Related papers: Counting single-qubit Clifford equivalent graph st…
We describe an algorithm with quasi-polynomial runtime $n^{\log_2(n)+O(1)}$ for deciding local unitary (LU) equivalence of graph states. The algorithm builds on a recent graphical characterisation of LU-equivalence via generalised local…
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…
Verifying prepared quantum states is crucial for hybrid systems whose subsystems may have different local dimensions. We present a generalized stabilizer framework and associated test that apply to general multi-qudit states, including…
We introduce a class of multiqubit quantum states which generalizes graph states. These states correspond to an underlying mathematical hypergraph, i.e. a graph where edges connecting more than two vertices are considered. We derive a…
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 and their entanglement properties are pivotal for the development of quantum computing and technologies. For qubits, local complementation, a graphical rule that connects all the equivalent states under Local Clifford (LC)…
A graph state and a graph code respectively are defined based on a mathematical simple graph. In this work, we examine a relation between a graph state and a graph code both obtained from the same graph, and show that a graph state is a…
The classification of stabilizer states under local Clifford (LC) equivalence is of particular importance in quantum error-correction and measurement-based quantum computation. Two stabilizer states are called LC equivalent if there exists…
Any 8-qubit graph state belongs to one of the 101 equivalence classes under local unitary operations within the Clifford group. For each of these classes we obtain a representative which requires the minimum number of controlled-Z gates for…
We propose a method to calculate the purity of reduced states of graph states entirely within the stabilizer formalism, using only the stabilizer generators for a given state. We apply this method to find the Concentratable Entanglement of…
Graph states are multi-particle entangled states that correspond to mathematical graphs, where the vertices of the graph take the role of quantum spin systems and edges represent Ising interactions. They are many-body spin states of…
Deciding if a given family of quantum states is topologically ordered is an important but nontrivial problem in condensed matter physics and quantum information theory. We derive necessary and sufficient conditions for a family of graph…
In quantum computing and quantum information processing, graph states are a specific type of quantum states which are commonly used in quantum networking and quantum error correction. A recurring problem is finding a transformation from a…
The class of entangled $N$-qubit states known as graph states, and the corresponding stabilizer groups of $N$-qubit Pauli observables, have found a wide range of applications in quantum information processing and the foundations of quantum…
The form of a local Clifford (LC, also called local Gaussian (LG)) operation for the continuous-variable (CV) weighted graph states is presented in this paper, which is the counterpart of the LC operation of local complementation for qubit…
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…
Following on our previous work arXiv:2204.07593 and arXiv:2306.01043 studying the orbits of quantum states under Clifford circuits via `reachability graphs', we introduce `contracted graphs' whose vertices represent classes of quantum…
Graph states are the main computational building blocks of measurement-based computation and a useful tool for error correction in the gate model architecture. The graph states form a class of quantum states which are eigenvectors for the…
Verification is a task to check whether a given quantum state is close to an ideal state or not. In this paper, we show that a variety of many-qubit quantum states can be verified with only sequential single-qubit measurements of Pauli…
We tackle the problem of Clifford isometry compilation, i.e, how to synthesize a Clifford isometry into an executable quantum circuit. We propose a simple framework for synthesis that only exploits the elementary properties of the Clifford…