A quantum computer system packs quantum circuits into quantum memory so the circuits can be run concurrently. A quantum-circuit packer includes a resource mapper and a packing evaluator. The resource mapper characterizes the task of identifying candidate packings of pending quantum circuits as an integer linear problem (ILP), for which solutions are known. The packing evaluator applies an optimization criterion to select an optimum packing from the candidate packings. The optimum packing is run; the results are assigned to respective circuits that make up the packing.