Abstract Following any quantum information processing protocol, it is essential to reset a mixed state of a many-body interacting spin-network to the computational-zero pure state. This task is challenging, both theoretically and experimentally, because of the quantum correlations. There is currently no effective cooling strategy for both high and low temperatures in such networks. Here we put forth a universal cooling strategy for multi-spin interacting networks. The strategy is based on the collective coupling of the system to an ancilla spin that intermittently dumps part of its entropy into an ultracold bath. Yet this strategy should overcome the symmetry-imposed correlations that impede the cooling. To avoid the prohibitive complexity of computing the dynamics, we resort to graph analysis of the network. We show that a unique choice of alternating, non-commuting system-ancilla interaction Hamiltonians exists that breaks the symmetry constraints and allows the network to approach the desired pure state. We illustrate this universal purification strategy in diverse experimental settings. Code availability The code supporting the findings of this study are available from the corresponding authors upon reasonable request. References Loss, D. & DiVincenzo, D. P. Quantum computation with quantum dots. Phys. Rev. A 57, 120–126 (1998). Benjamin, S. C. & Bose, S. Quantum computing with an always-on Heisenberg interaction. Phys. Rev. Lett. 90, 247901 (2003). Yamamoto, Y. et al. Coherent ising machines—optical neural networks operating at the quantum limit. NPJ Quantum Inf. 3, 49 (2017). Johnson, M. W. et al. Quantum annealing with manufactured spins. Nature 473, 194–198 (2011). King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nat. Phys. 18, 1324–1328 (2022). Georgescu, I. M., Ashhab, S. & Nori, F. Quantum simulation. Rev. Mod. Phys. 86, 153–185 (2014). Wang, Z.-M., Byrd, M., Shao, B. & Zou, J. Quantum communication through anisotropic Heisenberg XY