Invariant Measures and Weak-Magic-Injection Asymptotics in Random Monitored Quantum Circuits
Published in arXiv preprint, 2026
This work develops an analytical theory for random monitored Clifford circuits subject to weak non-Clifford perturbations. It establishes existence and uniqueness of the stationary distribution and determines the leading steady-state magic scaling in the weak-injection regime. Gross–Wigner mana scales linearly in odd-prime local dimensions, whereas qubit 2-stabilizer Rényi entropy has quadratic scaling. The contrast is traced to the different local geometries of these resource measures near stabilizer states.