Quantum Computing Stack Exchange
Quantum Computing Stack Exchange

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 defining graph states using $d$-dimensional qudits,…
SLesslyTall
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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 $V$. The reduced state $\rho_{G}^{A}:=…
John Doe
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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 whether or not I got it right, it seemed as a lot of…
MohamedSU
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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 parameters this is easy, for example it is known that…
Ian Gershon Teixeira
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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?
narip
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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 $$G \to G^{\text{dephasing}} = \sum_{\vec{k}}p^{k}(1-p)^{n-k}Z_{\vec{k}}GZ_{\vec{k}}$$…
John Doe
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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 graph state $|G\rangle$ that corresponds to the…
John Doe
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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 adjacency matrix) to a set of stabilizers and the corresponding…
unknown
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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 there any particular rule? And by looking at a…
Upstart
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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, does it mean that my problem has to have at most…
Kenenbek Arzymatov
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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?
SLesslyTall
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Graph Limits in Quantum Computing

Lovasz's book Large networks and Graph Limits mentions that their study of graph limits is motivatived applications to quantum computers, statistical physics, and models for the internet. They don't mention any specific applications in quantum…
user22511
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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} := c_0 I - \tilde{S}_{k}^{(GHZ_N)} -…
John Doe
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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 $|G\rangle$, and the $/$ symbol denotes contraction of an…
NNN
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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 band-coloring method" on page 8 as well. I've been…
QCQCQC
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