  The von Neumann architecture for a classical computer comprises a central
processing unit and a memory holding instructions and data. We demonstrate a
quantum central processing unit that exchanges data with a quantum
random-access memory integrated on a chip, with instructions stored on a
classical computer. We test our quantum machine by executing codes that involve
seven quantum elements: Two superconducting qubits coupled through a quantum
bus, two quantum memories, and two zeroing registers. Two vital algorithms for
quantum computing are demonstrated, the quantum Fourier transform, with 66%
process fidelity, and the three-qubit Toffoli OR phase gate, with 98% phase
fidelity. Our results, in combination especially with longer qubit coherence,
illustrate a potentially viable approach to factoring numbers and implementing
simple quantum error correction codes.
