Realizing the Petz Recovery Map on an NMR Quantum Processor

The Petz recovery map is a central construct in quantum information theory, providing an explicit, channel-aware prescription for reversing the effects of noise. Unlike standard quantum operations, the Petz map is intrinsically dependent on a chosen reference state, which makes its physical implementation and experimental validation particularly challenging. Here, we report an experimental realization of Petz recovery maps on a nuclear magnetic resonance (NMR) quantum processor using the duality quantum computing (DQC) algorithm. We investigate two paradigmatic single-qubit noise models: amplitude damping and phase damping, and construct corresponding families of Petz recovery maps for varying reference states. By systematically tuning the reference state, we experimentally demonstrate the state-adapted nature of Petz recovery, observing both enhanced recovery when the reference state is well matched and fidelity degradation for mismatched choices. Our experimental results show close quantitative agreement with theoretical predictions, providing direct evidence that the Petz recovery map constitutes a physically realizable, reference-state-dependent recovery channel rather than a purely formal inverse of noise. This work bridges the gap between the abstract information-theoretic formulation of Petz recovery and its implementation on a realistic quantum platform, and establishes an experimental benchmark for testing noise-adapted recovery strategies on near-term quantum devices.