Degree Distribution in Quantum Walks on Complex Networks
arXiv:1305.6078 · doi:10.1103/PhysRevX.3.041007
Abstract
In this theoretical study, we analyze quantum walks on complex networks, which model network-based processes ranging from quantum computing to biology and even sociology. Specifically, we analytically relate the average long time probability distribution for the location of a unitary quantum walker to that of a corresponding classical walker. The distribution of the classical walker is proportional to the distribution of degrees, which measures the connectivity of the network nodes and underlies many methods for analyzing classical networks including website ranking. The quantum distribution becomes exactly equal to the classical distribution when the walk has zero energy and at higher energies the difference, the so-called quantumness, is bounded by the energy of the initial state. We give an example for which the quantumness equals a Renyi entropy of the normalized weighted degrees, guiding us to regimes for which the classical degree-dependent result is recovered and others for which quantum effects dominate.
arXiv comment8 pages, 4 figures; improved description and new examples; accepted for publication in Phys. Rev. X
References in corpus (29)
- Emergence of scaling in random networks
- Statistical mechanics of complex networks
- The structure and function of complex networks
- Finding community structure in networks using the eigenvectors of matrices
- Cooperative Game Theory Approaches for Network Partitioning
- The diameter of the world wide web
- The spread of epidemic disease on networks
- Community detection in complex networks using Extremal Optimization
- Self-similar community structure in organisations
- Quantum random walks - an introductory overview
- Quantum Computation and Decision Trees
- Environment-Assisted Quantum Walks in Photosynthetic Energy Transfer
- Identity and Search in Social Networks
- Universal computation by quantum walk
- Highly efficient energy excitation transfer in light-harvesting complexes: The fundamental role of noise-assisted transport
- Continuous-Time Quantum Walks: Models for Coherent Transport on Complex Networks
- Quantum complex networks
- Quantum stochastic walks: A generalization of classical random walks and quantum walks
- Google in a Quantum Network
- Quantum Navigation and Ranking in Complex Networks
- Adiabatic quantum algorithm for search engine ranking
- Coherent exciton transport in dendrimers and continuous-time quantum walks
- Entanglement percolation in quantum complex networks
- Quantum Transport Enhancement by Time-Reversal Symmetry Breaking
- Dynamical simulations of classical stochastic systems using matrix product states
- Multipartite entanglement percolation
- Asymmetries in symmetric quantum walks on two-dimensional networks
- A Noether Theorem for Markov Processes
- Thermodynamic formalism for dissipative quantum walks
Cited by in corpus (31)
- Spectral entropies as information-theoretic tools for complex network comparison
- Spatial search by quantum walk is optimal for almost all graphs
- Complex Quantum Network Geometries: Evolution and Phase Transitions
- Chiral Quantum Walks
- Optimal quantum spatial search on random temporal networks
- Complex Quantum Networks: a Topical Review
- Community Detection in Quantum Complex Networks
- Complex networks with complex weights
- Supersymmetric multiplex networks described by coupled Bose and Fermi statistics
- From classical to quantum walks with stochastic resetting on networks
- Driving interconnected networks to supercriticality
- Complex Quantum Networks: From Universal Breakdown to Optimal Transport
- Noisy quantum walks of two indistinguishable interacting particles
- How fast do quantum walks mix?
- Quantized recurrence time in iterated open quantum dynamics
- Quantum-classical dynamical distance and quantumness of quantum walks
- Multiple transitions between normal and hyperballistic diffusion in quantum walks with time-dependent jumps
- Implementation of a 3 x 3 directionally-unbiased linear optical multiport
- Discrete dynamics and non-Markovianity
- Thermodynamics of network model fitting with spectral entropies
- Controlled quantum search on structured databases
- Topological classification of time-asymmetry in unitary quantum processes
- Quantum transport senses community structure in networks
- Short time behavior of continuous time quantum walks on graphs
- Response of quantum spin networks to attacks
- Multiple-scale integro-differential perturbation method for generic non-Markovian environments
- Discovering hidden layers in quantum graphs
- Effective one-dimension reduction of multi-compartment complex systems dynamics
- Clustering-induced localization of quantum walks on networks
- Universal scaling hypothesis of quantum spatial search in complex networks
- Reshaping coupled bosonic networks: A bipartite-graph framework for optimal quantum excitation transfer