Generation of Three-Qubit Entangled States using Superconducting Phase Qubits

Entanglement is one of the key resources required for quantum computation, so experimentally creating and measuring entangled states is of crucial importance in the various physical implementations of a quantum computer. In superconducting qubits, two-qubit entangled states have been demonstrated and used to show violations of Bell's Inequality and to implement simple quantum algorithms. Unlike the two-qubit case, however, where all maximally-entangled two-qubit states are equivalent up to local changes of basis, three qubits can be entangled in two fundamentally different ways, typified by the states $|\mathrm{GHZ}> = (|000> + |111>)/\sqrt{2}$ and $|\mathrm{W}> = (|001> + |010> + |100>)/\sqrt{3}$. Here we demonstrate the operation of three coupled superconducting phase qubits and use them to create and measure $|\mathrm{GHZ}>$ and $|\mathrm{W}>$ states. The states are fully characterized using quantum state tomography and are shown to satisfy entanglement witnesses, confirming that they are indeed examples of three-qubit entanglement and are not separable into mixtures of two-qubit entanglement.Comment: 9 pages, 5 figures. Version 2: added supplementary information and fixed image distortion in Figure 2

Quantum process tomography of two-qubit controlled-Z and controlled-NOT gates using superconducting phase qubits

We experimentally demonstrate quantum process tomography of controlled-Z and controlled-NOT gates using capacitively-coupled superconducting phase qubits. These gates are realized by using the $|2\rangle$ state of the phase qubit. We obtain a process fidelity of 0.70 for the controlled-phase and 0.56 for the controlled-NOT gate, with the loss of fidelity mostly due to single-qubit decoherence. The controlled-Z gate is also used to demonstrate a two-qubit Deutsch-Jozsa algorithm with a single function query.Comment: 10 pages, 8 figures, including supplementary informatio

Spectral signatures of many-body localization with interacting photons

Statistical mechanics is founded on the assumption that a system can reach thermal equilibrium, regardless of the starting state. Interactions between particles facilitate thermalization, but, can interacting systems always equilibrate regardless of parameter values\,? The energy spectrum of a system can answer this question and reveal the nature of the underlying phases. However, most experimental techniques only indirectly probe the many-body energy spectrum. Using a chain of nine superconducting qubits, we implement a novel technique for directly resolving the energy levels of interacting photons. We benchmark this method by capturing the intricate energy spectrum predicted for 2D electrons in a magnetic field, the Hofstadter butterfly. By increasing disorder, the spatial extent of energy eigenstates at the edge of the energy band shrink, suggesting the formation of a mobility edge. At strong disorder, the energy levels cease to repel one another and their statistics approaches a Poisson distribution - the hallmark of transition from the thermalized to the many-body localized phase. Our work introduces a new many-body spectroscopy technique to study quantum phases of matter