Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2605.00772

Entanglement capacity of complex networks from quantum walks

Pravy Prerana, Sascha Wald

quant-phcond-mat.stat-mechSubmitted May 1, 2026• Announced May 4, 2026• 0 citations
arXivHTMLPDF

Abstract

Discrete-time quantum walks provide a natural framework for quantum transport on complex networks. On regular structures, coin-walker entanglement has been widely used to characterize quantum transport and to support quantum algorithmic protocols. However, this notion relies on a fixed Hilbert space factorization separating coin and position and is therefore not directly applicable to more complex, irregular structures. Here we introduce an entanglement measure for general networks based on a bipartition that assigns each node two roles, acting as both a source and a target. The resulting bipartition defines the source-target entanglement, a measure for general networks, motivated by coin-walker entanglement. We show that the connectivity of the network imposes an upper bound on this entanglement and identify graph matchings as the underlying structure governing entanglement generation. We further illustrate that in random graphs improving graph connectivity reduces the attainable entanglement, establishing a structure-dependent constraint on quantum correlations.

Comments
6+ pages, 6 figures

Related papers

Robust Genuine Multipartite Entanglement in Two Walker Quantum Walks

Sandipan Hazra, Tamoghna Das, Sougato Bose +1 more

Discrete-time quantum walks provide a versatile framework for investigating the generation, redistribution, and transport of quantum correlations in composite quantum systems. Here, we study the dynamics of bipartite and genuine multipartite entanglement in a two-walker discrete-time quantum walk on a one-dimensional lattice. By employing logarithmic negativity and the generalized geometric measure (GGM), we systematically characterize the redistribution of bipartite entanglement among different subsystem partitions and the emergence of genuine multipartite entanglement involving the two coin and two position degrees of freedom. We show that the entanglement dynamics are strongly influenced by the lattice topology. The open-boundary regime exhibits a monotonic redistribution of quantum correlations, whereas the closed-boundary regime gives rise to pronounced oscillatory behavior due to boundary-induced interference and recurrent wave-packet overlap. In the open-boundary regime, the GGM rapidly approaches its theoretical maximum value of $1/2$ and remains largely insensitive to the choice of the initial Bell state as well as to continuous variations of the local coin operator over a broad parameter range, except near the Pauli-$X$ coin. These results demonstrate that maximal genuine multipartite entanglement generation is a robust and generic feature of open-boundary two-walker discrete-time quantum walks, establishing them as promising platforms for engineering multipartite quantum correlations in quantum information processing and quantum simulation.

quant-pharXiv:2608.13338•Aug 14, 2026•0 citations

Coined quantum walk on a quantum network

Jigyen Bhavsar, Shashank Shekhar, Siddhartha Santra

We explore a discrete-time, coined quantum walk on a quantum network where the coherent superposition of walker moves originates from the unitary interaction of the walker coin with the qubit degrees of freedom in the quantum network. The walk dynamics leads to a growth of entanglement between the walker and the network on one hand and, on the other, between the network qubits among themselves. The initial entanglement among the network qubits plays a crucial role in determining the asymptotic values of these entanglement measures and the quantum walk statistics. Specifically, the entanglement entropy of the walker-network state and the negativity of the quantum network-qubit state saturate to values increasing with the initial network entanglement. The asymptotic time-averaged walker-position probability distribution shows increasing localization around the initial walker position with higher initial network entanglement. A potential application of these results as a characterization tool for quantum network properties is suggested.

