I had the idea of fusing Jupiter in 1973. I was learning about nuclear reactions and wondered what it would take. The first thought is to use a thermonuclear device, but can it reach a depth where ignition would be self-sustaining? The US military hoped that the Earth would not ignite when they did the first H-bomb test. Hydrogen bombs use Lithium and Deuterium fusing in the flash plasma of the uranium or plutonium fission device (or so I recall). Maybe if one packs a large enough quantity of LiD2 ? The mainly hydrogen composition of Jupiter may be less inclined to fuse unless temperature and compression are still hotter that a nuke can provide. If so, a bomb won't do it. The crashing of comets into the Jovian surface yield terrific scars from the burn-up, and I'm sure Jupiter has seen much worse. Thermal or thermonuclear explosions probably can't start it. So yeah, you need a million obelisks.

so jupiter is not dense enough or hot enough to convert. to get to conversion, you need to radiate all of jupiters energy quickly. this can't be done photonically.. nucleonics would suggest that neutrinos are the path to dump 10^47 ergs.
just because i can't see how to do it doesnt mean it can't be done.