– Two years ago, Xi Jinping and Barack Obama took a stroll in their shirtsleeves in the California sunshine. The getting-to-know-you chat on the Sunnylands estate went so well Obama declared it "terrific."

This week, when the presidents of the world's two biggest economies meet in Washington, things will be different. On the surface, the trip will go smoothly, if not exactly Sunnylands 2.0. Months of shuttling diplomats will ensure Xi and Obama's public comments are sufficiently nuanced and that the Chinese president gets polite pomp on his first state visit to the United States, including a banquet and 21-gun salute.

Underneath, the relationship is being rattled along several fault lines. There are tensions over China's heavy-handed intervention to prop up shares, access to each others' markets, cyber-hacking, disputed Asian waterways and China's human rights record. The broader question is how these two very big — but very different — countries can continue to get along.

For Xi, fresh off a large military parade in Beijing, the visit is about recognition of China's status as a resurgent world power. For Obama, the conversation is about preserving U.S. clout in a region it has dominated since World War II, including access for its companies. The U.S. presidential election provides a noisy backdrop, as candidates cast China as a foe seeking to erode American strength.

"The atmosphere is a bit nasty, a far cry from two years ago. At this moment, there is a long list of negativities in bilateral ties, while the so-called bright spots, those cooperative areas, are too vague to be seen clearly," said Niu Jun, an international relations professor at Peking University. "The imperatives now are to control the negative areas."

Xi and Obama will both seek to come away from meetings that start Thursday claiming results. Prospective areas for agreement include climate change, anti-terrorism efforts, North Korea, the U.S.-led Iranian nuclear deal and progress toward a two-way investment treaty.

"This is going to be a difficult summit; the best they can hope is to shore up joint ideas that the U.S. and China can still collaborate and do things together," said Orville Schell, the director of the Center on U.S.-China Relations at the Asia Society in New York. "It's difficult to have an enthusiastic and open conversation under the current circumstances."

Cyber-espionage, human rights and China's claims to sovereignty over most of the South China Sea, which contains some of the world's busiest shipping lanes, are the thorniest issues, said Jeffrey Bader, who formerly advised Obama on Asia policy at the National Security Council.

Obama last week escalated the fight over cyberspace, saying the U.S. was preparing measures to show that economic espionage won't be tolerated. "This is not just a matter of us being mildly upset," Obama said.

"Those are the big three problems," said Bader, a visiting scholar at the Brookings Institution. "None is solvable in the near future, but the administration will want dialogue or reassurance from the Chinese that they will not take steps to aggravate any of these problems."