# 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.

17 questions
Filter by
Sorted by
Tagged with
129 views

### 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 ...
36 views

### Quantum Error Correcting Codes and Graphs

Couple of weeks ago I asked this question on theory CS but I didn't get an answer. So trying it here. I was reading combinatorial approach towards quantum correction. A lot of work in this is on ...
131 views

### 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 ...
66 views

### 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 ...
75 views

### 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 ...
43 views

### 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?
40 views

### $X$ 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 $|G\rangle$,...
37 views

### 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 ...
39 views

### 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 ...
64 views

### 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 for a graph $G = (V,E)$ and $B = V\setminus A$ the corresponding complement ...
52 views

### Dephasing in graph states

In a recent paper Graph States as a Resource for Quantum Metrology. In the Appendix it states: We model an $n$ qubit graph state $G$ undergoing iid dephasing via G \to G^{\text{dephasing}} = \...
225 views

### 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 ...
43 views

### 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,...
258 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 ...
77 views

### 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?