arXiv:2406.01558•Physical Review A•Nov 20, 2024•2 citations

Discrete-time quantum walk on complex networks for community detection

Kanae Mukai, Naomichi Hatano

Many systems such as social networks and biological networks take the form of complex networks, which have a community structure.Community detection in complex networks is of great interest to many researchers in statistical physics and mathematical physics.There have been studies on community detection that use the classical random walk.The present study utilizes the discrete-time quantum walk instead.The quantum walk plays an important role in various fields, especially in research on quantum computers, and attracts much attention from mathematical physics too.The discrete-time quantum walk has two properties: it linearly spreads on a flat space, and it localizes in some cases because of quantum coherence.We demonstrate that these properties of the quantum walk are useful for community detection on complex networks.We define the discrete-time quantum walk on complex networks and utilize it for community detection.We numerically show that the quantum walk with a Fourier coin is localized in a community to which the initial node belongs.Meanwhile, the quantum walk with a Grover coin tends to be localized around the initial node, not over a community.The probability of a classical random walk on the same network converges to a uniform distribution with a relaxation time generally unknown a priori.We thus claim that the time average of the probability of a Fourier-coin quantum walk on complex networks reveals the community structure more explicitly than that of a Grover-coin quantum walk and a snapshot of the classical random walk.We first demonstrate our method of community detection for a prototypical three-community network, producing the correct grouping.We then apply our method to two real-world networks, namely, Zachary's karate club and the U.S. Airport network.We successfully reveal the community structure, the two communities of the instructor and the administrator in the former and major airline companies in the latter.

arXiv:2005.13104•Physical Review Research•Jun 22, 2020•37 citations

Quantum walk-based protocol for secure communication between any two directly connected nodes on a network

Prateek Chawla, Adithi Ajith, C. M. Chandrashekar

Abstract The utilization of quantum entanglement as a cryptographic resource has superseded conventional approaches to secure communication. Security and fidelity of intranetwork communication between quantum devices is the backbone of a quantum network. This work presents an protocol that generates entanglement between any two directly connected nodes of a quantum network to be used as a resource to enable quantum communication across that pair in the network. The protocol is based on a directed discrete-time quantum walk and paves the way for private inter-node quantum communication channels in the network. We also present the simulation results of this protocol on random networks generated from various models. We show that after implementation, the probability of the walker being at all nodes other than the source and target is negligible and this holds independent of the random graph generation model. This constitutes a viable method for the practical realisation of secure communication over any random network topology.

arXiv:2211.12938•Physica Scripta•Sep 18, 2023•3 citations

A hybrid quantum walk model unifying discrete and continuous quantum walks

Tianen Chen, Yun Shang

Quantum walks, both discrete and continuous, serve as fundamental tools in quantum information processing with diverse applications. This work introduces a hybrid quantum walk model that integrates the coin mechanism of discrete walks with the Hamiltonian-driven time evolution of continuous walks. Through systematic analysis of probability distributions, standard deviations, and entanglement entropy on fundamental graph structures, we reveal distinctive dynamical characteristics that differentiate our model from conventional quantum walk paradigms. The proposed framework demonstrates unifying capabilities by naturally encompassing existing quantum walk models as special cases. Two significant applications emerge from this hybrid architecture: (1) We develop a novel protocol for perfect state transfer(PST) in general connected graphs, overcoming the limitations of previous graph-specific approaches. A PST on a tree graph has been implemented on a quantum superconducting processor. (2) We devise a quantum algorithm for multiplying K adjacency matrices of n -vertex regular graphs with time complexity O ( n 2 d 1 ⋯ d K ), outperforming classical matrix multiplication ( O ( n 2.371552 )) when vertex degrees d i are bounded. The algorithm’s efficacy for triangle counting is experimentally validated through the quantum simulation on PennyLane. These results establish the hybrid quantum walk as a versatile framework bridging discrete and continuous paradigms while enabling practical quantum advantage in graph computation tasks.

