Fusion at the solar center proceeds very slowly, as is evident from the several billion year lifetime of the sun. The sun's break-even time is tens of millions of years, corresponding to pre-nuclear-physics estimates of its lifetime, based on gravitational energy only.
Soooo, to break even in a few nanoseconds, one must naturally far exceed the pressure and temperature at the center of the sun.
... tell me where I'm wrong, and I'll listen.
Particles can't tell time and have no memory. They only know the temperature and pressure they experience moment by moment. The sun converts 4 million tons of matter into pure energy every second and the density at the core is about 15 times that of lead.
The reaction at the sun’s core is the fusion of hydrogen-1, which in spite of the temperatures generated, is extremely slow. With conditions where the density is equivalent of a specific gravity of about 150, and temperatures in hundreds of Kelvins, the power density is only 275 watts per cubic meter. That’s really slower than mammalian metabolism, as a comparison. Much of this is due to the comparitive electrostatic repulsion to be overcome to slam protons together. Not so much for deuterons and tritons, which is also the fuel for thermonukes. The power density in a fusion weapon going off is far higher than the core of the sun. Another evidence of the lower energy threshold for D-T fusion is brown dwarf objects. While not massive enough to initiate P-P fusion (minimum mass is around 0.08 to 0.10 solar masses), if there are traces of deuterium or lithium, there would be short lived fusion reactions, although they will not last long at all on an astronomical timescale.
There is one problem with using laser based inertial confinement. After a pulse, the neodynium glass rods used by the lasers need to cool down. Even a speck of dust on the rods will cause them to shatter when the xenon flashtubes go off to pump the rods into lasing. Electron beams for internal confinement might work better, look up the “Z-Machine” in use at Sandia.
There are two issues:
First, the efficiency of a particular reaction is entirely a function of nuclear reaction kinetics, so, you hit the temperature and pressure necessary to overcome the activation energy and you're good to go, regardless of whether that takes you a few nanoseconds or a few million years. It took a long time to get there in the sun because gravity is weak, and gravitational collapse takes a long time. But, once you get there, you're there. With lasers doing the inertial confinement you can get to temperature and pressure much faster.
If you think of it as nuclear chemistry, how you reach the threshold thermodynamic variables will not affect what values the state variables need to have to have enough free energy to push the reaction.
Second, far less importantly, AFAIK, nobody is going to try to recreate the P-P chain that goes on in the sun. It would be nice if we could, but the reason it proceeds so slowly is that the reaction kinetics for P-P fusion basically suck: it requires a weak interaction to stabilize the P-P fused nucleus. Most of the time the diproton (2He nucleus) is unstable and dissociates. An improbably weak decay flips a proton into a neutron in a very small number of cases. (I can't remember the number, but it's miniscule. This is why the sun is burning so "slowly.") The flipped neutron changes the diproton into deuterium, which is stable.
Most fusion researchers have been trying to do fusion with various combinations of deuterium, tritium, 3He, or even 3Li. These lead to more stable nuclei result products, with much more favorable reaction kinetics. Unfortunately, they also produce fast neutrons, which the P-P chain doesn't. As a result, there are radioactive byproducts our sun doesn't produce (in its primary reaction.)
So, to do fusion at achievable energies with decent Q's, we can't rely on the process used in the sun, anyway.