Reexamination of decoherence in quantum walks on the hypercube

Abstract

The effect of decoherence on the continuous-time quantum walk on the hypercube is revisited. Previously, an exact solution was found for a decoherence model that preserved the effective tensor-product form of the dynamics. Here a new model is presented, inspired by perfect quantum state transfer in qubit networks. A perturbative solution is found for the dynamics of this model which is not of a tensor-product form. In contrast to previous results, the hitting probability has a lower bound that is independent of the hypercube dimension.

8 pages, 4 figures, revised title and text for PRA

References in corpus (10)

• Quantum random walks - an introductory overview
• Environment-Assisted Quantum Walks in Photosynthetic Energy Transfer
• Perfect state transfer in quantum spin networks
• A Quantum Random Walk Search Algorithm
• Dephasing assisted transport: Quantum networks and biomolecules
• Decoherence can be useful in quantum walks
• Hitting time for quantum walks on the hypercube
• Decoherence in Quantum Walks on the Hypercube
• Mixing Times in Quantum Walks on the Hypercube
• Theoretical analysis of perfect quantum state transfer with superconducting qubits

Cited by in corpus (6)

• Quantum walks: a comprehensive review
• Quantum stochastic walks: A generalization of classical random walks and quantum walks
• Superdiffusive quantum stochastic walk definable of arbitrary directed graph
• Efficient simulation of sparse Markovian quantum dynamics
• Thermodynamic formalism for dissipative quantum walks
• The effect of large-decoherence on mixing-time in Continuous-time quantum walks on long-range interacting cycles