Cooperative control and geometric amplification in dissipative quantum systems

In the control of dissipative quantum systems, the slow relaxation modes usually set the ultimate manipulation timescale. Here we show that this apparent bottleneck can be bypassed: dissipation itself becomes a control resource when fast relaxation channels are deliberately exploited. We demonstrate this mechanism for a qubit subject to non-unital and anisotropic Bloch relaxation. A short coherent pulse first reorients the Bloch vector onto a fast dissipative eigendirection; the subsequent free relaxation then carries the state close to the target, with at most one final corrective pulse. The resulting bang-drift-bang strategy is cooperative: coherent control selects the dissipative channel, while the bath performs most of the transfer. For axial targets, we obtain a closed-form speedup over passive relaxation by a factor of order $\kappa=T_1/T_2\gg1$. For out-of-equilibrium non-axial targets, an additional off-axis interception mechanism provides a further geometric amplification, allowing the hitting-time speedup, still normalized to the axial passive-reset time, to exceed the axial $\kappa\xi$ benchmark by an extra factor of four to five. The mechanism therefore directly connects to standard Bloch-vector qubit platforms, including magnetic-resonance spins, nitrogen-vacancy centers, and superconducting circuits, with potential relevance for quantum-control and fast-reset protocols.