Quantum control using quantum memory

Mathieu Roget,Basile Herzog,Giuseppe Di Molfetta

doi:10.1038/s41598-020-78455-3

Abstract

We propose a new quantum numerical scheme to control the dynamics of a quantum walker in a two dimensional space–time grid. More specifically, we show how, introducing a quantum memory for each of the spatial grid, this result can be achieved simply by acting on the initial state of the whole system, and therefore can be exactly controlled once for all. As example we prove analytically how to encode in the initial state any arbitrary walker’s mean trajectory and variance. This brings significantly closer the possibility of implementing dynamically interesting physics models on medium term quantum devices, and introduces a new direction in simulating aspects of quantum field theories (QFTs), notably on curved manifold.

Highlights

We propose a new quantum numerical scheme to control the dynamics of a quantum walker in a two dimensional space–time grid
In this work we do not claim to offer a general theory of quantum control, we provide a new approach in which the control scheme is encoded once and for all into its initial state
The manuscript is organised as follows: in “The model” we will provide the definition of the model with and without memory, in one spatial dimension; in “Control the walker’s dynamics”, we will prove analytically and numerically how to control the variance and the mean trajectory of a quantum walker, solely via the initial condition of the whole system

Summary

Introduction

We propose a new quantum numerical scheme to control the dynamics of a quantum walker in a two dimensional space–time grid. We will prove that the initial condition of the whole system, memory + walker, is sufficient to control, e.g., the variance and the mean position of the walker for all times. The manuscript is organised as follows: in “The model” we will provide the definition of the model with and without memory, in one spatial dimension; in “Control the walker’s dynamics”, we will prove analytically and numerically how to control the variance and the mean trajectory of a quantum walker, solely via the initial condition of the whole system.

Results

Conclusion