WASHINGTON—Several quantum-computing companies are in talks to give the Commerce Department equity stakes in exchange for federal funding, a signal that the Trump administration is expanding its interventions in what it sees as critical segments of the economy. 

Companies including IonQ, Rigetti Computing and D-Wave Quantum are discussing the government becoming a shareholder as part of agreements to get funding earmarked for promising technology companies, according to people familiar with the matter. Other companies such as Quantum Computing Inc. and Atom Computing are considering similar arrangements.

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