Determining the ability for universal quantum computing: Testing controllability via dimensional expressivity

TL;DR

This paper introduces a hybrid quantum-classical algorithm that assesses the controllability of quantum systems by analyzing the dimensional expressivity of parametrized circuits, aiding efficient quantum chip design.

Contribution

It presents a novel method linking controllability to dimensional expressivity, enabling resource-efficient quantum device development.

Findings

Controllability correlates with the number of independent parameters.

The algorithm effectively analyzes qubit arrays with local controls.

Provides a systematic approach for quantum chip design.

Abstract

Operator controllability refers to the ability to implement an arbitrary unitary in SU(N) and is a prerequisite for universal quantum computing. Controllability tests can be used in the design of quantum devices to reduce the number of external controls. Their practical use is hampered, however, by the exponential scaling of their numerical effort with the number of qubits. Here, we devise a hybrid quantum-classical algorithm based on a parametrized quantum circuit. We show that controllability is linked to the number of independent parameters, which can be obtained by dimensional expressivity analysis. We exemplify the application of the algorithm to qubit arrays with nearest-neighbour couplings and local controls. Our work provides a systematic approach to the resource-efficient design of quantum chips.