# 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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### Are these two codes the same?

There is an $((11,2,5))$ CWS code given in table B2 at the end of https://kth.diva-portal.org/smash/get/diva2:894450/FULLTEXT01.pdf I know that some CWS codes are equivalent to stabilizer codes, but ...
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### How to get the surviving stabilisers of a fusion network

In Fig. 5 of PsiQuantum's Fusion-based quantum computation paper, it's clear to me how to get R, F, and C. How do I get S? Just by looking at (a), I could obviously tell you that we end up with <...
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### Finding all small (e.g. 7 qubit) 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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1 vote
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### Do we have a sample of interest for Graph State Generation?

I'd like to do some tests on Graph State Generation algorithms. Rather than generating random $CZ$ operator, it would be nice to have a sample online of given circuits.
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### how to go from a stabilizer state to a graph

A comment (by Marcus Heinrich) in a previous post says : "any stabiliser state is locally Clifford equivalent to a graph state and vice versa". I can go from a graph (defined by its ...
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1 vote
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### Representing networks with qubits as edges

I am looking to take a classical non-negative real valued network and generalize it to the quantum case for processing. A network is given by an adjacency matrix, essentially edge weights $e_{ij}$ for ...
1 vote
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### Solving max/min problem for graphs based on Grover

Basis is for this post ist the paper https://arxiv.org/pdf/1902.00445.pdf I want to do something similar using graph data encoded in quantum states. The circuit structure should look like this (first ...
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1 vote
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### What is the structure of quantum graph code [[4,0,3]]? Or does it exist? [closed]

What is the structure of quantum graph code [[4,0,3]]? Or does it exist? How the edges are connected?
1 vote
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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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### 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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1 vote
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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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1 vote
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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,...
468 views

### 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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