  Implementing quantum error correction (QEC) protocols is a challenging task
in today's era of noisy intermediate-scale quantum devices. We present quantum
circuits for a universal, noise-adapted recovery map, often referred to as the
Petz map, which is known to achieve close-to-optimal fidelity for arbitrary
codes and noise channels. While two of our circuit constructions draw upon
algebraic techniques such as isometric extension and block encoding, the third
approach breaks down the recovery map into a sequence of two-outcome POVMs. In
each of the three cases we improve upon the resource requirements that
currently exist in the literature. Apart from Petz recovery circuits, we also
present circuits that can directly estimate the fidelity between the encoded
state and the recovered state. As a concrete example of our circuit
constructions, we implement Petz recovery circuits corresponding to the
$4$-qubit QEC code tailored to protect against amplitude-damping noise. The
efficacy of our noise-adapted recovery circuits is then demonstrated through
ideal and noisy simulations.
