Quantum state engineering using one-dimensional discrete-time quantum walks

TL;DR

This paper demonstrates how one-dimensional discrete-time quantum walks can be used as a versatile framework for engineering arbitrary quantum states, with practical implementation prospects in photonic systems.

Contribution

It introduces a general method to engineer any superposition state using quantum walks, including conditions for reachability and an efficient computation approach.

Findings

Identifies conditions for reachable states in quantum walks.

Provides a method to compute coin parameters for state engineering.

Proposes a feasible linear optics implementation.

Abstract

Quantum state preparation in high-dimensional systems is an essential requirement for many quantum-technology applications. The engineering of an arbitrary quantum state is, however, typically strongly dependent on the experimental platform chosen for implementation, and a general framework is still missing. Here we show that coined quantum walks on a line, which represent a framework general enough to encompass a variety of different platforms, can be used for quantum state engineering of arbitrary superpositions of the walker's sites. We achieve this goal by identifying a set of conditions that fully characterize the reachable states in the space comprising walker and coin, and providing a method to efficiently compute the corresponding set of coin parameters. We assess the feasibility of our proposal by identifying a linear optics experiment based on photonic orbital angular momentum technology.