Questions tagged [graph-states]

Graph-states are a class of quantum state that can be efficiently and uniquely represented by graphs. In the case of qubit graph states, each edge corresponds to a CZ operation applied between two qubits in the +1 X eigenstate. Graph states have a number of useful properties that make them useful objects for the analysis of large quantum systems and play a prominent role in the analysis of quantum computation and communication architectures and protocols.

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Quantum Mathematics with Linear Algebra [closed]

Consider the 4-cycle graph G with edges (1, 2), (2,3), (3, 4), and (1,4). Construct the corresponding graph state (@G) without the second bank of Hadamard gates. Call the nodes Alice, Bob, Charlie, ...
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How to measure and get the result in a Graph state

According to this definition, suppose I have a graph on $3$ vertices, $v_1,v_2,v_3$, such that I have the Graph state vector $$|G\rangle= |0++\rangle+|1++\rangle$$ Suppose I have a secret say $S=1$,so ...
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Quantum Graph state paper query (Phy Rev A)

The authors of the paper Graph States for Quantum Secret Sharing https://journals.aps.org/pra/abstract/10.1103/PhysRevA.78.042309 define a 'labeled state' as $$|G_{\vec{l}}\rangle=\bigotimes_{i}X_i^{...
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Possible typo in the paper "Graph states for quantum secret sharing"

Continuing from my last question that I posted about a paper on Graph States. I have another doubt regarding a possible typo error in the paper. Here it goes. The authors define a 'labeled state' as $$...
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Quantum Graph states hand computation

I am reading an article on Quantum Graph states. I wanted to ask a few questions. The Graph state is $$|G\rangle=\prod_{e\in G}CZ |+\rangle^{\otimes n}$$ Now my first question is if I apply the ...
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Unitary interaction term of two-qubit graph state

Consider the controlled phase gate $$U_{ab}(\varphi_{ab}) := e^{-i \varphi_{ab}H_{ab}}~~~~\text{where}~~~~H_{ab} := |1 \rangle^{a} \langle 1 | \otimes |1 \rangle^{b} \langle 1 |$$ is the two-qubit ...
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Graph States subjected to finite erasures

The appendix to the paper Graph States as a Resource for Quantum Metrology states that when graph states subjected to finite erasures, $$G\Rightarrow Tr_\vec{y}G.$$ While more explicitly he explains ...
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How can one check whether a given quantum state is a graph state?

We can build a quantum state from a graph, which is a mathematical concept. But, vice versa, how can one check whether or not a given quantum state is a graph state?
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How are the two definitions of graph state mathematically equivalent?

There are at least two definitions of Graph State, two of them are shown in Wikipedia. The first definition is via quantum states, while the second one is from the point of view of the stabilizer ...
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Entanglement Witnesses close to GHZ states

Consider page 2 of Toth's paper 'Entanglement detection in the stabilizer formalism (2005)'. To detect entanglement close to GHZ states, they construct entanglement witnesses of the form $$\mathcal{W} ...
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QiskitError: 'No statevector for experiment

This is the code that I have used. Why can't i use get_statevecto when i use quantum computer. I got a state_vector when i have used qasm_simulator. ...
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Does Qiskit offer a stack of functions to generate and manipulate graph states?

I'm looking for a way to test graph state verification protocols on the IBM Q. Has anyone yet written code to generate a graph state on IBM Q and also generate its stabilizer generators given the ...
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Quantum Error Correcting Codes and Graphs

Couple of weeks ago I asked this question on theory CS but I didn't get an answer. So trying it here. I was reading combinatorial approach towards quantum correction. A lot of work in this is on ...
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Creating a specific cluster state

I have a state $$\dfrac{1}{2}(|00000\rangle+|00111\rangle+|11101\rangle+|11010\rangle).$$ How does one create this state? In general, how does one create for instance an $n$-bit cluster state, is ...
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Transferring GHZ state onto some qubits

This question is just my effort that I made by understanding the previous answers to my questions . I have a GHZ state $|000\rangle+|111\rangle$ (please ignore the normalizing constant). For ...
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Cluster/Graph state teleportation

I came across somewhere about the circuit diagram that depicts the teleportation of a 4-qubit cluster state. Here it is Let me tell what i understood. The qubits on the first two wires give the state ...
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Quantum Circuit explaination

I have a circuit that generates a 4 qubit linear cluster. The steps i understand are Initialize the 4 qubits to $|0000\rangle$. Apply Hadamard $H$ on all. Then apply a controlled $Z$ gate . All ...
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Is there a tool that shows me all $2^n$ stabilizers for a given graph state?

Is there a tool which takes the adjacency matrix of a graph as input and prints out a table with all stabilizer measurements?
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Constructing an eigenbasis of graph states for a set of stabilizers

The stabilizers of a given graph all commute, thus it must be possible to diagonalize them simultaneously. If I start with one graph state and write down all its stabilizers is there an easy way to ...
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$X$ measurement on graph state leads to edge contraction

I cannot understand the proof of Lemma 5 from the paper "Resources Required for Preparing Graph States". Here it is: (In this paper, $|G:S\rangle$ denotes $Z_S$ applied to the graph state $|G\rangle$,...
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Graph coloring to reduce the number of qubits in VQE

I am reading through the following article: https://arxiv.org/abs/1312.2579 and I really struggle to understand anything of the section "D. The standard graph-coloring method" on page 7 and "E. The ...
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Query on Reduced Graph States

Reduced graph states are characterized as follows (from page 46 of this paper): Let $A \subseteq V$ be a subset of vertices of a graph $G = (V,E)$ and $B = V\setminus A$ the complement of $A$ in $V$. ...
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Dephasing in graph states

The Appendix to a recent paper Graph States as a Resource for Quantum Metrology states: We model an $n$ qubit graph state $G$ undergoing iid dephasing via $$G \to G^{\text{dephasing}} = \sum_{\vec{...
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Query on paper on entanglement in graph states

Quick question on the paper Entanglement in Graph States. On page 14. a definition of a graph state: Given $|+\rangle=\frac{1}{\sqrt{2}}(|0\rangle + |1\rangle)$. Let $G=(V,E)$ be a graph. The ...
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What does it mean to have 2000 qubits and 6016 couplers?

From official D-Wave docs: The D-Wave 2000Q QPU has up to 2048 qubits and 6016 couplers. For example, I have the optimization problem defined as the QUBO problem. If I want to solve it on D-Wave,...
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Graph state and maximally entangled state

How can I show that a multi-qudit graph state $|G\rangle$ is the maximally entangled state? What kind of measure of entanglement can be used to quantify the amount of entanglement in a given graph ...
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The classical simulation of 2D graph state and the measurement based quantum computation

In my former post on Physics SE I deduced a contradiction in the classical simulation of 2D graph state and the classical simulation of general measurement-based quantum computation. In Norbert's ...
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How to calculate the number of ebits in a graph state?

Given an arbitrary graph state $|G\rangle$ represented by the graph $G$, can one use the graphical structure to calculate the number of ebits (entanglement bits) present in the state? If so, how?
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Does local Clifford equivalence have a direct graphical representation for qudit graph states of non-prime dimension?

This question is a follow-up to the previous QCSE question: "Are qudit graph states well-defined for non-prime dimension?". From the question's answer, it appears that there is nothing wrong in ...