The USA is attempting to allow China to peacefully rise by use of commercial power rather than military power. Commerce creates consumption which addicts citizens to consumerism, which then makes it difficult for governments to jeopardize without insurrection. That is the only strategy. The USA prefers the world consist of good commercial citizens. The fundamental problem though, is that China is a populous and very poor country that also contains conquered and rebellious territories, open to insurrection, and the wealthy coasts can be militarily devastated, and driven to starvation by blockading access to the South China Sea. The Chinese are quite aware of this vulnerability, plus they have a ‘chip’ on their shoulders from both british conquest, the failure of Marxism, and extended poverty, and the impact of those events upon the cultural mythology of Chinese superiority as the center of the world.
Furthermore, their rise is complicated by the fact that they do not subscribe to the western moral code that currently is enforced by the United States on world trade — a code we take for granted but is antithetical to the Chinese. (We resolve conflicts quickly and rely upon honesty and they wait for opportunity using deception. This difference in ethics pervades both cultures.)
The USA currently polices the world system of trade (largely the seas) because it took over the British naval bases at the end of the world wars. And petrodollars allow us to fund that policing. We sell dollars to other countries as debt, which they then use to buy oil, and then we inflate away the debt. This is how we ‘tax’ the developed world for our expensive military services.
However, this system of abstract taxation which is breaking down, and the USA can no longer count on those advantages because of demographic reasons, competitive reasons due to internationalization of labor and technology, and monetary reasons due to the use of other currencies as petroleum and reserve currencies.
General consensus among strategic thinkers is that the USA’s power will decline slowly and that Chinese rise will be moderated at some near point by simple economic pressures. The more radical thinkers suggest that most empires like the USA do not decline slowly, but very rapidly over a period of less than 50 years, and that the standard of living of the average american will be so significantly affected by the loss in purchasing power, that existing political tensions will be drastically exacerbated, sufficiently so that we will have our own problems of insurrection.
In other words, both countries are more vulnerable to internal pressures due to China’s rise than they are to conflict with one another. The alternative school of thought suggests that when empires succumb to internal conflict, then they exaggerate external threats in order to pressure the citizens to stay united (see Iran for example). So that once the states and china experience internal pressures they will conduct a war over it. I tend to think this is unlikely because the USA’s citizens will have internalized it’s decline by that time.
As I understand it, that is the current thinking in as short a summary as I can place it.