The federal government said Friday it will spend $425 million to advance supercomputer technology, the latest sign of its determination to leapfrog China in a field often linked to national security and economic competitiveness.

The U.S. Department of Energy plans to install two International Business Machines Corp. systems valued at $325 million at Lawrence Livermore National Laboratory in California and Oak Ridge National Laboratory in Tennessee The project, called Coral, also includes Argonne National Laboratory. The machines,...