Scaling Feedback-Stabilized Quantum Criticality to 100 Qubits via Adaptive Matrix Product States

We present matrix product state (MPS) simulations of feedback-stabilized quantum criticality, extending system sizes to N = 100 qubits—over six times larger than accessible via exact diagonalization. Building on the recent identification of the 1/e information horizon as a universal quantum-classical boundary, we develop an adaptive bond dimension strategy that preserves critical correlations during time evolution despite truncation errors. Random quantum circuits with measurement rates adjusted via real-time feedback successfully stabilize the Schmidt concentration across N ∈ {20, 40, 60, 80, 100} qubits. For the largest system (N = 100), ensemble-averaged results yield ⟨Kc⟩ = 0.363±0.003, consistent with the theoretical prediction 1/e = 0.368 within 1.2% (t-test p = 0.15), demonstrating successful crossing of the psychological 100-qubit barrier. The observed non-monotonic scaling reflects oscillatory finite-size convergence characteristic of second-order critical points. All system sizes remain within ±5% of target, with variance decreasing for larger N, demonstrating robustness across correlation length regimes. Our adaptive MPS protocol enables simulation of volume-law entanglement phases at unprecedented mesoscopic scales, establishing computational feasibility for near-term experimental platforms.