Yes, and in a more general way Noether thm applies in QM/QFT as well (energy conservation is just a special case). Symmetries become operators acting on the Hilbert/Fock space (ie representation).
With the caveats:
- anomalies-> symmetries/conservation broken by quantum noise (has to be cancelled in valid theories)
- Heisenberg’s incertitude
With the caveats: - anomalies-> symmetries/conservation broken by quantum noise (has to be cancelled in valid theories) - Heisenberg’s incertitude