Yes. That's right.
Gun-type assembly is so simple that even Taliban or militias might be able to pull it off if they can acquire enough enriched uranium. You just split your fissile material in two halves and keep them apart until you drop the bomb, when the two halves join each other and create a supercritical mass for explosion. The problem is that it is very inefficient and it has a risk of predetonation, although it is a very small chance. In other words, it has a very low yield/weight ratio and its storage can be risky (even though the risk is very small). The main reason for its low yield is that once explosion starts, only a small portion of your fissile material (uranium) goes under fission and the rest of the material expands so fast due to rising temperature that it becomes subcritical immediately and the chain reaction stops after microseconds.
Then there's the implosion technique which has a higher yield but it's much more complicated. Criticality is achieved mainly by converging shock waves that result in the compression of the fissile material. It has a higher yield than the gun-type assembly because your fissile material stays compressed for a longer period and more of your fissile material has time to go under fission before the chain reaction stops. The main technical challenge is to compress your fissile material with converging shock waves and keep it compressed. Compressing uranium/plutonium becomes exponentially more difficult. 2 times compression is easy, 3 times compression is very difficult but doable, and 4 times compression is insanely difficult.
Then it's time for fusion-boosted fission. Based on the details of the AMAD project, I guess this is where Iran might be now. Basically, any country that wants to declare itself a nuclear state in the 21st century should start from here to be taken seriously. The main feature of this design is that a small fusion reaction takes place to provide a high number of fast neutrons. Usually, a mixture of deuterium and tritium is used as an additional source of neutrons in the early stage of explosion. The fusion reaction starts almost immediately after the fission reaction that provides the required energy for fusion to take place. After that, because it all happens very fast and still in the early stages of the explosion, the additional neutrons that are created very early by the fusion reaction will exponentially contribute to the fission of the fissile material, greatly enhance the yield of the weapon.
Now, you can say that miniaturization is basically increasing yield to weight ratio. You can remove or decrease the weight of some components of your weapon. For example, if you use a hollow-pit, you can remove the pusher (which reflects the shockwave backwards) and reduce the size of your tamper (which prevents neutrons from escaping). Also, you can inject deuterium-tritium before implosion to boost the fission.
Can Iran do this sort of thing? I don't know. I think the details of the AMAD project indicate that Iran has already mastered a levitated pit.
@Shawnee previously posted a picture of a possible Iranian design in the Iranian Chill Thread. Maybe he can post it here again. From what I remember, it seemed like a levitated pit. If so, that puts Iran in 2003 somewhere near Mark 4 or Mark 5 in terms of US nuclear weapons. But a better question is, how much miniaturization does Iran need actually? Realistically, Iran's only legitimate target for establishing nuclear deterrence is Israel. Khorramshahr can lift 1,800 kilograms to a distance of 2,000 kilometers with a CEP of under 10 meters. That's more than enough to carry a 2 tonne warhead to Israel, and probably even some Eastern European countries. What else does Iran need realistically?
As for whether Iran can do all of this using computer simulations, again, I don't know. But you can obviously simulate the hydrodynamics of shockwave generation with computers and experiment with it without getting caught. You can also insert sensors to calculate the number of neutrons without a hot test. It seems that least in theory, you can get an idea of how well your design should work. But does it mean that it should work as expected? Plus, if your goal is to establish nuclear deterrence, at the end of the day, it is established only when your adversaries detect and estimate on their own the yield of your weapon. If it's a fizzle yield like North Korea in 2006, it won't make them leave you alone.