arXiv:2509.09221•npj Quantum Information•Dec 30, 2025•2 citations

Scaling Laws of Quantum Networks: An Entanglement Transport Framework

Jaemin Kim, Petar Popovski

As quantum networks move toward multi-user architectures, a central question is how the performance of entanglement distribution scales with the numbers of network nodes $N$ and active users $M$, yet existing studies use different objectives, resource assumptions, and normalizations. To account for delivery distance under multi-user demand, we define entanglement transport, which weights each delivered Bell pair meeting a fixed fidelity threshold by its endpoint separation. In a two-layer framework, (i) a resource layer measures capacity per activation slot under different aggregation regimes, and (ii) a physical layer measures service per second under implementation constraints. For matched implementations with a bounded number of activation slots per second, asymptotic-aggregation capacity sets a service ceiling, whereas achievable service must be established separately. On expanding honeycomb lattices with one random session, fixed-window entanglement-percolation constructions achieve $Θ(N^{-1})$ entanglement transport per activation slot below their thresholds and $Θ(\sqrt N)$ above them. For homogeneous chains, asymptotic aggregation exceeds fixed-window capacity by a factor $Θ(N^2/M)$, and in spatial expansion a noisy physical implementation achieves $Θ(M/N)$ service per second. These examples show that entanglement-transport scaling depends not only on connectivity but also on resource aggregation and physical implementation. The framework provides a common basis on which quantum-network scaling laws can be established.

