Stability of Continuous Time Quantum Walks in Complex Networks

• URL: http://arxiv.org/abs/2507.17880v1
• Date: Wed, 23 Jul 2025 19:13:26 GMT
• Title: Stability of Continuous Time Quantum Walks in Complex Networks
• Authors: Adithya L J, Johannes Nokkala, Jyrki Piilo, Chandrakala Meena,
• Abstract summary: We investigate the stability of continuous time quantum walks (CTQWs) in a range of network topologies.<n>The interplay of both network topology and decoherence model influences coherence.
• Score: 0.7864304771129751
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We investigate the stability of continuous time quantum walks (CTQWs) in a range of network topologies under different decoherence mechanisms, defining stability as the system's ability to preserve quantum properties over time. The networks studied range from homogeneous to heterogeneous structures, including cycle, complete, Erd\H{o}s-R\'enyi, small-world, scale-free, and star topologies. The decoherence models considered are intrinsic decoherence, Haken-Strobl noise, and quantum stochastic walks (QSWs). To assess quantum stability, we employ several metrics: node occupation probabilities, the $\ell_1$-norm of coherence, fidelity with the initial state, quantum-classical distance, and von Neumann entropy. Our results reveal that the interplay of both network topology and decoherence model influences coherence preservation. Intrinsic decoherence results in the slowest decay of coherence, followed by Haken-Strobl noise, while QSW causes the most rapid loss of coherence. The stability ranking among network topologies varies depending on the decoherence model and quantifier used. For example, under Haken-Strobl and intrinsic decoherence, the quantum-classical distance ranks the cycle network more stable than scale-free networks, although other metrics consistently favour scale-free topologies. In general, heterogeneous networks, such as star and scale-free networks, exhibit the highest stability, whereas homogeneous topologies, such as cycle and Erd\H{o}s-R\'enyi networks, are more vulnerable to decoherence. The complete graph, despite its homogeneity, remains highly stable due to its dense connectivity. Furthermore, in heterogeneous networks, the centrality of the initialised node, measured by degree or closeness, has a pronounced impact on stability, underscoring the role of local topological features in quantum dynamics.

Related papers

• Quantum and Semi-Classical Signatures of Dissipative Chaos in the Steady State [0.40498500266986387]
  We investigate the quantum-classical correspondence in open quantum many-body systems using the SU(3) Bose-Hubbard trimer as a minimal model.<n>We show that classical dynamical behavior, as quantified by the sign of the Lyapunov exponent, governs the level statistics of the steady-state density matrix.
  arXiv  Detail & Related papers  (2025-06-17T20:21:06Z)
• Open-systems tools for non-thermalizing closed quantum systems [0.0]
  We study constrained, symmetric quantum circuit dynamics that generate non-equilibrium steady states.<n>Each network can be described as an ensemble of open systems, a collection of qubits evolving with phase-covariant dynamics.<n>We quantify the distance of the steady states from the homogeneous steady state and further characterize them using the complexity of their mutual information networks.
  arXiv  Detail & Related papers  (2025-04-30T18:38:08Z)
• Non-stabilizerness of Neural Quantum States [41.94295877935867]
  We introduce a methodology to estimate non-stabilizerness or "magic", a key resource for quantum complexity, with Neural Quantum States (NQS)<n>We study the magic content in an ensemble of random NQS, demonstrating that neural network parametrizations of the wave function capture finite non-stabilizerness besides large entanglement.
  arXiv  Detail & Related papers  (2025-02-13T19:14:15Z)
• Characterizing randomness in parameterized quantum circuits through expressibility and average entanglement [39.58317527488534]
  Quantum Circuits (PQCs) are still not fully understood outside the scope of their principal application.<n>We analyse the generation of random states in PQCs under restrictions on the qubits connectivities.<n>We place a connection between how steep is the increase on the uniformity of the distribution of the generated states and the generation of entanglement.
  arXiv  Detail & Related papers  (2024-05-03T17:32:55Z)
• Predicting Instability in Complex Oscillator Networks: Limitations and Potentials of Network Measures and Machine Learning [0.0]
  We collect 46 relevant network measures and find that no small subset can reliably predict stability. The performance of GNNs can only be matched by combining all network measures and nodewise machine learning. This suggests that correlations of network measures and function may be misleading, and that GNNs capture the causal relationship between structure and stability substantially better.
  arXiv  Detail & Related papers  (2024-02-27T13:34:08Z)
• Decoherence in Exchange-Coupled Quantum Spin Qubit Systems: Impact of Multiqubit Interactions and Geometric Connectivity [6.222054066855025]
  We investigate the impact of different connectivities on the decoherence time in quantum systems under quasi-static Heisenberg noise. We find that rings exhibit greater stability compared to chains, contrary to the expectation that higher average connectivity leads to decreased stability.
  arXiv  Detail & Related papers  (2024-01-01T11:11:05Z)
• Dissipative preparation and stabilization of many-body quantum states in a superconducting qutrit array [55.41644538483948]
  We present and analyze a protocol for driven-dissipatively preparing and stabilizing a manifold of quantum manybody entangled states. We perform theoretical modeling of this platform via pulse-level simulations based on physical features of real devices. Our work shows the capacity of driven-dissipative superconducting cQED systems to host robust and self-corrected quantum manybody states.
  arXiv  Detail & Related papers  (2023-03-21T18:02:47Z)
• 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)
• Dynamics with autoregressive neural quantum states: application to critical quench dynamics [41.94295877935867]
  We present an alternative general scheme that enables one to capture long-time dynamics of quantum systems in a stable fashion. We apply the scheme to time-dependent quench dynamics by investigating the Kibble-Zurek mechanism in the two-dimensional quantum Ising model.
  arXiv  Detail & Related papers  (2022-09-07T15:50:00Z)
• Stability of Neural Networks on Manifolds to Relative Perturbations [118.84154142918214]
  Graph Neural Networks (GNNs) show impressive performance in many practical scenarios. GNNs can scale well on large size graphs, but this is contradicted by the fact that existing stability bounds grow with the number of nodes.
  arXiv  Detail & Related papers  (2021-10-10T04:37:19Z)

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.