Star-connected computer networks are explored using the example of terahertz modeling. Existence conditions for the complete synchronization between constituent lasers are found numerically. Numerical simulations were conducted using the Matrix Laboratory (MATLAB) software to solve Delay Differential Equations. Extensive numerical simulations with different initial states confirm that high-quality, near-perfect complete synchronization between terahertz lasers occurs. As in the real world, parameters can differ; we simulated the star-connected computer network model with parameter mismatches of 3–5%. Still, we have obtained close to 100% of correlation between the dynamics of terahertz lasers. Synchronization is important in chaos-based communication. It is underlined that chaos-based communication security between computer networks can offer an additional layer of security to the traditional cryptography based on the Rivest, Shamir, and Adleman (RSA) algorithm. This algorithm uses the mathematical challenge of factoring very large prime numbers. The extra layer of security is of immense importance in light of the exponential increase in central processing units (CPUs) in computers. This is especially true in light of the quantum processing unit (QPU), which is the core processor of a quantum computer, using qubits in superposition and entanglement to perform complex, parallel calculations far beyond classical CPUs. Unlike traditional binary CPUs, QPUs excel at optimization, cryptography, and artificial intelligence tasks.