Deterministic Quantum Information Engine with Topological Protection and Entanglement-Catalyzed Algorithmic Cooling on Superconducting Processors

We present a deterministic quantum information engine designed for active algorithmic purification of a superconducting qubit register. Unlike passive radiative cooling, our protocol exploits mid-circuit measurements and real-time feed-forward (IBM Dynamic Circuits if_test) to execute a closed measurement-feedback cycle without post-selection. Working qubits are embedded in a topological XY-SSH Hamiltonian (ν = 1, bulk gap Δ ≈ 1.83) providing robustness against static coupling and frequency disorder. An ancillary catalyst qubit maintained in the ensemble state ρ_C = I/2 mediates work extraction without net purity loss, satisfying the catalysis conditions of Lipka-Bartosik et al. (PRX 2021). Exact density-matrix simulation yields: information amplification W_info = 0.272 versus W_thermal = 0.015 (18×); apparent COP = 1.00 under the quantum accounting boundary; ΔS_universe = +0.049 ≥ 0 (Sagawa–Ueda second law satisfied). Topology-aware IBM heavy-hex mapping (A→q1, B→q2, C→q4) eliminates SWAP overhead (≤12 native gates per cycle). The protocol is directly applicable to ancilla reset in surface-code QEC architectures and to noise reduction in quantum sensor registers.