Continuous-Time Quantum Walks on Dynamic Graphs
arXiv:1902.01346 · doi:10.1103/PhysRevA.100.012306
Abstract
Continuous-time quantum walks (CTQWs) on static graphs provide efficient methods for search and sampling as well as a model for universal quantum computation. We consider an extension of CTQWs to the case of dynamic graphs, in which an ordered sequence of graphs governs free evolution of the quantum walk. We then consider how perfect state transfer during the quantum walk can be used to design dynamic graphs that implement a universal set of quantum logic gates. We give explicit examples for a complete logical basis, and we validate implementations using numerical simulations for quantum teleportation and addition circuits. Finally, we discuss the potential for realizing CTQWs on dynamic graphs using actively controlled quantum optical waveguides.
References in corpus (21)
- Quantum random walks - an introductory overview
- Quantum Computation and Decision Trees
- Perfect state transfer in quantum spin networks
- Quantum computation with ions in thermal motion
- Universal computation by quantum walk
- Quantum walks: a comprehensive review
- Quantum Networks for Elementary Arithmetic Operations
- Spatial search by quantum walk
- Perfect Transfer of Arbitrary States in Quantum Spin Networks
- Universal computation by multi-particle quantum walk
- A Review of Perfect State Transfer and its Application as a Constructive Tool
- Experimental Two-dimensional Quantum Walk on a Photonic Chip
- Experimental Perfect Quantum State Transfer
- Two-particle quantum walks applied to the graph isomorphism problem
- Quantum Navigation and Ranking in Complex Networks
- Efficient Quantum Walk on a Quantum Processor
- Universal quantum computation by discontinuous quantum walk
- Optimal quantum spatial search on random temporal networks
- Continuous-Time Quantum Search on Balanced Trees
- Continuous Time Quantum Walks in finite Dimensions
- Perfect state transfer in products and covers of graphs
Cited by in corpus (12)
- Review on Quantum Walk Computing: Theory, Implementation, and Application
- Complex Quantum Networks: a Topical Review
- The effect of quantum noise on algorithmic perfect quantum state transfer on NISQ processors
- Generating highly entangled states via discrete-time quantum walks with Parrondo sequences
- Isolated Vertices in Continuous-Time Quantum Walks on Dynamic Graphs
- Continuous-time quantum walks in the presence of a quadratic perturbation
- Simplifying Continuous-Time Quantum Walks on Dynamic Graphs
- High-fidelity state transfer via quantum walks from delocalized states
- Multimarked Spatial Search by Continuous-Time Quantum Walk
- Efficient Sparse State Preparation via Quantum Walks
- Implementing Quantum Gates Using Length-3 Dynamic Quantum Walks
- Quantum Search with the Signless Laplacian