# 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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### 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 ...
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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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### 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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### 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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### Finding all small stabilizer codes

Given some choice of parameters $[[n,k,d]]$ with $n$ small, is there any computationally easy way to find all of (or at least many of) the stabilizer codes with those parameters? For certain ...
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### Difference between a star graph state and GHZ graph state

I saw in a class that star state and GHZ state are local-Clifford equivalent (Hadamard on n-1 qubits for a n star state). But then, when I wanted to draw a GHZ state and check on the litterature ...
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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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### 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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### 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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### 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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### 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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### $X$ 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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### 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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### 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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### Distance of one dimensional quantum error correcting code

Consider one dimensional quantum codes $[[ n,k=0]]$. One way to describe them is using stabilizer framework with $n$ independent Pauli matrices. Usually, one considers them in the graph state model ...
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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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### 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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### 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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### 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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### Entanglement entropy for graph states defined on a tree graph

Consider a $k-\text{ary}$ tree $T$, for a constant $k$. Consider the corresponding graph state $|\mathsf{G}_T \rangle$ that is defined on $T$. Is it true that $|\mathsf{G}_T \rangle$ saturates the ...
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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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