  The terahertz communications have the potential to revolutionize data
transfer with unmatched speed and facilitate the development of new
high-bandwidth applications. This paper studies the performance of downlink
terahertz system assisted by beyond diagonal intelligent reconfigurable surface
(BD-IRS). For enhanced energy efficiency and low cost, a joint precoding and
BD-IRS phase shift design satisfying the $1$-bit resolution constraints to
maximize the spectral efficiency is presented. The original problem is
non-linear, NP-hard, and intricately coupled, and obtaining an optimal solution
is challenging. To reduce the complexity, we first transform the optimization
problem into two problems and then iteratively solve them to achieve an
efficient solution. Numerical results demonstrate that the proposed approach
for the BD-IRS assisted terahertz system significantly enhances the spectral
efficiency compared to the conventional diagonal IRS assisted system.
