Properties of multiqubit variational quantum states representing weighted graphs and their computing with quantum programming

• URL: http://arxiv.org/abs/2604.00958v1
• Date: Wed, 01 Apr 2026 14:33:09 GMT
• Title: Properties of multiqubit variational quantum states representing weighted graphs and their computing with quantum programming
• Abstract summary: We study multiqubit variational quantum states that can be considered as weighted quantum graph states.<n>We derive the geometric measure of entanglement and evaluate quantum correlators.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study multiqubit variational quantum states that can be considered as weighted quantum graph states. These states are constructed as single-layer variational circuits with $RX$ rotations and $RZZ$ entangling gates, corresponding to graphs of arbitrary structure. In general case of quantum graph states of arbitrary structure we derive the geometric measure of entanglement and evaluate quantum correlators. It is shown that these quantities are directly related to the degrees of the corresponding vertices in graph. As an example, we analyze the state associated with the star graph $K_{1,4}$ using noisy quantum computing on the AerSimulator. The results are in good agreement with theoretical predictions. These findings demonstrate a connection between graph structure and quantum properties, enabling the study of classical graphs via quantum computing.

Related papers

• Entanglement of multi-qubit quantum graph states and studies structural properties of tripartite graphs with quantum programming [0.0]
  We propose a method for constructing multi-qubit entangled quantum states representing weighted tripartite graphs.<n>An expression for the entanglement distance for multi-qubit states corresponding to arbitrary tripartite graph structures is obtained.
  arXiv  Detail & Related papers  (2026-04-30T13:18:04Z)
• Quantum Graph Theory by Example [0.0]
  We present a collection of non-trivial quantum graphs that can be thought of in discrete terms.<n>The examples arise as the quantum graphs acted on by increasingly smaller classical matrix groups.<n>We give exact formulas or establish bounds for quantum graph parameters.
  arXiv  Detail & Related papers  (2026-03-24T18:51:14Z)
• Studies of properties of bipartite graphs with quantum programming [0.0]
  Multi-qubit quantum states corresponding to bipartite graphs $G(U,V,E)$ are examined.<n>The entanglement distance of the resulting states is derived analytically for an arbitrary bipartite graph structure.
  arXiv  Detail & Related papers  (2025-07-22T14:49:57Z)
• High-dimensional graphs convolution for quantum walks photonic applications [41.94295877935867]
  We suggest a new method for lattices and hypercycle convolution that preserves quantum walk dynamics.<n>Our findings may be useful for saving a significant number of qubits required for algorithms that use quantum walk simulation on quantum devices.
  arXiv  Detail & Related papers  (2025-07-21T18:28:34Z)
• Many-body quantum resources of graph states [0.0]
  Characterizing the non-classical correlations of a complex many-body system is an important part of quantum technologies. We consider four topologies, namely the star graph states with edges, Tur'an graphs, $r$-ary tree graphs, and square grid cluster states. We characterize many-body entanglement depth in graph states with up to $8$ qubits in $146$ classes non-equivalent under local transformations and graph isomorphisms.
  arXiv  Detail & Related papers  (2024-10-16T12:05:19Z)
• Entanglement of multi-qubit states representing directed networks and its detection with quantum computing [0.0]
  We consider quantum graph states that can be mapped to directed weighted graphs, also known as directed networks. The geometric measure of entanglement of the states is calculated for the quantum graph states corresponding to arbitrary graphs.
  arXiv  Detail & Related papers  (2024-07-13T19:36:11Z)
• QuanGCN: Noise-Adaptive Training for Robust Quantum Graph Convolutional Networks [124.7972093110732]
  We propose quantum graph convolutional networks (QuanGCN), which learns the local message passing among nodes with the sequence of crossing-gate quantum operations. To mitigate the inherent noises from modern quantum devices, we apply sparse constraint to sparsify the nodes' connections. Our QuanGCN is functionally comparable or even superior than the classical algorithms on several benchmark graph datasets.
  arXiv  Detail & Related papers  (2022-11-09T21:43:16Z)
• Compilation of algorithm-specific graph states for quantum circuits [55.90903601048249]
  We present a quantum circuit compiler that prepares an algorithm-specific graph state from quantum circuits described in high level languages. The computation can then be implemented using a series of non-Pauli measurements on this graph state.
  arXiv  Detail & Related papers  (2022-09-15T14:52:31Z)
• From Quantum Graph Computing to Quantum Graph Learning: A Survey [86.8206129053725]
  We first elaborate the correlations between quantum mechanics and graph theory to show that quantum computers are able to generate useful solutions. For its practicability and wide-applicability, we give a brief review of typical graph learning techniques. We give a snapshot of quantum graph learning where expectations serve as a catalyst for subsequent research.
  arXiv  Detail & Related papers  (2022-02-19T02:56:47Z)
• Benchmarking Small-Scale Quantum Devices on Computing Graph Edit Distance [52.77024349608834]
  Graph Edit Distance (GED) measures the degree of (dis)similarity between two graphs in terms of the operations needed to make them identical. In this paper we present a comparative study of two quantum approaches to computing GED.
  arXiv  Detail & Related papers  (2021-11-19T12:35:26Z)
• Geometric measure of entanglement of multi-qubit graph states and its detection on a quantum computer [0.0]
  The entanglement of a qubit with other qubits is found for the graph states represented by arbitrary graphs. The geometric measure of entanglement of the graph states is quantified on the quantum computer.
  arXiv  Detail & Related papers  (2021-06-20T12:47:09Z)
• Graph-Theoretic Framework for Self-Testing in Bell Scenarios [37.067444579637076]
  Quantum self-testing is the task of certifying quantum states and measurements using the output statistics solely. We present a new approach for quantum self-testing in Bell non-locality scenarios.
  arXiv  Detail & Related papers  (2021-04-27T08:15:01Z)
• Spectra of Perfect State Transfer Hamiltonians on Fractal-Like Graphs [62.997667081978825]
  We study the spectral features, on fractal-like graphs, of Hamiltonians which exhibit the special property of perfect quantum state transfer. The essential goal is to develop the theoretical framework for understanding the interplay between perfect quantum state transfer, spectral properties, and the geometry of the underlying graph.
  arXiv  Detail & Related papers  (2020-03-25T02:46:14Z)
• PBS-Calculus: A Graphical Language for Coherent Control of Quantum Computations [77.34726150561087]
  We introduce the PBS-calculus to represent and reason on quantum computations involving coherent control of quantum operations. We equip the language with an equational theory, which is proved to be sound and complete. We consider applications like the implementation of controlled permutations and the unrolling of loops.
  arXiv  Detail & Related papers  (2020-02-21T16:15:58Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.