quant-pharXiv:2609.39690•Oct 1, 2026•0 citations
Discrete-time quantum walks provide a natural framework for quantum transport on complex networks. On regular structures, coin-walker entanglement has been widely used to characterize quantum transport and to support quantum algorithmic protocols. However, this notion relies on a fixed Hilbert space factorization separating coin and position and is therefore not directly applicable to more complex, irregular structures. Here we introduce an entanglement measure for general networks based on a bipartition that assigns each node two roles, acting as both a source and a target. The resulting bipartition defines the source-target entanglement, a measure for general networks, motivated by coin-walker entanglement. We show that the connectivity of the network imposes an upper bound on this entanglement and identify graph matchings as the underlying structure governing entanglement generation. We further illustrate that in random graphs improving graph connectivity reduces the attainable entanglement, establishing a structure-dependent constraint on quantum correlations.
Discrete-time quantum walks provide a versatile framework for investigating the generation, redistribution, and transport of quantum correlations in composite quantum systems. Here, we study the dynamics of bipartite and genuine multipartite entanglement in a two-walker discrete-time quantum walk on a one-dimensional lattice. By employing logarithmic negativity and the generalized geometric measure (GGM), we systematically characterize the redistribution of bipartite entanglement among different subsystem partitions and the emergence of genuine multipartite entanglement involving the two coin and two position degrees of freedom. We show that the entanglement dynamics are strongly influenced by the lattice topology. The open-boundary regime exhibits a monotonic redistribution of quantum correlations, whereas the closed-boundary regime gives rise to pronounced oscillatory behavior due to boundary-induced interference and recurrent wave-packet overlap. In the open-boundary regime, the GGM rapidly approaches its theoretical maximum value of 1/21/21/2 and remains largely insensitive to the choice of the initial Bell state as well as to continuous variations of the local coin operator over a broad parameter range, except near the Pauli-XXX coin. These results demonstrate that maximal genuine multipartite entanglement generation is a robust and generic feature of open-boundary two-walker discrete-time quantum walks, establishing them as promising platforms for engineering multipartite quantum correlations in quantum information processing and quantum simulation.
We explore a discrete-time, coined quantum walk on a quantum network where the coherent superposition of walker moves originates from the unitary interaction of the walker coin with the qubit degrees of freedom in the quantum network. The walk dynamics leads to a growth of entanglement between the walker and the network on one hand and, on the other, between the network qubits among themselves. The initial entanglement among the network qubits plays a crucial role in determining the asymptotic values of these entanglement measures and the quantum walk statistics. Specifically, the entanglement entropy of the walker-network state and the negativity of the quantum network-qubit state saturate to values increasing with the initial network entanglement. The asymptotic time-averaged walker-position probability distribution shows increasing localization around the initial walker position with higher initial network entanglement. A potential application of these results as a characterization tool for quantum network properties is suggested.
Many systems such as social networks and biological networks take the form of complex networks, which have a community structure.Community detection in complex networks is of great interest to many researchers in statistical physics and mathematical physics.There have been studies on community detection that use the classical random walk.The present study utilizes the discrete-time quantum walk instead.The quantum walk plays an important role in various fields, especially in research on quantum computers, and attracts much attention from mathematical physics too.The discrete-time quantum walk has two properties: it linearly spreads on a flat space, and it localizes in some cases because of quantum coherence.We demonstrate that these properties of the quantum walk are useful for community detection on complex networks.We define the discrete-time quantum walk on complex networks and utilize it for community detection.We numerically show that the quantum walk with a Fourier coin is localized in a community to which the initial node belongs.Meanwhile, the quantum walk with a Grover coin tends to be localized around the initial node, not over a community.The probability of a classical random walk on the same network converges to a uniform distribution with a relaxation time generally unknown a priori.We thus claim that the time average of the probability of a Fourier-coin quantum walk on complex networks reveals the community structure more explicitly than that of a Grover-coin quantum walk and a snapshot of the classical random walk.We first demonstrate our method of community detection for a prototypical three-community network, producing the correct grouping.We then apply our method to two real-world networks, namely, Zachary's karate club and the U.S. Airport network.We successfully reveal the community structure, the two communities of the instructor and the administrator in the former and major airline companies in the latter.
Abstract The utilization of quantum entanglement as a cryptographic resource has superseded conventional approaches to secure communication. Security and fidelity of intranetwork communication between quantum devices is the backbone of a quantum network. This work presents an protocol that generates entanglement between any two directly connected nodes of a quantum network to be used as a resource to enable quantum communication across that pair in the network. The protocol is based on a directed discrete-time quantum walk and paves the way for private inter-node quantum communication channels in the network. We also present the simulation results of this protocol on random networks generated from various models. We show that after implementation, the probability of the walker being at all nodes other than the source and target is negligible and this holds independent of the random graph generation model. This constitutes a viable method for the practical realisation of secure communication over any random network topology.
Quantum walks, both discrete and continuous, serve as fundamental tools in quantum information processing with diverse applications. This work introduces a hybrid quantum walk model that integrates the coin mechanism of discrete walks with the Hamiltonian-driven time evolution of continuous walks. Through systematic analysis of probability distributions, standard deviations, and entanglement entropy on fundamental graph structures, we reveal distinctive dynamical characteristics that differentiate our model from conventional quantum walk paradigms. The proposed framework demonstrates unifying capabilities by naturally encompassing existing quantum walk models as special cases. Two significant applications emerge from this hybrid architecture: (1) We develop a novel protocol for perfect state transfer(PST) in general connected graphs, overcoming the limitations of previous graph-specific approaches. A PST on a tree graph has been implemented on a quantum superconducting processor. (2) We devise a quantum algorithm for multiplying K adjacency matrices of n -vertex regular graphs with time complexity O ( n 2 d 1 ⋯ d K ), outperforming classical matrix multiplication ( O ( n 2.371552 )) when vertex degrees d i are bounded. The algorithm’s efficacy for triangle counting is experimentally validated through the quantum simulation on PennyLane. These results establish the hybrid quantum walk as a versatile framework bridging discrete and continuous paradigms while enabling practical quantum advantage in graph computation tasks.
As quantum networks move toward multi-user architectures, a central question is how the performance of entanglement distribution scales with the numbers of network nodes NNN and active users MMM, yet existing studies use different objectives, resource assumptions, and normalizations. To account for delivery distance under multi-user demand, we define entanglement transport, which weights each delivered Bell pair meeting a fixed fidelity threshold by its endpoint separation. In a two-layer framework, (i) a resource layer measures capacity per activation slot under different aggregation regimes, and (ii) a physical layer measures service per second under implementation constraints. For matched implementations with a bounded number of activation slots per second, asymptotic-aggregation capacity sets a service ceiling, whereas achievable service must be established separately. On expanding honeycomb lattices with one random session, fixed-window entanglement-percolation constructions achieve Θ(N−1)Θ(N^{-1})Θ(N−1) entanglement transport per activation slot below their thresholds and Θ(N)Θ(\sqrt N)Θ(N​) above them. For homogeneous chains, asymptotic aggregation exceeds fixed-window capacity by a factor Θ(N2/M)Θ(N^2/M)Θ(N2/M), and in spatial expansion a noisy physical implementation achieves Θ(M/N)Θ(M/N)Θ(M/N) service per second. These examples show that entanglement-transport scaling depends not only on connectivity but also on resource aggregation and physical implementation. The framework provides a common basis on which quantum-network scaling laws can be established.