# 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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### 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 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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### 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 ...
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?