A repetition code of 15 qubits

The repetition code is an important primitive for the techniques of quantum error correction. Here we implement repetition codes of at most $15$ qubits on the $16$ qubit \emph{ibmqx3} device. Each experiment is run for a single round of syndrome measurements, achieved using the standard quantum technique of using ancilla qubits and controlled operations. The size of the final syndrome is small enough to allow for lookup table decoding using experimentally obtained data. The results show strong evidence that the logical error rate decays exponentially with code distance, as is expected and required for the development of fault-tolerant quantum computers. The results also give insight into the nature of noise in the device.Comment: 7 page

Nonergodic measurements of qubit frequency noise

Slow fluctuations of a qubit frequency are one of the major problems faced by quantum computers. To understand their origin it is necessary to go beyond the analysis of their spectra. We show that characteristic features of the fluctuations can be revealed using comparatively short sequences of periodically repeated Ramsey measurements, with the sequence duration smaller than needed for the noise to approach the ergodic limit. The outcomes distribution and its dependence on the sequence duration are sensitive to the nature of noise. The time needed for quantum measurements to display quasi-ergodic behavior can strongly depend on the measurement parameters

Binary Pulsar Tests of General Relativity in the Presence of Low-Frequency Noise

The influence of the low-frequency timing noise on the precision of measurements of the Keplerian and post-Keplerian orbital parameters in binary pulsars is studied. Fundamental limits on the accuracy of tests of alternative theories of gravity in the strong-field regime are established. The gravitational low-frequency timing noise formed by an ensemble of binary stars is briefly discussed.Comment: 4 pages, contributed paper to the proceedings of the IAU167 colloquium on pulsars, Bonn, August-September 199

Robust CS reconstruction based on appropriate minimization norm

Noise robust compressive sensing algorithm is considered. This algorithm allows an efficient signal reconstruction in the presence of different types of noise due to the possibility to change minimization norm. For instance, the commonly used l1 and l2 norms, provide good results in case of Laplace and Gaussian noise. However, when the signal is corrupted by Cauchy or Cubic Gaussian noise, these norms fail to provide accurate reconstruction. Therefore, in order to achieve accurate reconstruction, the application of l3 minimization norm is analyzed. The efficiency of algorithm will be demonstrated on examples

Dynamic scaling form in wavelet-discriminated Edwards-Wilkinson growth equation

We present an analysis of dynamic scaling of the Edwards-Wilkinson growth model from wavelets' perspective. Scaling function for the surface width is determined using wavelets' formalism, by computing the surface width for each wavelet scale, we show that an exact and simple form of the scaling function is obtained. These predictions are confirmed by computer simulation of a growth model described by the EW equation, and by numerical calculations