Lifetime and Coherence of Two-Level Defects in a Josephson Junction

We measure the lifetime ($T_{1}$) and coherence ($T_{2}$) of two-level defect states (TLSs) in the insulating barrier of a Josephson phase qubit and compare to the interaction strength between the two systems. We find for the average decay times a power law dependence on the corresponding interaction strengths, whereas for the average coherence times we find an optimum at intermediate coupling strengths. We explain both the lifetime and the coherence results using the standard TLS model, including dipole radiation by phonons and anti-correlated dependence of the energy parameters on environmental fluctuations.Comment: 4 pages, 4 figures and supplementary material (3 pages, 2 figures, 1 table

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

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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

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

OpenFermion: The Electronic Structure Package for Quantum Computers

Quantum simulation of chemistry and materials is predicted to be an important application for both near-term and fault-tolerant quantum devices. However, at present, developing and studying algorithms for these problems can be difficult due to the prohibitive amount of domain knowledge required in both the area of chemistry and quantum algorithms. To help bridge this gap and open the field to more researchers, we have developed the OpenFermion software package (www.openfermion.org). OpenFermion is an open-source software library written largely in Python under an Apache 2.0 license, aimed at enabling the simulation of fermionic models and quantum chemistry problems on quantum hardware. Beginning with an interface to common electronic structure packages, it simplifies the translation between a molecular specification and a quantum circuit for solving or studying the electronic structure problem on a quantum computer, minimizing the amount of domain expertise required to enter the field. The package is designed to be extensible and robust, maintaining high software standards in documentation and testing. This release paper outlines the key motivations behind design choices in OpenFermion and discusses some basic OpenFermion functionality which we believe will aid the community in the development of better quantum algorithms and tools for this exciting area of research.Comment: 22 page