Quantum random walks without walking

Abstract

Quantum random walks have received much interest due to their non-intuitive dynamics, which may hold the key to a new generation of quantum algorithms. What remains a major challenge is a physical realization that is experimentally viable and not limited to special connectivity criteria. We present a scheme for walking on arbitrarily complex graphs, which can be realized using a variety of quantum systems such as a BEC trapped inside an optical lattice. This scheme is particularly elegant since the walker is not required to physically step between the nodes; only flipping coins is sufficient.

12 manuscript pages, 3 figures

References in corpus (12)

• Coupling Superconducting Qubits via a Cavity Bus
• Spatial search by quantum walk
• The Mott insulator transition in two dimensions
• Experimental demonstration of single-site addressability in a two-dimensional optical lattice
• Coherent Quantum Optical Control with Subwavelength Resolution
• Sublattice addressing and spin-dependent motion of atoms in a double-well lattice
• Classical approach to the graph isomorphism problem using quantum walks
• Continuous-time Quantum Walks on a Cycle Graph
• Addressing individual atoms in optical lattices with standing-wave driving fields
• Spin qubits in antidot lattices
• Critical scaling in standard biased random walks
• Single atom quantum walk with 1D optical superlattices

Cited by in corpus (6)

• Quantum walks: a comprehensive review
• Two-particle quantum walks applied to the graph isomorphism problem
• Non-interacting multi-particle quantum random walks applied to the graph isomorphism problem for strongly regular graphs
• Qcompiler: quantum compilation with CSD method
• Solid State Implementation of Quantum Random Walks on General Graphs
• An efficient quantum circuit analyser on qubits and qudits