This paper studies entanglement dynamics in small N-qubit systems by combining theoretical analysis with numerical simulations of stochastic quantum circuits. Using the Schmidt decomposition and the Rényi entropy framework, bipartite entanglement is quantified. An entanglement "heating" procedure is implemented with random quantum gates, along with a Monte Carlo based "cooling" algorithm with Metropolis–Hastings acceptance criteria to reverse it. For systems with 2 ? N ? 6, it is found that reversibility depends critically on the gate set: the Clifford generators {CNOT, NOT, H} and {CNOT, H, S} enable complete entropy reduction, while universal sets do not. This indicates effective irreversibility despite underlying unitary dynamics of quantum circuits.

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