Floquet-engineered quantum walks

Haruna Katayama,Noriyuki Hatakenaka,Toshiyuki Fujii

doi:10.1038/s41598-020-74418-w

Haruna Katayama, Noriyuki Hatakenaka + Show 1 more

Open Access

https://doi.org/10.1038/s41598-020-74418-w

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Abstract

The quantum walk is the quantum-mechanical analogue of the classical random walk, which offers an advanced tool for both simulating highly complex quantum systems and building quantum algorithms in a wide range of research areas. One prominent application is in computational models capable of performing any quantum computation, in which precisely controlled state transfer is required. It is, however, generally difficult to control the behavior of quantum walks due to stochastic processes. Here we unveil the walking mechanism based on its particle-wave duality and then present tailoring quantum walks using the walking mechanism (Floquet oscillations) under designed time-dependent coins, to manipulate the desired state on demand, as in universal quantum computation primitives. Our results open the path towards control of quantum walks.

Highlights

The quantum walk is the quantum-mechanical analogue of the classical random walk, which offers an advanced tool for both simulating highly complex quantum systems and building quantum algorithms in a wide range of research areas
Quantum walks with arbitrary time-dependent coins have been studied both numerically and analytically
The numerical simulations have been reproduced almost perfectly by the analytical solutions, and together have revealed the walking mechanism hidden in the quantum walks in the wave picture, i.e., that the coin flipping rate plays the role of the wave speed of the quantum walk governing the walker’s trajectories

Summary

Introduction

The quantum walk is the quantum-mechanical analogue of the classical random walk, which offers an advanced tool for both simulating highly complex quantum systems and building quantum algorithms in a wide range of research areas. One prominent application is in computational models capable of performing any quantum computation, in which precisely controlled state transfer is required It is, generally difficult to control the behavior of quantum walks due to stochastic processes. Precise control of quantum state transfer between arbitrary distant sites is critical for quantum information processing[13,14,15,16] It is, not easy to manipulate quantum states using quantum walks due to their essentially random n ature[17,18,19]. The resulting probability distribution for the quantum walk changed significantly This implies that coin transformation is certainly involved in the walking mechanism and explicitly designing the sequence of coin transformations could lead to a desired state transfer

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