In the thesis, we aim to develop and implement algorithms that effectively simulate the dissipative, non-unitary dynamics governed by the Lindblad master equation, using an ancillary system within a quantum circuit framework and driving the system into a desired state. The Lindblad equation is widely used to describe the evolution of open quantum systems, where the interaction with an external environment introduces decoherence and dissipation. Our approach focuses on leveraging ancillary qubits and quantum measurements to effectively simulate the non-reversible effects produced by the damping operators in the Lindblad equation, which are responsible for phenomena such as energy loss, decoherence, and thermalization. These damping operators have filtered artificially in order to collapse the system into a lower energy state. Several methods for simulating such open quantum systems have already been proposed and published in the literature, employing various techniques to model the dissipative processes. Our work builds upon these existing frameworks, with the goal of improving their accuracy and computational efficiency. By enhancing these methods, we aim to create a more robust and scalable solution for simulating a wide range of physical systems that experience non-unitary evolution. We have also implemented the developed algorithm into a Python library, making it accessible for practical simulations. In the final section of the thesis, we present numerical results generated by this library, applied to various quantum models, such as the transverse-field Ising model (TFIM) and the Fermi-Hubbard model. These results demonstrate the effectiveness of our approach in capturing the dissipative dynamics of these systems, providing valuable insights into the behavior of open quantum systems and offering a versatile tool for future research in quantum simulation and quantum computing.     «

In the thesis, we aim to develop and implement algorithms that effectively simulate the dissipative, non-unitary dynamics governed by the Lindblad master equation, using an ancillary system within a quantum circuit framework and driving the system into a desired state. The Lindblad equation is widely used to describe the evolution of open quantum systems, where the interaction with an external environment introduces decoherence and dissipation. Our approach focuses on leveraging ancillary qubits...     »