nuclear fusion is possible. there are a few diferent types of nuclear weaponary. i will start with the most basic.

a fission (atom) bomb - urnaium 235 is smashed with a neutron causing it to break up into two smaller atoms and two or three neutrons. these then go and hit other atoms in a chain reaction. this releases a huge amount of energy as mass is lost somewhere and converted into energy (e=mc2)

that is how atom bombs work, by splitting the atom, fission. it's far more complicated than that really but i am not going to go into supercriticality, gun triggered or imploded starts or how a neurton gun works, or a tamper. unless someone asks me to.

atomic bombs are very ineffecient, the atoms bomb in japan had a 1.5 and a 17 percent effeciency (different types of detonation)

nuclear (hydrogen) bombs use fusion and are much harder to get to work. they use deutrium or tritium (hydrogen with added neutrons), both are hard to store or get to react o last very long at all. so deutrium is mixed with lithium to be stored in a solid state. also to work a fusion bomb is stored in a fission bomb to get it to work (to make tritium which you can't store fromt he lithium) and to give off enough heat to make the fusion possible.

deutrium combines with tritium and releases masses amount of energy and is very effecient (but you still had to detonate an atom bomb to make it work). it's a very complicated system and i would be happy to explain how both bombs work if it is required.

but fusion is possible. what hasn't be managed yet is cold or controllable fusion which could be used for nuclear power.