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

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.

18 pages, 7 figures, 3 tables, 3 algorithms

References in corpus (3)

• Analysis of parametrically driven exchange-type (iSWAP) and two-photon (bSWAP) interactions between superconducting qubits
• Complete Controllability Despite Degeneracy: Quantum Control of Enantiomer-Specific State Transfer in Chiral Molecules
• Lie algebra for rotational subsystems of a driven asymmetric top

Cited by in corpus (3)

• Quantum control of ro-vibrational dynamics and application to light-induced molecular chirality
• Determining the ability for universal quantum computing: Testing controllability via dimensional expressivity
• Building globally controlled quantum processors with ZZ interactions