Quantum circuits for the realization of equivalent forms of one-dimensional discrete-time quantum walks on near-term quantum hardware
arXiv:2001.11197 · doi:10.1103/PhysRevA.104.062401
Abstract
Quantum walks are a promising framework for developing quantum algorithms and quantum simulations. They represent an important test case for the application of quantum computers. Here we present different forms of discrete-time quantum walks (DTQWs) and show their equivalence for physical realizations. Using an appropriate digital mapping of the position space on which a walker evolves to the multiqubit states of a quantum processor, we present different configurations of quantum circuits for the implementation of DTQWs in one-dimensional position space. We provide example circuits for a five-qubit processor and address scalability to higher dimensions as well as larger quantum processors.
Published version, 14 pages, 15 figures, 9 tables
References in corpus (18)
- Quantum walks of correlated particles
- Quantum Walk in Position Space with Single Optically Trapped Atoms
- Exploring Topological Phases With Quantum Walks
- Realization of quantum walks with negligible decoherence in waveguide lattices
- Detecting arbitrary quantum errors via stabilizer measurements on a sublattice of the surface code
- Discrete single-photon quantum walks with tunable decoherence
- Quantum Computer Systems for Scientific Discovery
- Symmetries, Topological Phases and Bound States in the One-Dimensional Quantum Walk
- Optimizing the discrete time quantum walk using a SU(2) coin
- Relationship Between Quantum Walk and Relativistic Quantum Mechanics
- Classical approach to the graph isomorphism problem using quantum walks
- Mimicking the probability distribution of a two-dimensional Grover walk with a single-qubit coin
- Experimental Implementation of Quantum Walks on IBM Quantum Computers
- Quantum walks and Dirac cellular automata on a programmable trapped-ion quantum computer
- Faster transport with a directed quantum walk
- Bounds on the dynamics of periodic quantum walks and emergence of the gapless and gapped Dirac equation
- A Comparison of Quantum Walk Implementations on NISQ Computers
- Decoherence on a two-dimensional quantum walk using four- and two-state particle