Perfect State Transfer in Two and Three Dimensional Structures

TL;DR

This paper presents a novel scheme for perfect quantum state transfer in two- and three-dimensional lattice structures with minimal control, utilizing a Hadamard switch for efficient routing and read-write operations.

Contribution

It introduces a new quantum routing scheme in 2D and 3D lattices using a Hadamard switch, simplifying control requirements for quantum state transfer.

Findings

Achieves perfect state transfer with less control complexity.

Utilizes a Hadamard switch based on four-dimensional Hadamard matrices.

Supports uploading and downloading qubits to built-in read-write heads.

Abstract

We introduce a scheme for perfect state transfer in regular two and three dimensional structures. The interactions on the lattices are of XX spin type with uniform couplings. In two dimensions the structure is a hexagonal lattice and in three dimensions it consists of hexagonal planes joined to each other at arbitrary points. We will show that compared to other schemes, i) much less control is needed for routing, ii) the algebra of global control is quite simple, iii) the same kind of control can upload and download qubit states to or from built-in Read-Write (RW) heads. Pivotal use is made of a quantum switch which we introduce and call it Hadamard switch, since its operation depends on the existence of a Hadamard matrix in four dimensions.