A major exhibit of over 400 objects spanning several millenia of art history will arrive at the National Gallery next spring from the Hermitage Museum in Leningrad to begin a two-year tour of American museums. And it will arrive courtesy of an unusual international arrangement by Control Data Corporation, a computer company eager to trade with the Soviet Union.

"The Hermitage of Leningrad: Doorway to World Art," will be the first traveling exhibit representing all departments of the vast, many-faceted museum ever to leave the Soviet Union. Previous exhibits from the Hermitage shown at the National Gallery have concentrated on a particular period such as French Impressionism or the Italian Renaissance.

Included in the exhibit will be prehistoric artifacts of ivory, wood, metal, leather and cloth, remarkably preserved in premafrost that were excavated in this century. Also represented will be Assyrian, ancient Greek and Roman, Oriental, Russian and Western European art.

Besides paintings, sculptures and engravings, the exhibit will include furniture, coins, textiles and objects of silver and gold, including some Scythian gold never before shown in the United States.

The exhibit is being organized by the Minneapolis Institute of Arts with the cooperation of the National Gallery and museums in San Francisco, Brooklyn and Detriot. However, the sponsor and contracting party is Control Data, a Minneapolis-based firm that sells computers and business services. The agreement between Control Data and the Soviet Ministry of Culture was announced yesterday in Moscow.

James Bowe, Control Data vice president for corporate relations, said yesterday from Minneapolis that sponsorship of the exhibit is part of his company's complex effort to sell computers to the Russians - specifically to the Hermitage Museum.

Although it is not unusual for corporations to sponsor art exhibits, the coming Hermitage show apparently marks the first time that a private firm has dealt directly with a foreign government for an exhibition.

The National Gallery is empowered to indemnify traveling exhibits of this kind up to $50 million, but in this case it is not doing so. Instead the exhibit - worth far in excess of $50 million - will be insured by the Soviet Union's national insurance agency, with Control Data paying for the coverage.

Cost figures for the tour have not yet been established, Bowe said: "I can's even tell you whether it will be in seven or eight figures."

"We hope that with the sale of tickets we can more or less break even on the cost of the exhibit - transportation, insurance, etc. - and we expect to take full advantage of public interest in the exhibit with the sales of posters, books and reproductions.

"We hope to realize a profit that will be shared among the museums, Control Data and the Soviet Ministry of Culture, with the expectation that the Ministry of Culture will use the money to buy a Control Data computer system for the Hermitage."

Bowe said that the project began to take form when Control Data's representative in Leningrad became friendly with some of the officials of the Hermitage and they began talking about the possible uses of a computer in the administration of the museum's priceless 2.5 million objects.

"Our man's response was an obvious one," Bowe said: "'Why don't you buy one of our computers?' And the answer was that that takes hard currency, that takes dollars, and they don't get dollars for that."

As part of its effort to raise dollars for the Hermitage, Control Data has already established a subsidiary, Control Data Arts, which is distributing Russian art books, printed in English by Aurora, a Leningrad publisher. There will be 28 titles in the fall lines, mostly based on the collections in various Russian museums.

J. Carter Brown, director of the National Gallery, described the Hermitage exhibit as "unprecendented" and added that it "will give Americans their first opportunity to understand The Hermitage in its true character as an encyclopedic museum." The National Gallery's interest, he said, is part of his continuing effort "to supplement our permanent holdings with exhibits that our visitors would otherwise not be able to see. The exhibit will really be a portrait of a museum. It will have a tremendous range, and we hope to recreate the feeling of that palace."

There will be no admission charge at the National Gallery, but there will at other museums showing the exhibit.

Interestingly, Control Data owns Ticketron, which devised a plan for selling tickets to the King Tut exhibit at the Metropolitan Museum in New York that eliminated the long waiting lines encountered here and elsewhere. Visitors were able to reserve, weeks ahead of time, a half-hour period during which their tickets would be accepted without waiting.

"I would dearly love to see that happen with this exhibit," said Bowe. "I hope the lines will be so long we will need to use that system again." CAPTION: Picture, "A Dog," by 17th-century Dutch painter Paul Potter, part of the Hermitage exhibition.