the sum of the distances between all unordered pairs of vertices of $G$. In this paper we show that the well-known upper bound $\big( \frac{n}{\delta+1}+2\big) {n…
While stabilizer tableaus have proven useful as a descriptive tool for additive quantum codes, they otherwise offer little guidance for concrete constructions or algorithm analysis. We introduce a representation of stabilizer codes as…
While a number of bounds are known on the zero forcing number $Z(G)$ of a graph $G$ expressed in terms of the order of a graph and maximum or minimum degree, we present two bounds that are related to the (upper) total domination number…
We study the notion of $k$-stabilizer universal quantum state, that is, an $n$-qubit quantum state, such that it is possible to induce any stabilizer state on any $k$ qubits, by using only local operations and classical communications.…
The circumference denoted by $c(G)$ of a graph $G$ is the length of its longest cycle. Let $\delta(G)$ and $\omega(G)$ denote the minimum degree and the clique number of a graph $G$, respectively. In [\emph{Electron. J. Combin.} 31(4)(2024)…
Graph states are a class of multi-partite entangled quantum states that are ubiquitous in quantum information. We study equivalence relations between graph states under local unitaries (LU) to obtain distinguishing methods both in local and…
Graph states are ubiquitous in quantum information with diverse applications ranging from quantum network protocols to measurement based quantum computing. Here we consider the question whether one graph (source) state can be transformed…
Let $G$ be a graph of order $n$. A classical upper bound for the domination number of a graph $G$ having no isolated vertices is $\lfloor\frac{n}{2}\rfloor$. However, for several families of graphs, we have $\gamma(G) \le…
Verifying quantum states is central to certifying the correct operation of various quantum information processing tasks. In particular, in measurement-based quantum computing, checking whether correct graph states are generated is essential…
Motivated by an old question of Gallai (1966) on the intersection of longest paths in a graph and the well-known conjectures of Lov\'{a}sz (1969) and Thomassen (1978) on the maximum length of paths and cycles in vertex-transitive graphs, we…
We study the hardness of the problem of finding the distance of quantum error-correcting codes. The analogous problem for classical codes is known to be NP-hard, even in approximate form. For quantum codes, various problems related to…
Graph states are a fundamental class of multipartite entangled quantum states with wide-ranging applications in quantum information and computation. In this work, we develop a systematic framework for constructing and analyzing…
Highly entangled quantum states are an ingredient in numerous applications in quantum computing. However, preparing these highly entangled quantum states on currently available quantum computers at high fidelity is limited by ubiquitous…
The graph state formalism is a useful abstraction of entanglement. It is used in some multipartite purification schemes and it adequately represents universal resources for measurement-only quantum computation. We focus in this paper on the…
The equivalence of stabilizer states under local transformations is of fundamental interest in understanding properties and uses of entanglement. Two stabilizer states are equivalent under the usual stochastic local operations and classical…