Related papers: Counting single-qubit Clifford equivalent graph st…
The Clifford group is the set of gates generated by the controlled not gates, the Hadamard gate and the P={{1,0},{0,i}} gate. We will say that a n-qubit state is a Clifford state if it can be prepared using Clifford gates. In this paper we…
A set of Pauli stings is well characterized by the graph that encodes its commutatitivity structure, i.e., by its frustration graph. This graph provides a natural interface between graph theory and quantum information, which we explore in…
We investigate a graph-theoretic approach to the problem of distinguishing quantum product states in the fundamental quantum communication framework called local operations and classical communication (LOCC). We identify chordality as the…
Highly entangled multipartite states such as k-uniform (k-UNI) and absolutely maximally entangled (AME) states serve as critical resources in quantum networking and other quantum information applications. However, there does not yet exist a…
Gibbs states of an infinite system of interacting quantum particles are considered. Each particle moves on a compact Riemannian manifold and is attached to a vertex of a graph (one particle per vertex). Two kinds of graphs are studied: (a)…
Graph states (or cluster states) are the entanglement resource that enables one-way quantum computing. They can be grown by projective measurements on the component qubits. Such measurements typically carry a significant failure…
We present a quantum circuit compiler that prepares an algorithm-specific graph state from quantum circuits described in high level languages, such as Cirq and Q#. The computation can then be implemented using a series of non-Pauli…
The Pauli groups are ubiquitous in quantum information theory because of their usefulness in describing quantum states and operations and their readily understood symmetry properties. In addition, the most well-understood quantum error…
Given a graph $G$, the graph $[G]$ obtained by adding, for each pair of vertices of $G$, a unique vertex adjacent to both vertices is called the binding graph of $G$. In this work, we show that the class of binding graphs is…
Characterizing the non-classical correlations of a complex many-body system is an important part of quantum technologies. A versatile tool for such a task is one that scales well with the size of the system and which can be both easily…
The graph isomorphism problem is theoretically interesting and also has many practical applications. The best known classical algorithms for graph isomorphism all run in time super-polynomial in the size of the graph in the worst case. An…
Measurement based quantum computing is preformed by adding non-Clifford measurements to a prepared stabilizer states. Entangling gates like CZ are likely to have lower fidelities due to the nature of interacting qubits, so when preparing a…
We consider graph states generated by the action of controlled phase shift operators on a separable state of a multi-qubit system. The case when all the qubits are initially prepared in arbitrary states is investigated. We obtain the…
Hypergraph states form a family of multiparticle quantum states that generalizes cluster states and graph states. We study the action and graphical representation of nonlocal unitary transformations between hypergraph states. This leads to…
Hypergraph states are multiqubit states whose combinatorial description and entanglement properties generalize the well-studied class of graph states. Graph states are important in applications such as measurement-based quantum computation…
We investigate the Bell inequalities derived from the graph states with violations detectable even with the presence of noises, which generalizes the idea of error-correcting Bell inequalities [Phys. Rev. Lett. 101, 080501 (2008)]. Firstly…
In this work, we present a novel method to express the stabilizer of a k-uniform complete hypergraph state as a linear combination of local operators. Quantum hypergraph states generalize graph states and exhibit properties that are not…
The ZX-calculus is a graphical calculus for reasoning about quantum systems and processes. It is known to be universal for pure state qubit quantum mechanics, meaning any pure state, unitary operation and post-selected pure projective…
It is confirmed in this work that the graph isomorphism can be tested in polynomial time, which resolves a longstanding problem in the theory of computation. The contributions are in three phases as follows. 1. A description graph…
As it follows from G\"odel's incompleteness theorems, any consistent formal system of axioms and rules of inference should imply a true unprovable statement. Actually, this fundamental principle can be efficiently applicable in…