Quantum logic using correlated one-dimensional quantum walks

Yoav Lahini,Gregory R Steinbrecher,Adam D Bookatz,Dirk Englund

doi:10.1038/s41534-017-0050-2

Yoav Lahini, Gregory R Steinbrecher + Show 2 more

Open Access

https://doi.org/10.1038/s41534-017-0050-2

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Abstract

Quantum Walks are unitary processes describing the evolution of an initially localized wavefunction on a lattice potential. The complexity of the dynamics increases significantly when several indistinguishable quantum walkers propagate on the same lattice simultaneously, as these develop non-trivial spatial correlations that depend on the particle’s quantum statistics, mutual interactions, initial positions, and the lattice potential. We show that even in the simplest case of a quantum walk on a one dimensional graph, these correlations can be shaped to yield a complete set of compact quantum logic operations. We provide detailed recipes for implementing quantum logic on one-dimensional quantum walks in two general cases. For non-interacting bosons—such as photons in waveguide lattices—we find high-fidelity probabilistic quantum gates that could be integrated into linear optics quantum computation schemes. For interacting quantum-walkers on a one-dimensional lattice—a situation that has recently been demonstrated using ultra-cold atoms—we find deterministic logic operations that are universal for quantum information processing. The suggested implementation requires minimal resources and a level of control that is within reach using recently demonstrated techniques. Further work is required to address error-correction.

Highlights

Quantum walks (QWs) are unitary processes describing the propagation of quantum particles on lattice potentials.[1,2,3]
Experiments demonstrated the behavior of single-particle QWs; these dynamics can be desribed by classical wave equations5– 7,9), and cannot display non-classical features
For interacting bosonic quantum walkers we find that a complete set of highfidelity quantum logic gates can be realized using a linear array of potential wells with nearest-neighbor coupling and only two sites per qubit, demonstrating the universality of this architecture for quantum computation

Summary

INTRODUCTION

Quantum walks (QWs) are unitary processes describing the propagation of quantum particles on lattice potentials.[1,2,3] Originally described as a quantum-mechanical analog of the classical random walk, QWs were found to exhibit faster propagation and enhanced sensitivity to lattice parameters due to their coherent nature.[3]. We show how controlling the lattice potential of a QW can impose certain spatial correlations between walkers Using this approach, we design quantum logic gates on a simple one-dimensional array of potential wells using minimal resources: one quantum walker and a small number of lattice sites per qubit. For interacting bosonic quantum walkers (e.g., ultra-cold atoms in optical potentials or photons in non-linear devices) we find that a complete set of highfidelity quantum logic gates can be realized using a linear array of potential wells with nearest-neighbor coupling and only two sites per qubit, demonstrating the universality of this architecture for quantum computation. While our analysis is general to any system that can support quantum walk dynamics, here we focus on two physical systems in which our results can be implemented using existing experimental capabilities: non-interacting, indistinguishable photons in waveguide lattices and interacting ultra-cold bosonic atoms trapped in an optical lattice.

RESULTS

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METHODS