BEIJING — When Wang Huning, a policy adviser to the Chinese president, made a six-month trip to the United States in 1988, he returned with notes for a 400-page memoir.

“The Americans care for strength,” he wrote after watching a football game at the United States Naval Academy. “This reflects the American spirit — that is, to achieve a goal in a short time with power. The Americans adhere to this spirit in many fields, like the military, politics, economics and so on.”

As President Xi Jinping made his first state visit to the United States, including a day of pageantry and diplomacy at the White House on Friday, Mr. Wang was among a small group of advisers at his side.

A member of the Communist Party’s elite Politburo, Mr. Wang, 59, studied American society as a politics professor in Shanghai and an adviser to Mr. Xi’s two predecessors. In the process, he got to know American scholars and officials.