Eur. Phys. J. Plus (2022) 137: 720
https://doi.org/10.1140/epjp/s13360-022-02904-3

Regular Article

Time optimal realization of two-qubit entangler

¹ Department of Theoretical Physics and Astrophysics, University of Tabriz, 51664, Tabriz, Iran
² Physics Department, Faculty of Science, Imam Khomeini International University, Qazvin, Iran

^b f.naqdi@tabrizu.ac.ir

Received: 12 February 2022
Accepted: 23 May 2022
Published online: 22 June 2022

Abstract

Optimal control theory is a versatile tool applied to decompose unitary quantum operations into a sequence of entangling and single-qubit gates. Here, we seek a systematic way to find time-optimal pulse sequences to transfer coherence in both mixed and pure states and produce an entangling gate in quantum networks. To this end, we use the algebra of Dirac $\gamma$ matrices to reduce the problem to actual variables and, by applying a Cartan decomposition to SO(4), we formulate the optimal control problem and give an operational approach to realize the entangler gate experimentally. We produce an arbitrary perfect two-qubit entangler, creating a maximally-entangled state out of some initial product state. Also, we calculate the geometric discord and the optimal time required to steer an initial state with zero discord into a mixed state with maximum discord in two-qubit systems.