Eur. Phys. J. D 45, 331-334 (2007)
https://doi.org/10.1140/epjd/e2007-00236-0

Controllability of multiple qubit systems^*

¹ College of Mechatronics Engineering and Automation, National University of Defense Technology, Changsha, 410073, P.R. China
² College of Science, National University of Defense Technology, Changsha, 410073, P.R. China

Corresponding author: ^a This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 3 April 2007
Revised: 18 April 2007
Published online: 18 July 2007

Abstract

This paper explores the problem of manipulating multiple-qubit systems when only single-qubit operations or two-qubit-interactive operations are permitted. It is demonstrated that if there exist 2 directional control Hamiltonian for each individual qubit, and one interactive Hamiltonian for each pair of qubits, then multiple qubit systems are open-loop controllable. An important observation of physical interest is emphasized: when only single-qubit operations or two-qubit-interactive operations are permitted, only n(n+3)/2 control Hamilton may guarantee open-loop controllability of n qubit systems, and n(n+3) is, in the restricted sense, also the lower limit on the number of operators needed for controllability. At last, we demonstrate that an n-quantum-dot system is open-loop controllable even when only single-qubit operations or two-qubit-interactive operations are permitted.