Peking — The Reagan administration cannot have its Taiwan cake and eat it too. That seems to be the first signal the Chinese leadership has sent to Washington in the wake of Secretary of State George Shultz's visit here last week.
Premier Zhao Ziyang has accepted President Reagan's invitation to visit the United States. But a controversy over whether he is or is not coming this year illustrates how little mutual trust and confidence there is between Washington and Peking despite Mr. Shultz's visit.
President Reagan came to office as a man known to be sympathetic to Taiwan but also conscious of the need to make common cause with China against the Soviet Union. He ordered Mr. Shultz to visit Peking and took the occasion to renew a longstanding invitation to Mr. Zhao to visit the US.
Mr. Zhao accepted the invitation but left the specific date to be negotiated through diplomatic channels. While Shultz was still in Peking, the White House announced Feb. 5 that Zhao had accepted the President's invitation to come to Washington ''in 1983.'' Media stories from Washington quoted an American official as saying that Reagan himself was unlikely to visit China during his current term because he would have to consider the impact on Taiwan.
Up to that point Peking's coverage of the Shultz visit had been restrained, pointing out that there were problems and obstacles in relations between the US and Washington but without going into great detail about Peking's contentions regarding Taiwan.
The White House announcement, however, and the tendency American officials had displayed at briefings to downplay the Taiwan problem, apparently raised tempers in Peking. There followed a swift, stinging account of the Shultz visit from Peking's viewpoint, stressing that without solving the Taiwan problem ''mutual trust between China and the US is out of the question.''
The following day, Feb. 7, Peking's foreign office issued another curt statement noting that Zhao had indeed accepted Reagan's invitation but that the date was yet to be fixed and that ''it has not been decided he will go this year.''
It now appears that the White House statement Feb. 5 was made without Shultz's knowledge and that it seriously undercut his patient effort to convince Peking that the Reagan administration was a government with which China could enjoy a relationship of mutual trust and confidence despite continuing differences over Taiwan.
Meanwhile, Peking and Washington have been involved in other disputes having little or nothing to do with Taiwan. The protracted negotiations over China's textile exports to the US are one such issue. The kind of high technology the US is willing to export to China is another.
The first dispute has to do with the current recession in the US and other industrialized nations. The second has to do first with what kind of high technology the US is willing to export at all, and second to what categories of countries these exports may go.
The US has had great difficulties in both areas even with close friends and allies. How should it categorize China? As a potential foe, like the Soviet Union? As a nonaligned friend, like India or Yugoslavia?
In terms of US global strategic interests, Reagan administration sources see China as an important partner in the global effort to contain Soviet expansionism. Peking largely shares the White House view of the Soviet Union as an expansion-minded ''hegemonist'' power, although to Washington's intense irritation Peking also faults the US for manifestations of ''hegemonism.''
As regards Taiwan, Peking is not asking President Reagan to abandon the relationship the Carter administration so carefully worked out with ''the people of Taiwan'' nor does it demand an immediate halt to the supply of defensive arms to Taiwan.
It does, however, demand strict compliance with a premise President Reagan inherited from his predecessor, that there is but one China, the People's Republic, and that Taiwan is part of this one China.
Tactics such as the White House announcement of Feb. 5 suggest to the Chinese leadership that while President Reagan wants a Sino-American partnership in the global strategic arena against the Soviet Union, in bilateral relations the President's heart remains with Taiwan. Unless and until this perception changes, there can be neither warmth nor trust in this administration's relations with China.