A graph-theoretical approach to analyze controllability and its application to qubit systemsMonika Leibscher*

The ability to implement any quantum logic gate in a system of coupled qubits is equivalent to evolution-operator controllability of the qubit system. Controllability analysis can thus be utilized to determine the minimal number of external controls and qubit-qubit couplings required for universal quantum computing in a given qubit array [1]. Analyzing controllability of qubit systems faces two main challenges, the exponential scaling of the Hilbert space dimension with the number of qubits and the inherent existence of multiple transitions with equal energy gaps. We present a graphical method that is suitable to handle both challenges [2,3]. As a working example, we apply this graph test to 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 [1].

 

[1] F. Gago-Encinas, M. Leibscher, C. P. Koch, Quantum Sci. Technol. 8 045002 (2023)

[2] E. Pozzoli, M. Leibscher, M. Sigalotti, U. Boscain and C. P. Koch, J. Phys. A: Math. Theor. 55, 215301 (2022).

[3] M. Leibscher, E. Pozzoli, C. Pérez, M. Schnell, M. Sigalotti, U. Boscain, C. P. Koch, Commun. Phys. 5, 110 (2022).