The construction and local distinguishability of multiqubit unextendible product bases

• URL: http://arxiv.org/abs/2102.11553v1
• Date: Tue, 23 Feb 2021 08:50:19 GMT
• Title: The construction and local distinguishability of multiqubit unextendible product bases
• Authors: Yize Sun, Lin Chen
• Abstract summary: An important problem in quantum information is to construct multiqubit unextendible product bases (UPBs) We show that the UPB is locally indistinguishable in the bipartite systems of two qubits and five qubits, respectively. Taking the graphs as product vectors, we show that they are in three different orbits up to local unitary equivalence.
• Score: 7.238541917115604
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: An important problem in quantum information is to construct multiqubit unextendible product bases (UPBs). By using the unextendible orthogonal matrices, we construct a 7-qubit UPB of size 11. It solves an open problem in [Quantum Information Processing 19:185 (2020)]. Next, we graph-theoretically show that the UPB is locally indistinguishable in the bipartite systems of two qubits and five qubits, respectively. It turns out that the UPB corresponds to a complete graph with 11 vertices constructed by three sorts of nonisomorphic graphs. Taking the graphs as product vectors, we show that they are in three different orbits up to local unitary equivalence. Moreover, we also present the number of sorts of nonisomorphic graphs of complete graphs of some known UPBs and their orbits.

Related papers

• Detecting Homeomorphic 3-manifolds via Graph Neural Networks [0.0]
  We study the homeomorphism problem for a class of graph-manifolds using Graph Neural Network techniques. We train and benchmark a variety of network architectures within a supervised learning setting by testing different combinations of two convolutional layers.
  arXiv  Detail & Related papers  (2024-09-01T12:58:09Z)
• Discrete Graph Auto-Encoder [52.50288418639075]
  We introduce a new framework named Discrete Graph Auto-Encoder (DGAE) We first use a permutation-equivariant auto-encoder to convert graphs into sets of discrete latent node representations. In the second step, we sort the sets of discrete latent representations and learn their distribution with a specifically designed auto-regressive model.
  arXiv  Detail & Related papers  (2023-06-13T12:40:39Z)
• An efficient algebraic representation for graph states for measurement-based quantum computing [0.0]
  Graph states are main computational building blocks of measurement-based computation. We show how to efficiently express a graph state through the generators of the stabilizer group. We provide a framework to manipulate the graph states with a reduced number of stabilizers.
  arXiv  Detail & Related papers  (2022-12-23T01:40:03Z)
• Graphon Pooling for Reducing Dimensionality of Signals and Convolutional Operators on Graphs [131.53471236405628]
  We present three methods that exploit the induced graphon representation of graphs and graph signals on partitions of [0, 1]2 in the graphon space. We prove that those low dimensional representations constitute a convergent sequence of graphs and graph signals. We observe that graphon pooling performs significantly better than other approaches proposed in the literature when dimensionality reduction ratios between layers are large.
  arXiv  Detail & Related papers  (2022-12-15T22:11:34Z)
• GrannGAN: Graph annotation generative adversarial networks [72.66289932625742]
  We consider the problem of modelling high-dimensional distributions and generating new examples of data with complex relational feature structure coherent with a graph skeleton. The model we propose tackles the problem of generating the data features constrained by the specific graph structure of each data point by splitting the task into two phases. In the first it models the distribution of features associated with the nodes of the given graph, in the second it complements the edge features conditionally on the node features.
  arXiv  Detail & Related papers  (2022-12-01T11:49:07Z)
• Optimization on Large Interconnected Graphs and Networks Using Adiabatic Quantum Computation [0.0]
  We create an adiabatic quantum computing algorithm that solves the shortest path between any two vertices on an undirected graph with at most 3V qubits. The objective of this paper is to demonstrate the fact that it is possible to model large graphs on an adiabatic quantum computer using the maximum number of qubits available.
  arXiv  Detail & Related papers  (2022-02-06T13:47:31Z)
• Graph Neural Networks with Learnable Structural and Positional Representations [83.24058411666483]
  A major issue with arbitrary graphs is the absence of canonical positional information of nodes. We introduce Positional nodes (PE) of nodes, and inject it into the input layer, like in Transformers. We observe a performance increase for molecular datasets, from 2.87% up to 64.14% when considering learnable PE for both GNN classes.
  arXiv  Detail & Related papers  (2021-10-15T05:59:15Z)
• Sparse Partial Least Squares for Coarse Noisy Graph Alignment [10.172041234280865]
  Graph signal processing (GSP) provides a powerful framework for analyzing signals arising in a variety of domains. We propose a novel regularized partial least squares method which both incorporates the observed graph structures and imposes sparsity in order to reflect the underlying block community structure.
  arXiv  Detail & Related papers  (2021-04-06T21:52:15Z)
• Factorizable Graph Convolutional Networks [90.59836684458905]
  We introduce a novel graph convolutional network (GCN) that explicitly disentangles intertwined relations encoded in a graph. FactorGCN takes a simple graph as input, and disentangles it into several factorized graphs. We evaluate the proposed FactorGCN both qualitatively and quantitatively on the synthetic and real-world datasets.
  arXiv  Detail & Related papers  (2020-10-12T03:01:40Z)
• Wasserstein-based Graph Alignment [56.84964475441094]
  We cast a new formulation for the one-to-many graph alignment problem, which aims at matching a node in the smaller graph with one or more nodes in the larger graph. We show that our method leads to significant improvements with respect to the state-of-the-art algorithms for each of these tasks.
  arXiv  Detail & Related papers  (2020-03-12T22:31:59Z)
• Generation and Robustness of Quantum Entanglement in Spin Graphs [0.0]
  Entanglement is a crucial resource for quantum information processing. We show how a graph structure can be used to generate high fidelity entangled states. We also investigate how fabrication errors affect the entanglement generation protocol.
  arXiv  Detail & Related papers  (2020-02-18T16:11:57Z)

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.