Share Your Experience: Take the 2024 Developer Survey

# 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.

42 questions
Filter by
Sorted by
Tagged with
103 views

### 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 <...
36 views

### 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 ...
321 views

### 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 ...
71 views

### 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 ...
1 vote
121 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 ...
157 views

### 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 ...
1 vote
29 views

### 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 vote
85 views

### 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
49 views

### 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
36 views

402 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 ...
79 views

### 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 ...
165 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 ...
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 vote
107 views

142 views

### 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 ...
89 views

### 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 ...
88 views

### 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 ...
646 views

### 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?
131 views

### 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 ...
108 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,...
161 views

132 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 of a graph $G = (V,E)$ and $B = V\setminus A$ the complement of $A$ in $V$. ...
243 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 $|G\rangle$,...
1 vote
2k views

### 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. ...
1 vote
201 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 ...
134 views

### Does Qiskit offer a stack of functions to generate and manipulate graph states?

I'm looking for a way to test graph state verification protocols on the IBM Q. Has anyone yet written code to generate a graph state on IBM Q and also generate its stabilizer generators given the ...
1 vote
399 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 ...
209 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?
276 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 ...
67 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 ...
367 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 ...
464 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 ...
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?