We show that a quantum harmonic oscillator can be prepared in its exact ground state |0⟩ in finite time without violating the third law of thermodynamics. The protocol combines quantum non‑demolition (QND) projective measurements of photon number with a structured electromagnetic vacuum engineered by a three‑dimensional photonic bandgap, a chiral quantum Hall edge, and a parity‑protected superconducting island. These structures enforce a vanishing environmental spectral density at the oscillator frequency, eliminating thermal back‑action. A unitary feedback operation reduces excitations when measurement outcomes are non‑zero. Iteration yields convergence to |0⟩ in a finite number of steps with unit probability. Entropy is conserved globally through measurement back‑action and ancilla consumption, fully consistent with the second and third laws.
Noah Embaye (Tue,) studied this question.