Local controllability of quantum networks

TL;DR

This paper establishes a criterion for controlling many-body quantum systems through local Hamiltonian manipulation, applicable to various systems, enabling quantum algorithms via single-qubit operations on chains.

Contribution

It introduces a topology-based sufficient condition for local controllability in quantum networks, including specific chains like Heisenberg and AKLT.

Findings

Heisenberg and AKLT chains are controllable via end spins

Control is independent of coupling details, relying only on topology

Arbitrary quantum algorithms can be implemented on these chains

Abstract

We give a sufficient criterion that guarantees that a many-body quantum system can be controlled by properly manipulating the (local) Hamiltonian of one of its subsystems. The method can be applied to a wide range of systems: it does not depend on the details of the couplings but only on their associated topology. As a special case, we prove that Heisenberg and Affleck-Kennedy-Lieb-Tasaki chains can be controlled by operating on one of the spins at their ends. In principle, arbitrary quantum algorithms can be performed on such chains by acting on a single qubit.