Quantum simulation describes a great variety of process observed in laboratories and daily life, however, as soon as the computer programs involve more particles, time and storage turn out to be critical issues that constraint the execution of larger simulations. Tensor Contraction Schemes for 2D Problems in Quantum Simulation is based on the ideas of Huckle and Waldherr and is a courageous attempt to describe many-body systems accurately without the intrinsic dimensional problems. To achieve this goal, two well-established techniques are applied to represent large vectors implicitly and, through a variational-based numerical method, minimise the related optimisation problem. Remarkably, the contraction schemes demand linear storage and time resources only. As result, the proposed scheme was able to produce solutions up to the first significant digit for 12-particle system, taking no more than few iteration.Finally, there are still open issues regarding the accuracy in the vector representation and the local optimality of the iterative method that must to be addressed in future investigations.