Some speculation on the insides compared to QE class:
QE class is powered by 2x Rolls Royce gas turbines at 36 MW each and 4x Wartsila diesels at 12 MW each. Total power ~120 MW
(see 9L46F configuration). I doubt it can get much better than this.
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But what if 003 is a CONAG configuration with an evolved version of existing HTR-10 reactors and existing QC-280 gas turbines at 28 MW each???
OD, 5 m3 volume, produces ~10 MW, and was put in service 20+ years ago.
An evolutionary improvement would be increasing power to 20 MW with increase in size to 4m x 1.8m OD (doubling of volume, no increase in efficiency) which is still small compared to a marine diesel which is literally 2x larger. 4x evolved HTR-10s and 2x QC-280 turbines for sprinting would produce 136 MW of energy, greater than QE class, with an engine room smaller than the 055 (which requires 4x QC-280 turbines; each turbine likely ~9m x 3m x 3m). If you accept an equal engine room as the 055 which is still small for a carrier, you can add 1x additional QC-280 for more sprinting power or more HTR-10s for baseline power.
4m x 1.8m OD wouldn't require a large hole for installation (would in fact be indistinguishable from installing some minor backup diesel) and refuelling is done by pebbles instead of whole fuel rod assemblies, meaning you can literally just cart the pebbles aboard.
This would shrink the engine room area, vastly increase fuel efficiency, while requiring 0 new technologies.
The HTR-10 is still just a prototype design.
The commercial modular Pebble Bed reactors are a larger version (250 MWth / 105 MWe) and actually take up a lot more space because of the automated pebble inspection and associated storage equipment. Plus the pebbles have a low energy density in comparison to existing nuclear rods.
But if you strip out the pebble inspection and storage equipment, you could put these larger Pebble Bed reactors in, once they've been proven out on land.
EDIT
Come to think of it, an icebreaker would be a better ship to test and prove out a new shipborne nuclear reactor design.