The Control Data Corp. -- which has agreed to cancel its Soviet loan show "Art From the Hermitage Museum in Leningrad" -- said yesterday that it would ask the U.S. government to pay the company's estimated $1 million in bills for the canceled exhibition.

The Minneapolis computer firm, which has long been eager to do business with the Soviets, had agreed to bear the costs of the 400-item show that was to start a two-year tour here at the National Gallery of Art in May. On Monday, explaining that the exhibition was not now "in the national interest," the State Department declined to grant the show the usually pro forma "waiver of judicial seizure" without which the Soviets would not let it proceed.

While saying that it "supports the government," a Control Data statement noted that preparations for this major exhibition have cost Control Data more than $1 million." Requesting "equity" and "fairness," a spokesman for the firm said it wants to be paid back.

The spokesman said, however, that he had no idea what branch of the government might come up with the money.

Following the president's first statement of displeasure with the Soviet invasion of Afghanistan, a Commerce Department official here had mentioned possible reimbursement for high-technology firms whose plans for trade with the U.S.S.R. were suddenly in jeopardy. His discussion of canceled export licenses was cited in yesterday's Control Data statement.

But a Commerce Department spokesman said yesterday that "no existing law covers such reimbursement. They [Control Data] didn't even need an export license for an art show. I don't know what they're talking about. When you trade with the Russians, you take your chances."

The computer firm, which had hoped to recoup much of it investment from museum admissions and catalogue sales, also distributes Russian art books. Control Data had hoped that the Hermitage exhibit would increase interest in the firm's art books. The company had also hoped the Hermitage would buy one of its computers with the royalties received from the sale of such books.