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

• URL: http://arxiv.org/abs/2212.04828v1
• Date: Fri, 9 Dec 2022 12:59:44 GMT
• Title: Graph test of controllability in qubit arrays: A systematic way to determine the minimum number of external controls
• Authors: Fernando Gago-Encinas, Monika Leibscher, and Christiane P. Koch
• Abstract summary: 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 find that the number of controls can be reduced from five to one for complex qubit-qubit couplings.
• Score: 62.997667081978825
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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