We develop a measurement-based protocol for purifying logical states of a quantum system, including quantum error correcting codes, in arbitrary thermal states with unit fidelity and finite probability, using a single auxiliary qubit. The protocol entails a time evolution caused by an engineered Hamiltonian realizable using current technology, which results in transitions between the logical and error subspaces of the system mediated by the auxiliary qubit, followed by a projective measurement in an optimum basis on the auxiliary qubit and an appropriate postselection of the measurement outcomes. We show that the protocol is flexible in using suboptimal measurements to achieve a fidelity as high as $90\%$ via multiple iterations of the purifying procedure, thereby highlighting its robustness against variations in the measurement basis. We demonstrate the applicability of the developed protocol in quantum error correcting codes as well as in paradigmatic quantum spin models. We observe that the performance of the protocol is robust even when the thermal noise persists during the purification process, and discuss a number of possible generalizations of the prescription.

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• Quantum computation
• Quantum error correction
• Quantum information theory