Compressed sensing quantum process tomography for superconducting quantum gates

We apply the method of compressed sensing (CS) quantum process tomography (QPT) to characterize quantum gates based on superconducting Xmon and phase qubits. Using experimental data for a two-qubit controlled-Z gate, we obtain an estimate for the process matrix $\chi$ with reasonably high fidelity compared to full QPT, but using a significantly reduced set of initial states and measurement configurations. We show that the CS method still works when the amount of used data is so small that the standard QPT would have an underdetermined system of equations. We also apply the CS method to the analysis of the three-qubit Toffoli gate with numerically added noise, and similarly show that the method works well for a substantially reduced set of data. For the CS calculations we use two different bases in which the process matrix $\chi$ is approximately sparse, and show that the resulting estimates of the process matrices match each ther with reasonably high fidelity. For both two-qubit and three-qubit gates, we characterize the quantum process by not only its process matrix and fidelity, but also by the corresponding standard deviation, defined via variation of the state fidelity for different initial states.Comment: 16 pages, 11 figure

On the NP-Hardness of Approximating Ordering Constraint Satisfaction Problems

We show improved NP-hardness of approximating Ordering Constraint Satisfaction Problems (OCSPs). For the two most well-studied OCSPs, Maximum Acyclic Subgraph and Maximum Betweenness, we prove inapproximability of $14/15+\epsilon$ and $1/2+\epsilon$. An OCSP is said to be approximation resistant if it is hard to approximate better than taking a uniformly random ordering. We prove that the Maximum Non-Betweenness Problem is approximation resistant and that there are width-$m$ approximation-resistant OCSPs accepting only a fraction $1 / (m/2)!$ of assignments. These results provide the first examples of approximation-resistant OCSPs subject only to P $\neq$ \NP

Improving the Coherence Time of Superconducting Coplanar Resonators

The quality factor and energy decay time of superconducting resonators have been measured as a function of material, geometry, and magnetic field. Once the dissipation of trapped magnetic vortices is minimized, we identify surface two-level states (TLS) as an important decay mechanism. A wide gap between the center conductor and the ground plane, as well as use of the superconductor Re instead of Al, are shown to decrease loss. We also demonstrate that classical measurements of resonator quality factor at low excitation power are consistent with single-photon decay time measured using qubit-resonator swap experiments.Comment: 3 pages, 4 figures for the main paper; total 5 pages, 6 figures including supplementary material. Submitted to Applied Physics Letter

Planar Superconducting Resonators with Internal Quality Factors above One Million

We describe the fabrication and measurement of microwave coplanar waveguide resonators with internal quality factors above 10 million at high microwave powers and over 1 million at low powers, with the best low power results approaching 2 million, corresponding to ~1 photon in the resonator. These quality factors are achieved by controllably producing very smooth and clean interfaces between the resonators' aluminum metallization and the underlying single crystal sapphire substrate. Additionally, we describe a method for analyzing the resonator microwave response, with which we can directly determine the internal quality factor and frequency of a resonator embedded in an imperfect measurement circuit.Comment: 4 pages, 3 figures, 1 tabl

Denaturation transition of stretched DNA

We generalize the Poland-Scheraga model to consider DNA denaturation in the presence of an external stretching force. We demonstrate the existence of a force-induced DNA denaturation transition and obtain the temperature-force phase diagram. The transition is determined by the loop exponent $c$ for which we find the new value $c=4\nu-1/2$ such that the transition is second order with $c=1.85<2$ in $d=3$. We show that a finite stretching force $F$ destabilizes DNA, corresponding to a lower melting temperature $T(F)$, in agreement with single-molecule DNA stretching experiments.Comment: 5 pages, 3 figure