"I know a guy" who worked on a similar project 25 years ago, but it was supposed to be a supersonic torpedo.
Actually it was a scam to make the Russians think we were developing it so they'd spend lots O'money on something that didn't work and had already given up on once. maybe we're doing it again with the Chinese?
Lots of design flaws and physics contradictions, like where do you get air to run a jet engine underwater?
If you use a solid rocket propellant or O2/fuel rocket engine it would only run for a matter of seconds, maybe a minute but it would have to be HUGE.
If you could capture all the gas directly behind the sub/torpedo whatever and recycle it and compress it and shoot it out of pores in the skin on the forward section it would work, but the energy and complexity required is staggering.
The only way I could see us making it work would be to have a tiny fission reactor in the nose going critical as soon as it is launched. Not zackly practical. Silly Chinese.
US Navy is developing 'supersonic submarine' that could cut through the ocean | Daily Mail Online