Kind of late to the party but I believe that China has a few possible options/goals when it comes to nuclear deterrence.
1. Minimum deterrence. The current arsenal. To be fair, even a small arsenal like the one used by North Korea is enough to deter a direct invasion from the US. However, given the fact that the US and China are fighting over interests in the Indo-Pacific region, such a small stockpile will mean that the US will be a lot more aggressive, knowing that they have a major advantage when it comes to nuclear warfare. They may even choose to escalate a conventional conflict to a nuclear with the use of tactical nuclear weapons knowing that China would lose in a large-scale exchange.
Not recommended but technically even 1 bomb constitutes minimum deterrence.
2. Credible deterrence (countervalue). The idea is that China can build a force capable of killing a large number of Americans by nuking cities. As I have mentioned earlier in this thread, 20 4.4Mt warheads can be used to cause 160 million casualties in the US, as well as contaminating American cities and food production areas. Thus, China will need to focus on building a force survivable enough to deliver such a strike. Again, as I have said previously in this thread, China needs around 500 silos to ensure that >20 warheads will be delivered to the US in the case of a US first strike. SSBNs and TELs are great but they have a smaller payload than silo-based ICBMs, meaning that you will need more mobile ICBMs to ensure that you are delivering the same destructive power to the US.
Around 500 silo-based ICBMs, plus existing mobile ICBM launchers and SSBNs.
3. Credible deterrence (flexible response). Similar to above. Assuming killing 1/3 of American population is enough to deter the Americans from launching a full-scale nuclear war, 500 silos are needed. However, the Americans nuclear doctrine is based on the idea of flexible response, where the US would use nuclear weapons to intentionally escalate a conventional war if they are losing. The idea is that the US can use nuclear weapons to deter further aggression and force the other side to negotiate without igniting full scale nuclear exchange. To deter the US from using tactical nuclear weapons, the best way is to have a stockpile of tactical nuclear weapons of your own. It does not have to be large but it does have to be survivable. This should allow China to retaliate in kind with tactical nuclear weapons. The targets will most likely be American fleets and bases to ensure that China is not escalating the war too much. After all, nuking American cities will likely generate a lot of hate and irrational reactions. After the initial exchange, both sides can start negotiating before all things go to hell.
Around 500 silo-based ICBMs, plus existing mobile ICBMs, SSBNs and <100 tactical nuclear weapons.
4. Credible deterrence (post war deterrence). This is more of a "what-if" scenario. China may have to launch most of its nuclear weapons against the US and its nuclear forces may not be in good shape after the war. To ensure other states do not take advantage of this situation, China should keep a small stockpile of nuclear weapons in case of a turbulent post-war environment. Thus, around 20-30 mobile ICBMs should be prepared beforehand. These missiles should not be fired unless the situation is very dire. Also, tactical nuclear weapons should be kept in case of the destruction of the conventional forces of China.
Same as above but with >20 more mobile launchers kept in underground tunnels. Also 150-200 tactical nuclear weapons.
5. MAD. Simple. The number of nuclear weapons needed to glass the US. There are around 360 cities in the US with a population of above 100000. Larger cities would require more warheads to totally destroy. Thus, cities with a population of >1000000 should be attacked with 3 nuclear warheads. The top 3 cities (NY, LA, Chicago) should be attacked with 6 warheads to ensure complete destruction. In total, it will take 3*6 + 53*3 + 305*1 = 482 warheads to destroy all American cities. Additionally, around 50 ground bursting warheads should be used to contaminate food production areas. Finally, 300-400 warheads should be spared for the destruction of American military bases and fleets. Smaller installations may survive though.
Again, assuming 5% of incoming American ICBMs will fail, it will take at least 16000 (!!) silos to ensure that China can completely glass the US after an American first strike. Fortunately, China can use a large number of mobile launchers to supplement a silo force. Assuming 20% of all mobile launchers (TEL/train/SSBNs) will survive a first strike, China will need 4000 weapons in total. Somewhat larger than the current Russian arsenal but way smaller than the Soviet one during the height of the cold war.
4000 warheads deployed on mobile launchers, plus tactical nuclear weapons and a large number of decoy silos to attract enemy fire.
Couple of points
If you want to cause the most destruction, it's better to use multiple smaller warheads to cover a larger area than one big warhead.
You can see the evolution in size from the W88 to the W76 warhead. It also reduces the risk from ABM defences and warhead failures.
Plus if you assume that a DF-41 ICBM has 10x W76-type nuclear warheads, then the number of DF-41 ICBMs required is far lower than the 350 silos currently under construction, for most scenarios.
Personally, I don't see China going above 1000 deliverable warheads against the continental USA. That is more than enough for MAD.
And there to be a total of 1500 warheads overall, which is just *equal* to what Russia or the USA has.
I also expect the USA to go ape when this happens, and then start a self-imposed arms race at its nuclear *inferiority* to a combined Russia+China arsenal.
But if China has an economy 2x larger than the USA in 10 years time and China is happy with the current size of its nuclear arsenal, who is going to go bankrupt first in an arms race?
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As I said previously, it's kind of sad this is happening
But it's the inevitable logic of cold war competition
And the more than the US talks about Taiwan, the faster China's military spending grows