Computation on Spin Chains with Limited Access

TL;DR

This paper demonstrates how to perform quantum computation on spin chains with limited control, using efficient control sequences on a single site and its neighbor, enabling fault-tolerant quantum circuits.

Contribution

It introduces a method for controlling a spin chain with minimal access, revealing insights into controllability and computational capabilities of such systems.

Findings

Efficient control sequences on a single site and neighbor enable quantum computation.

Array control provides parallelism for fault-tolerant circuits.

Contradictions between controllability and computational ability are exposed.

Abstract

We show how to implement quantum computation on a system with an intrinsic Hamiltonian by controlling a limited subset of spins. Our primary result is an efficient control sequence on a nearest-neighbor XY spin chain through control of a single site and its interaction with its neighbor. Control of an array of sites yields sufficient parallelism for the implementation of fault-tolerant circuits. The framework exposes contradictions between the control theoretic concept of controllability with the ability of a system to perform quantum computation.