Mimicking the probability distribution of a two-dimensional Grover walk with a single-qubit coin
arXiv:1010.2470 · doi:10.1103/PhysRevLett.106.080502
Abstract
Multi-dimensional quantum walks usually require large coin spaces. Here we show that the non-localized case of the spatial density probability of the two-dimensional Grover walk can be obtained using only a two-dimensional coin space and a quantum walk in alternate directions. We present a formal proof of this correspondence and analyze the behavior of the coin-position entanglement as well as the x-y spatial entanglement in our scheme with respect to the Grover one. We show that our experimentally simpler scheme allows to entangle the two orthogonal directions of the walk more efficiently.
arXiv comment5 pages, 2 figures, RevTeX4
References in corpus (23)
- Quantum entanglement
- Quantum random walks - an introductory overview
- Environment-Assisted Quantum Walks in Photosynthetic Energy Transfer
- A Quantum Random Walk Search Algorithm
- Universal computation by quantum walk
- Dephasing assisted transport: Quantum networks and biomolecules
- Quantum Walk in Position Space with Single Optically Trapped Atoms
- Implementing the quantum random walk
- Quantum walks in higher dimensions
- Quantum random walks in optical lattices
- Faster quantum walk algorithm for the two dimensional spatial search
- Quantum control and entanglement in a chemical compass
- Convex-roof extended negativity as an entanglement measure for bipartite quantum systems
- Quantum quincunx in cavity quantum electrodynamics
- Localization of Two-Dimensional Quantum Walks
- Entanglement in coined quantum walks on regular graphs
- Quantum walk on the line: entanglement and non-local initial conditions
- Limit distributions of two-dimensional quantum walks
- Simulation of quantum random walks using interference of classical field
- Recurrence properties of unbiased coined quantum walks on infinite -dimensional lattices
- One- and two-dimensional quantum walks in arrays of optical traps
- Asymptotic entanglement in a two-dimensional quantum walk
- Spatial entanglement using a quantum walk on a many-body system
Cited by in corpus (56)
- Quantum walks: a comprehensive review
- Observation of topologically protected bound states in a one dimensional photonic system
- Quantum walks of correlated photon pairs in two-dimensional waveguide arrays
- Voyage to Alpha Centauri: Entanglement degradation of cavity modes due to motion
- Two-dimensional topological quantum walks in the momentum space of structured light
- Dynamically Disordered Quantum Walk as a Maximal Entanglement Generator
- Experimental realisation of a delayed-choice quantum walk
- Two-component Dirac-like Hamiltonian for generating quantum walk on one-, two- and three-dimensional lattices
- Experimental Implementation of Quantum Walks on IBM Quantum Computers
- Quantum Walks and discrete Gauge Theories
- Alternate two-dimensional quantum walk with a single-qubit coin
- Entangling Power of Disordered Quantum Walks
- Review on Quantum Walk Computing: Theory, Implementation, and Application
- Two quantum walkers sharing coins
- Creating anomalous Floquet Chern insulators with magnetic quantum walks
- Dynamic-Disorder-Induced Enhancement of Entanglement in Photonic Quantum Walks
- Quantum walks of two correlated photons in a 2D synthetic lattice
- Two-dimensional quantum walk under artificial magnetic field
- Experimental demonstration of quantum walks with initial superposition states
- Implementation of a spatial two-dimensional quantum random walk with tunable decoherence
- Photonic quantum walks with four-dimensional coins
- Electric quantum walks in two dimensions
- Extraordinary behaviors in two-dimensional decoherent alternative quantum walk
- Generating highly entangled states via discrete-time quantum walks with Parrondo sequences
- Generic Quantum Walks with Memory
- Decomposition of split-step quantum walks for simulating Majorana modes and edge states
- N-dimensional alternate coined quantum walks from a dispersion relation perspective
- Localization and limit laws of a three-state alternate quantum walk on a two-dimensional lattice
- Generation of hyperentangled states and two-dimensional quantum walks using - ()- plates and polarization beamsplitters
- An efficient protocol of quantum walk in circuit QED
- One dimensional lazy quantum walks and occupancy rate
- Strongly trapped two-dimensional quantum walks
- Quantum walk on a cylinder
- Decoherence on a two-dimensional quantum walk using four- and two-state particle
- Maximal coin-position entanglement generation in a quantum walk for the third step and beyond regardless of the initial state
- Quantum circuits for the realization of equivalent forms of one-dimensional discrete-time quantum walks on near-term quantum hardware
- Localization-like effect in two-dimensional alternate quantum walks with periodic coin operations
- Maximal coin-walker entanglement in a ballistic quantum walk
- Lively quantum walks on cycles
- Sensitivity of quantum walks to boundary of two-dimensional lattices: approaches from the CGMV method and topological phases
- Multi-Dimensional Quantum Walks: a Playground of Dirac and Schrödinger Particles
- Controlled quantum search on structured databases
- Robust quantum state engineering through coherent localization in biased-coin quantum walks
- Role of symmetry in quantum search via continuous-time quantum walk
- Designing three-way entangled and nonlocal two-way entangled single particle states via alternate quantum walks
- Quantum cryptographic protocols with dual messaging system via 2D alternate quantum walk of a genuine single-photon entangled state
- Demonstration of Discrete-Time Quantum Walks and Observation of Topological Edge States in a Superconducting Qutrit Chain
- Entanglement transfer, accumulation and retrieval via quantum-walk-based qubit-qudit dynamics
- Path integral approach to one-dimensional discrete-time quantum walk
- Collective unitary evolution with linear optics by Cartan decomposition
- Quantum walk on a square lattice with identical particles
- Two-Dimensional Quantum Walk of Correlated Photons
- A quantum walk on the half line with a particular initial state
- Localization of a multi-dimensional quantum walk with one defect
- Two-dimensional quantum central limit theorem by quantum walks
- The simplest 2D quantum walk detects chaoticity