As I recall from Star Trek, the Romulans powered their star ships with a black hole.
This is likely not a new theory.
Yes, using quantum singularities as power sources, or weapons, has been in Sci-Fi for a while.
Instead of just letting the quantum singularity evaporate and capture it's mass/energy from the gamma radiation of the escaping Hawking Radiation, I might be tempted to "feed" it with a particle beam (It would have to be something like a partial Dyson sphere, ring, arc or "cap" to both capture enough energy from the Sun, and to be long enough to create the requisite energy as a particle accelerator.) I’d blast the singularity and make it “eat” positively charged ions/charged particles since one of the attributes a black hole still has outside it’s event horizon/ Schwarzschild radius besides it’s mass, and the Hawking Radiation from quantum tunneling/particle-antiparticle pair splits is “charge”. Then I could manipulate it and move it, or build a structure around it using magnetic fields.
Since it has enormous gravitational attraction, albeit very close to its sub-microscopic Event Horizon, can be “held” magnetically due to its charge, perhaps it would be possible to balance its charge with its gravitational attraction so it would both simultaneously hold and repel protons/hydrogen ions just above the event horizon, heated by the Hawking/gamma radiation to boost it, and get very high order fusion. If reactions were tailored to produce an excess of neutrons, being neutral, they’d only have gravitational attraction at the event horizon, not be repelled by the singularity’s positive charge, and add back mass-energy that had been lost through the Hawking radiation.
As such you’d have a mass/energy conversion machine. The downside is that it’s really no longer a quantum singularity, but perhaps an atom-sized one, for it to be able to ‘eat’ and be ‘fed’ particles in this manner. So we’re actually talking about a singularity that’s more like asteroid-mass, and as such is that much harder and more energy intensive to move. The upside is when quantum singularities evaporate and lose mass, it starts to accelerate geometrically as the event horizon gets ever smaller, it intersects and splits ever more virtual particle pairs, and eventually goes off with a final gamma burst that's something on the order of two million megatons...
So perhaps using this as a more permanent installation to power launch lasers for solar sails or somesuch might be a better application than using it as a ship’s drive or power source. But then that begs the question that it may just be better to use the Dyson arc’s or sphere solar collector in the first place rather than go through all this trouble. Or use it’s captured energy to make anti-matter instead.