Fourth, they should assert their commitment to a global free trade agreement in the decade ahead, because current arrangements under negotiation are partial and sometimes conflicting. China is embarking on a new round of reforms that is likely to make American and Chinese economic interests intersect more closely over time. So China should, when the time is ripe, welcome and be welcomed by members of the Trans Pacific Partnership, and the US should not be excluded from Asian regional arrangements.

Chinese investment in the US is growing, but is nowhere near as substantial as it should be for both US and Chinese interests. And since the US is locked out of some sectors in China's market, the leaders should instruct their commercial and financial officials to address these shortcomings.

If the expression of these principles proves possible, then Obama and Xi would do well to assign their governments the responsibility to follow up in a practical yet visionary fashion. The Strategic and Economic Dialogue, an important annual meeting of Chinese and American senior officials, is scheduled for July in the US. The S&ED has the virtue of assembling stakeholders across both systems to address issues. But it is also cumbersome and infrequent.

Therefore, the leaders should assign sub-cabinet level officials to meet more frequently. There are four broad areas that can be designated as sub-groups to the S&ED. These should be assigned ambitious objectives, taking advantage of the fact that Xi is likely to remain China's leader for 10 years. One goal is to keep the respective bureaucracies committed to constructive long-term objectives that can be a counterweight to the grinding competition that so often accompanies adjustments in the correlation of forces in the region and the world.

The four sub-S&ED umbrella talks should be on economics, military, non-traditional issues and regional security.

Economics: The leaders can ask their financial and commercial officials to establish the conditions for the US and China to pave the way for a global or large multilateral free trade agreement over the next decade.

Military: Since Xi assumed office in November, China's military has exhibited a much more open approach to improving relations with the US armed forces. Having been subjected to on-off, deeply suspicious relations for years, both sides should seize this opportunity to deepen contacts and understanding, dispelling problems of "transparency" along the way.

Non-traditional issues: Cyber hacking, threats in space, climate change, pandemics and energy policy are areas where American and Chinese interests intersect. Obama and Xi should instruct their officials to find ways to cooperate over the next decade and reach agreements on how to manage non-traditional challenges.

Regional security: The leaders should instruct their officials to cooperate in building a multi-lateral regional security mechanism for the Indo-Pacific region over the next decade. Tensions between China and Japan, Vietnam, the Philippines and India indicate what a difficult objective this will be. But they also show the need for such a mechanism. Mistrust must be overcome gradually with substantial step-by-step progress.

The California summit has great potential. The leaders need to assess their ledgers of benefit and risk, but they will rise to the occasion only if they see and respect their counterpart's needs as well. If Obama and Xi can rise to the conceptual challenge and articulate a path forward, they have a chance to contribute a richer chapter to history than the previous leaders have made in decades.

The author is vice-president for studies, The Carnegie Endowment for International Peace.