Graph test of controllability in qubit arrays: A systematic way to determine the minimum number of external controls

TL;DR

This paper introduces a graph-based method to efficiently determine the controllability of qubit arrays, enabling the reduction of external controls needed for universal quantum computation, demonstrated on five-qubit systems.

Contribution

It presents a novel graph-theoretic framework for controllability analysis, offering a practical alternative to Lie algebra methods for quantum control resource optimization.

Findings

Number of controls reduced from five to one for complex couplings

Controllability can be achieved with two controls for standard couplings

Framework demonstrated on five-qubit array inspired by ibmq_quito

Abstract

The ability to implement any desired quantum logic gate on a quantum processing unit is equivalent to evolution-operator controllability of the qubits. Conversely, controllability analysis can be used to minimize the resources, i.e., the number of external controls and qubit-qubit couplings, required for universal quantum computing. Standard controllability analysis, consisting in the construction of the dynamical Lie algebra, is, however, impractical already for a comparatively small number of qubits. Here, we show how to leverage an alternative approach, based on a graph representation of the Hamiltonian, to determine controllability of arrays of coupled qubits. We provide a complete computational framework and exemplify it for arrays of five qubits, inspired by the ibmq_quito architecture. We find that the number of controls can be reduced from five to one for complex qubit-qubit couplings and to two for standard qubit-qubit couplings.