Introduction and scope

The quantum-error-correction formulation of holographic subregion reconstruction is established, rather than introduced here. Almheiri, Dong, and Harlow connected bulk locality with quantum error correction; perfect-tensor networks subsequently supplied explicit finite encoders and reconstruction examples ADH,HaPPY. Operator-algebra quantum error correction separates correctable observables and subsystems BKK. Approximate reconstruction can be studied using approximate-correction and universal-recovery methods BenyApprox,Cotler. These results concern correctability or recovery maps. They do not, by themselves, specify the live-register ledger of an executable decoder.

The question addressed here is:

When a logical subsystem is reconstructible from an accessible boundary region, what quantum storage, records, scheduling, and communication are required to execute a declared recovery task?

Our contribution is a resource-certified finite construction. We give the code, gates, measurement branches, output conventions, and lower bounds together. We make no claim that the underlying five-qubit code, perfect tensor, or quantum-error-correction interpretation is new.