Quantum search on the two-dimensional lattice using the staggered model with Hamiltonians
arXiv:1701.01468 · doi:10.1103/PhysRevA.95.042341
Abstract
Quantum search on the two-dimensional lattice with one marked vertex and cyclic boundary conditions is an important problem in the context of quantum algorithms with an interesting unfolding. It avails to test the ability of quantum walk models to provide efficient algorithms from the theoretical side and means to implement quantum walks in laboratories from the practical side. In this paper, we rigorously prove that the recent-proposed staggered quantum walk model provides an efficient quantum search on the two-dimensional lattice, if the reflection operators associated with the graph tessellations are used as Hamiltonians, which is an important theoretical result for validating the staggered model with Hamiltonians. Numerical results show that on the two-dimensional lattice staggered models without Hamiltonians are not as efficient as the one described in this paper and are, in fact, as slow as classical random-walk-based algorithms.
arXiv comment8 pages, 2 figures
References in corpus (13)
- Quantum Mechanics helps in searching for a needle in a haystack
- A Quantum Random Walk Search Algorithm
- Faster quantum walk algorithm for the two dimensional spatial search
- The Staggered Quantum Walk Model
- Quantum Random Walks do not need a Coin Toss
- Staggered Quantum Walks on Graphs
- Quantum search algorithms on a regular lattice
- Staggered Quantum Walks with Hamiltonians
- One-Dimensional Coinless Quantum Walks
- General framework for quantum search algorithms
- Staggered quantum walks with superconducting microwave resonators
- Quantum Search on the Spatial Grid
- Discretization of continuous-time quantum walks via the staggered model with Hamiltonians
Cited by in corpus (10)
- Experimental Implementation of Quantum Walks on IBM Quantum Computers
- Faster Search by Lackadaisical Quantum Walk
- Discrete-Time Quantum-Walk & Floquet Topological Insulators via Distance-Selective Rydberg-Interaction
- Boundary-induced coherence in the staggered quantum walk on different topologies
- On Applying the Lackadaisical Quantum Walk Algorithm to Search for Multiple Solutions on Grids
- Second-order topological insulator in a coinless discrete-time quantum walk
- Decoherence on Staggered Quantum Walks
- Staggered Quantum Walk on Hexagonal Lattices
- Multimarked Spatial Search by Continuous-Time Quantum Walk
- Discrete-Time Quantum Walks on Oriented Graphs