eng Ansari Education and Research Society Journal of Ultra Scientist of Physical Sciences July 2026 38 7 82 84 http://dx.doi.org/10.22147/jusps-B/380701 1558 article PURAN SINGH MEHRA 1 HoD, Department of Mathematics Govt. P.G. College, Berinag, Pithoragarh, Uttarakhand - 262531 (India) <p style="text-align:justify">The exponential scaling of Hilbert spaces presents a major computational bottleneck in simulating and controlling large scale multi qubit systems. This paper establishes the tensor product space not just as composite vector space, but fundamentally as a multi linear mapping that describes quantum operations across desperate subsystems. By modelling quantum gates and straight through this lense, we preserve the internal structural integrity of quantum operations while exponentially decreasing the computational overhead needed for simulation and control.</p> https://ultraphysicalsciences.org/paper/1558/ Tensor Product Multilinear Mapping Quantum Technology