Controlling qubit networks in polynomial time

TL;DR

This paper establishes a polynomial-time upper bound for implementing unitary transformations on qubit networks with local controls, enabling efficient quantum gate operations crucial for scalable quantum computing.

Contribution

It introduces a polynomial-time bound for unitary control in qubit networks and demonstrates efficient concatenation of systems via controllable two-body interactions.

Findings

Polynomial upper bound for control time on qubit networks.

Efficient concatenation of qubit systems through two-body interactions.

Identification of a system with minimal control requirements.

Abstract

Future quantum devices often rely on favourable scaling with respect to the system components. To achieve desirable scaling, it is therefore crucial to implement unitary transformations in an efficient manner. We develop an upper bound for the minimum time required to implement a unitary transformation on a generic qubit network in which each of the qubits is subject to local time dependent controls. The set of gates is characterized that can be implemented in a time that scales at most polynomially in the number of qubits. Furthermore, we show how qubit systems can be concatenated through controllable two body interactions, making it possible to implement the gate set efficiently on the combined system. Finally a system is identified for which the gate set can be implemented with fewer controls. The considered model is particularly important, since it describes electron-nuclear spin interactions in NV centers.