scholarly journals The quantum entropy cone of hypergraphs

2020 ◽  
Vol 9 (5) ◽  
Author(s):  
Ning Bao ◽  
Newton Cheng ◽  
Sergio Hernández-Cuenca ◽  
Vincent P. Su
Keyword(s):  
Quantum State ◽  
Entanglement Entropy ◽  
Quantum Entropy ◽  
Graph Theoretic ◽  
Tensor Networks ◽  
Stabilizer States

In this work, we generalize the graph-theoretic techniques used for the holographic entropy cone to study hypergraphs and their analogously-defined entropy cone. This allows us to develop a framework to efficiently compute entropies and prove inequalities satisfied by hypergraphs. In doing so, we discover a class of quantum entropy vectors which reach beyond those of holographic states and obey constraints intimately related to the ones obeyed by stabilizer states and linear ranks. We show that, at least up to 4 parties, the hypergraph cone is identical to the stabilizer entropy cone, thus demonstrating that the hypergraph framework is broadly applicable to the study of entanglement entropy. We conjecture that this equality continues to hold for higher party numbers and report on partial progress on this direction. To physically motivate this conjectured equivalence, we also propose a plausible method inspired by tensor networks to construct a quantum state from a given hypergraph such that their entropy vectors match.

Platonic entanglement

2021 ◽  
Vol 21 (13&14) ◽  
pp. 1081-1090
Author(s):  
Jose I. Latorre ◽  
German Sierra
Keyword(s):  
Prime Number ◽  
Quantum State ◽  
Entangled States ◽  
Platonic Solid ◽  
Platonic Solids ◽  
Reed Solomon Codes ◽  
Tensor Networks

We present a construction of highly entangled states defined on the topology of a platonic solid using tensor networks based on ancillary Absolute Maximally Entangled (AME) states. We illustrate the idea using the example of a quantum state based on AME(5,2) over a dodecahedron. We analyze the entropy of such states on many different partitions, and observe that they come on integer numbers and are almost maximal. We also observe that all platonic solids accept the construction of AME states based on Reed-Solomon codes since their number of facets, vertices and edges are always a prime number plus one.

Reconstructing a quantum state with a variational autoencoder

2021 ◽  
Author(s):  
Chuangtao Chen ◽  
Zhimin He ◽  
Zhiming Huang ◽  
Haozhen Situ
Keyword(s):  
Quantum State ◽  
Circuit Simulation ◽  
Entanglement Entropy ◽  
Ghz State ◽  
High Fidelity ◽  
Training Samples ◽  
Variational Autoencoder ◽  
Minimum Number ◽  
Number Formula ◽  
State Tomography

Quantum state tomography (QST) is an important and challenging task in the field of quantum information, which has attracted a lot of attentions in recent years. Machine learning models can provide a classical representation of the quantum state after trained on the measurement outcomes, which are part of effective techniques to solve QST problem. In this work, we use a variational autoencoder (VAE) to learn the measurement distribution of two quantum states generated by MPS circuits. We first consider the Greenberger–Horne–Zeilinger (GHZ) state which can be generated by a simple MPS circuit. Simulation results show that a VAE can reconstruct 3- to 8-qubit GHZ states with a high fidelity, i.e., 0.99, and is robust to depolarizing noise. The minimum number ([Formula: see text]) of training samples required to reconstruct the GHZ state up to 0.99 fidelity scales approximately linearly with the number of qubits ([Formula: see text]). However, for the quantum state generated by a complex MPS circuit, [Formula: see text] increases exponentially with [Formula: see text], especially for the quantum state with high entanglement entropy.

scholarly journals Holographic Entanglement in Group Field Theory

Universe ◽  
2019 ◽  
Vol 5 (10) ◽  
pp. 211 ◽  
Author(s):  
Goffredo Chirco
Keyword(s):  
Field Theory ◽  
Entanglement Entropy ◽  
Bipartite Network ◽  
Spin Network ◽  
Network State ◽  
Tensor Networks ◽  
Holographic Entanglement Entropy ◽  
Group Field Theory ◽  
Network States ◽  
Random Tensor

This work is meant as a review summary of a series of recent results concerning the derivation of a holographic entanglement entropy formula for generic open spin network states in the group field theory (GFT) approach to quantum gravity. The statistical group-field computation of the Rényi entropy for a bipartite network state for a simple interacting GFT is reviewed, within a recently proposed dictionary between group field theories and random tensor networks, and with an emphasis on the problem of a consistent characterisation of the entanglement entropy in the GFT second quantisation formalism.

Entanglement Entropy and Energy Accuracy: Tensor Networks for Small Spin-Systems

2012 ◽  
Vol 81 (Suppl.B) ◽  
pp. SB052
Author(s):  
Masashi Orii ◽  
Hiroshi Ueda ◽  
Isao Maruyama
Keyword(s):  
Entanglement Entropy ◽  
Spin Systems ◽  
Tensor Networks

scholarly journals Quantum-inspired event reconstruction with Tensor Networks: Matrix Product States

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Jack Y. Araz ◽  
Michael Spannowsky
Keyword(s):  
Top Quark ◽  
Entanglement Entropy ◽  
Feature Space ◽  
Machine Learning Techniques ◽  
Stochastic Gradient Descent ◽  
Matrix Product ◽  
Density Matrix Renormalization ◽  
Matrix Product State ◽  
Tensor Networks ◽  
Many Body Systems

Abstract Tensor Networks are non-trivial representations of high-dimensional tensors, originally designed to describe quantum many-body systems. We show that Tensor Networks are ideal vehicles to connect quantum mechanical concepts to machine learning techniques, thereby facilitating an improved interpretability of neural networks. This study presents the discrimination of top quark signal over QCD background processes using a Matrix Product State classifier. We show that entanglement entropy can be used to interpret what a network learns, which can be used to reduce the complexity of the network and feature space without loss of generality or performance. For the optimisation of the network, we compare the Density Matrix Renormalization Group (DMRG) algorithm to stochastic gradient descent (SGD) and propose a joined training algorithm to harness the explainability of DMRG with the efficiency of SGD.

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