# 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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### 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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### 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 ...
• 3,807
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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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### 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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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.
• 1,870
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
118 views

### 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 ...
• 11
1 vote
151 views

### 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 ...
• 1,420
1 vote
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^{...