Direct Wigner tomography of a superconducting anharmonic oscillator

The analysis of wave-packet dynamics may be greatly simplified when viewed in phase-space. While harmonic oscillators are often used as a convenient platform to study wave-packets, arbitrary state preparation in these systems is more challenging. Here, we demonstrate a direct measurement of the Wigner distribution of complex photon states in an anharmonic oscillator - a superconducting phase circuit, biased in the small anharmonicity regime. We test our method on both non-classical states composed of two energy eigenstates and on the dynamics of a phase-locked wavepacket. This method requires a simple calibration, and is easily applicable in our system out to the fifth level.Comment: 5 figures, 1 table and supplementary materia

State tomography of capacitively shunted phase qubits with high fidelity

We introduce a new design concept for superconducting quantum bits (qubits) in which we explicitly separate the capacitive element from the Josephson tunnel junction for improved qubit performance. The number of two-level systems (TLS) that couple to the qubit is thereby reduced by an order of magnitude and the measurement fidelity improves to 90%. This improved design enables the first demonstration of quantum state tomography with superconducting qubits using single shot measurements.Comment: submitted to PR

Transformed Dissipation in Superconducting Quantum Circuits

Superconducting quantum circuits must be designed carefully to avoid dissipation from coupling to external control circuitry. Here we introduce the concept of current transformation to quantify coupling to the environment. We test this theory with an experimentally-determined impedance transformation of $\sim 10^5$ and find quantitative agreement better than a factor of 2 between this transformation and the reduced lifetime of a phase qubit coupled to a tunable transformer. Higher-order corrections from quantum fluctuations are also calculated with this theory, but found not to limit the qubit lifetime. We also illustrate how this simple connection between current and impedance transformation can be used to rule out dissipation sources in experimental qubit systems.Comment: 4 pages, 4 figure

Energy decay and frequency shift of a superconducting qubit from non-equilibrium quasiparticles

Quasiparticles are an important decoherence mechanism in superconducting qubits, and can be described with a complex admittance that is a generalization of the Mattis-Bardeen theory. By injecting non-equilibrium quasiparticles with a tunnel junction, we verify qualitatively the expected change of the decay rate and frequency in a phase qubit. With their relative change in agreement to within 4% of prediction, the theory can be reliably used to infer quasiparticle density. We describe how settling of the decay rate may allow determination of whether qubit energy relaxation is limited by non-equilibrium quasiparticles.Comment: Main paper: 4 pages, 3 figures, 1 table. Supplementary material: 8 pages, 3 figure

Reduced phase error through optimized control of a superconducting qubit

Minimizing phase and other errors in experimental quantum gates allows higher fidelity quantum processing. To quantify and correct for phase errors in particular, we have developed a new experimental metrology --- amplified phase error (APE) pulses --- that amplifies and helps identify phase errors in general multi-level qubit architectures. In order to correct for both phase and amplitude errors specific to virtual transitions and leakage outside of the qubit manifold, we implement "half derivative" an experimental simplification of derivative reduction by adiabatic gate (DRAG) control theory. The phase errors are lowered by about a factor of five using this method to $\sim 1.6^{\circ}$ per gate, and can be tuned to zero. Leakage outside the qubit manifold, to the qubit $|2\rangle$ state, is also reduced to $\sim 10^{-4}$ for $20\%$ faster gates.Comment: 4 pages, 4 figures with 2 page supplementa

Deterministic entanglement of photons in two superconducting microwave resonators

Quantum entanglement, one of the defining features of quantum mechanics, has been demonstrated in a variety of nonlinear spin-like systems. Quantum entanglement in linear systems has proven significantly more challenging, as the intrinsic energy level degeneracy associated with linearity makes quantum control more difficult. Here we demonstrate the quantum entanglement of photon states in two independent linear microwave resonators, creating N-photon NOON states as a benchmark demonstration. We use a superconducting quantum circuit that includes Josephson qubits to control and measure the two resonators, and we completely characterize the entangled states with bipartite Wigner tomography. These results demonstrate a significant advance in the quantum control of linear resonators in superconducting circuits.Comment: 11 pages, 11 figures, and 3 tables including supplementary materia

Dynamic quantum Kerr effect in circuit quantum electrodynamics

A superconducting qubit coupled to a microwave resonator provides a controllable system that enables fundamental studies of light-matter interactions. In the dispersive regime, photons in the resonator exhibit induced frequency and phase shifts which are revealed in the resonator transmission spectrum measured with fixed qubit-resonator detuning. In this static detuning scheme, the phase shift is measured in the far-detuned, linear dispersion regime to avoid measurement-induced demolition of the qubit quantum state. Here we explore the qubit-resonator dispersive interaction over a much broader range of detunings, by using a dynamic procedure where the qubit transition is driven adiabatically. We use resonator Wigner tomography to monitor the interaction, revealing exotic non-linear effects on different photon states, e.g., Fock states, coherent states, and Schrodinger cat states, thereby demonstrating a quantum Kerr effect in the dynamic framework.Comment: 7 pages, 4 figure

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