  Terahertz (THz) communications have been envisioned as a promising enabler to
provide ultra-high data transmission for sixth generation (6G) wireless
networks. To tackle the blockage vulnerability brought by severe path
attenuation and poor diffraction of THz waves, an intelligent reflecting
surface (IRS) is put forward to smartly control the incident THz waves by
adjusting the phase shifts. In this paper, we firstly design an efficient
hardware structure of graphene-based IRS with phase response up to 306.82
degrees. Subsequently, to characterize the capacity of the IRS-enabled THz
multiple-input multiple-output (MIMO) system, an adaptive gradient descent
(A-GD) algorithm is developed by dynamically updating the step size during the
iterative process, which is determined by the second-order Taylor expansion
formulation. In contrast with conventional gradient descent (C-GD) algorithm
with fixed step size, the A-GD algorithm evidently improves the achievable rate
performance. However, both A-GD algorithm and C-GD algorithm inherit the
unacceptable complexity. Then a low complexity alternating optimization (AO)
algorithm is proposed by alternately optimizing the precoding matrix by a
column-by-column (CBC) algorithm and the phase shift matrix of the IRS by a
linear search algorithm. Ultimately, the numerical results demonstrate the
effectiveness of the designed hardware structure and the considered algorithms.
