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If the goal is to classically simulate a noisy quantum circuit using discrete noise channels, there is an approximate simulation technique that avoids using density matrices (and therefore an exponential overhead) by simulating trajectories of the noisy quantum circuit. Suppose you are interested in simulating an $m$-qubit unitary $U$ that can be decomposed ...


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In addition to the rich physics answer by @user1271772 in terms of Hamiltonian, and computational approach answer by @3yakuya, I would like to add the quantum information picture here. The imperfect fidelity can be modeled by two realistic scenarios: The noisy gates (due to realistic crosstalk or decoherence via $T_1$ [amplitude damping] and $T_2$ [phase ...


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