QUEST Act of 2021 This bill directs the Department of Energy to establish and carry out a program (to be known as the Quantum User Expansion for Science and Technology program or the QUEST program) to encourage and facilitate access to U.S. quantum computing hardware and quantum computing clouds for research purposes in order to (1) enhance the quantum research enterprise of the United States, (2) educate the future quantum computing workforce, and (3) accelerate the advancement of U.S. quantum computing capabilities.