How to Compute Using Quantum Walks

Abstract

Quantum walks are widely and successfully used to model diverse physical processes. This leads to computation of the models, to explore their properties. Quantum walks have also been shown to be universal for quantum computing. This is a more subtle result than is often appreciated, since it applies to computations run on qubit-based quantum computers in the single walker case, and physical quantum walks in the multi-walker case (quantum cellular automata). Nonetheless, quantum walks are powerful tools for quantum computing when correctly applied. In this paper, I explain the relationship between quantum walks as models and quantum walks as computational tools, and give some examples of their application in both contexts.

In Proceedings QSQW 2020, arXiv:2004.01061

References in corpus (10)

• Environment-Assisted Quantum Walks in Photosynthetic Energy Transfer
• Universal computation by quantum walk
• Exponential algorithmic speedup by quantum walk
• Spatial search by quantum walk
• Quantum Walk in Position Space with Single Optically Trapped Atoms
• Realization of quantum walks with negligible decoherence in waveguide lattices
• Universal computation by multi-particle quantum walk
• Discrete single-photon quantum walks with tunable decoherence
• Experimental implementation of an adiabatic quantum optimization algorithm
• Using Quantum Computers for Quantum Simulation