Demonstration of two-qubit quantum algorithms with a solid-state electronic processor

We present the experimental implementation of two-qubit quantum algorithms in a superconducting circuit. Our processor incorporates local and fast flux biasing of two transmon qubits within a circuit QED architecture. An off-resonant cavity bus shields the qubits from the external environment and couples them to each other via virtual photon exchange. Meanwhile, integrated short-circuited coplanar waveguides proximal to each qubit allow nanosecond control of their frequencies. We demonstrate flux-controlled single-qubit z rotations and a qubit-qubit conditional phase (c-phase) interaction with a coupling strength tunable by two orders of magnitude. These operations are combined with frequency-multiplexed x and y rotations to form a set of gates universal for quantum computation. Dispersive frequency shifts of the cavity bus allow tomography of the two-qubit state, and accurate determination of state purity, fidelity and entanglement. The processor is first programmed to generate and detect entanglement on demand using sequences of five single-qubit operations and one c-phase. The four Bell states are generated with fidelities better than 90%, corresponding to a concurrence of 0.85 or an entanglement of formation of 0.8. Next, the Grover search algorithm is implemented by concatenating eight single-qubit and two c-phases operations. The fidelity of the algorithm output states to the theoretical ideal is ~ 80%, consistent with the observed T₁ times ~ 1 us and the total duration ~ 130 ns of the algorithm sequence. We also program and execute the Deutsch-Jozsa algorithm, finding similar performance. Prospects for scaling the processor beyond two qubits will be discussed. Research supported by NSF, NSA and ARO.