The President was in south Florida that afternoon, golfing nearby, but there is no indication he saw or interacted with her.
Once on the resort grounds, Zhang was approached by a receptionist and asked why she was there.
"After being asked several times, Zhang finally responded that she was there for a United Nations Chinese American Association event later in the evening," the complaint says.
"The Receptionist knew this event did not exist" but when the Secret Service agent, Ivanovich, followed up with additional questions, Zhang allegedly said she had arrived early for the event so she could "familiarise herself with the property and take pictures."
At that point, Zhang presented documentation that she said was her invitation to the event, but it was written in Chinese and the agent could not read it.
Laurence Leamer, a Palm Beach writer who recently wrote a book about Mar-a-Lago, said that anyone who got past the receptionist desk would have the run of the club's "living room," patio and pool area. He said a guest could not enter Trump's private quarters, but they could probably walk past the door to it.
"You can go anywhere. You're in the living room," he said. "There's no checkpoints once you're in there."
Toni Holt Kramer, a longtime member of the club, said Secret Service agents circulate beyond the reception desk, but their presence is not oppressive. "You don't feel intruded on," she said. "They're there, but they're invisible."
A person familiar with security procedures at the club when the President stays there said it is standard practice for everyone in the reception area to be greeted and questioned about who they are and where they are going.
Secret Service agents took Zhang to a different location to interview her, at which point she became "verbally aggressive," according to the charging document.
"During the second interview of Zhang, she claimed her Chinese friend 'Charles' told her to travel from Shanghai, China to Palm Beach, Florida, to attend this event and attempt to speak with a member of the President's family about Chinese and American foreign economic relations. Agents were unable to obtain any information more specifically identifying Zhang's purported contact, 'Charles,' " the complaint said.
It is unclear if she was referencing Charles Lee, an event promoter who runs a group called the United Nations Chinese Friendship Association - a name similar to the one Zhang had mentioned during her encounter with the receptionist. A lawyer for Zhang declined to comment, and Lee could not be reached.
Zhang also told the agents that she had never claimed she was going to the swimming pool, the complaint says.
After Zhang was stopped and questioned, a search of her belongings turned up four cellphones, a laptop, a hard drive, and a thumb drive which contained "malicious malware," according to the criminal complaint. Authorities said that despite her initial claim to be headed for the pool, she was not carrying a swimsuit.
She is charged with making false statements to a federal law enforcement officer and entering a restricted area, the complaint says.
A Secret Service spokeswoman declined to comment, saying the investigation was ongoing.
The Secret Service tries to keep a tight security cordon around the President to protect him from physical harm and any attempts to eavesdrop or electronically monitor his conversations.
In early 2017, Mar-a-Lago Club guests watched in surprise as the President and Japanese Prime Minister Shinzo Abe huddled with aides at a dinner table as they discussed a ballistic missile test North Korea had just conducted. Trump was criticised afterward for what critics called his loose attitude toward information security.
During the Obama Administration, the Secret Service was criticised by lawmakers for its handling of security breaches - particularly instances in which individuals scaled the White House fence and had to be chased down. A former Bush Administration official with experience in security issues called the Mar-a-Lago breach a significant blunder.
"When in doubt say no and ask up the chain," the official said. "Don't say yes."
People who have recently hosted events at Mar-a-Lago said they were surprised by the apparent ease with which Zhang breached the club's perimeter, saying that, for their own events, they had to submit guest lists days ahead of time.
Michael Barnett, head of the Palm Beach County Republican Party, said that when he submitted a guest list for the annual Lincoln Day Dinner, some people were rejected.
Holt Kramer, the Mar-a-Lago member, said the club closely scrutinises members and their guests, checking identification and cars.
"There's always security, and without a doubt you have to be checked, whether it's the 100th time you've been there, or the first," she said. "If you have guests, you call ahead, at least a couple of days, and you tell them who your guests are. And you tell your guests, 'Make sure you bring your full ID with you.' "
Leamer, the author, said he had been impressed by the security checks when he had visited recently. But, he said, Trump had created a massive security vulnerability at Mar-a-Lago by choosing to make it his "winter White House" while allowing it to remain open to hundreds of members and guests every week.
"How can the president of the United States be spending his weekends in this club with all these people coming in and out?" Leamer said, noting that Trump's private quarters are located in the middle of the busy grounds. "I thought inevitably something was going to happen. And thank God it was a fairly benign thing" in this case, he said, with no apparent physical danger to the President.