Quantum Singular Value Decomposer

We present a variational quantum circuit that produces the Singular Value Decomposition of a bipartite pure state. The proposed circuit, that we name Quantum Singular Value Decomposer or QSVD, is made of two unitaries respectively acting on each part of the system. The key idea of the algorithm is to train this circuit so that the final state displays exact output coincidence from both subsystems for every measurement in the computational basis. Such circuit preserves entanglement between the parties and acts as a diagonalizer that delivers the eigenvalues of the Schmidt decomposition. Our algorithm only requires measurements in one single setting, in striking contrast to the $3^n$ settings required by state tomography. Furthermore, the adjoints of the unitaries making the circuit are used to create the eigenvectors of the decomposition up to a global phase. Some further applications of QSVD are readily obtained. The proposed QSVD circuit allows to construct a SWAP between the two parties of the system without the need of any quantum gate communicating them. We also show that a circuit made with QSVD and CNOTs acts as an encoder of information of the original state onto one of its parties. This idea can be reversed and used to create random states with a precise entanglement structure.Comment: 6 + 1 pages, 5 figure

Multivectorial strategy to interpret a resistive behaviour of loads in smart buildings

In Smart buildings, electric loads are affected by an important distortion in the current and voltage waveforms, caused by the increasing proliferation of non linear electronic devices. This paper presents an approach on non sinusoidal power theory based on Geometric Algebra that clearly improves traditional methods in the optimization of apparent power and power factor compensation. An example is included that demonstrates the superiority of this approach compared with traditional methods.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Wavelets: a powerful tool for studying rotation, activity, and pulsation in Kepler and CoRoT stellar light curves

Aims. The wavelet transform has been used as a powerful tool for treating several problems in astrophysics. In this work, we show that the time-frequency analysis of stellar light curves using the wavelet transform is a practical tool for identifying rotation, magnetic activity, and pulsation signatures. We present the wavelet spectral composition and multiscale variations of the time series for four classes of stars: targets dominated by magnetic activity, stars with transiting planets, those with binary transits, and pulsating stars. Methods. We applied the Morlet wavelet (6th order), which offers high time and frequency resolution. By applying the wavelet transform to the signal, we obtain the wavelet local and global power spectra. The first is interpreted as energy distribution of the signal in time-frequency space, and the second is obtained by time integration of the local map. Results. Since the wavelet transform is a useful mathematical tool for nonstationary signals, this technique applied to Kepler and CoRoT light curves allows us to clearly identify particular signatures for different phenomena. In particular, patterns were identified for the temporal evolution of the rotation period and other periodicity due to active regions affecting these light curves. In addition, a beat-pattern signature in the local wavelet map of pulsating stars over the entire time span was also detected.Comment: Accepted for publication on A&

Type Ia supernovae and the ^{12}C+^{12}C reaction rate

The experimental determination of the cross-section of the ^{12}C+^{12}C reaction has never been made at astrophysically relevant energies (E<2 MeV). The profusion of resonances throughout the measured energy range has led to speculation that there is an unknown resonance at E\sim1.5 MeV possibly as strong as the one measured for the resonance at 2.14 MeV. We study the implications that such a resonance would have for the physics of SNIa, paying special attention to the phases that go from the crossing of the ignition curve to the dynamical event. We use one-dimensional hydrostatic and hydrodynamic codes to follow the evolution of accreting white dwarfs until they grow close to the Chandrasekhar mass and explode as SNIa. In our simulations, we account for a low-energy resonance by exploring the parameter space allowed by experimental data. A change in the ^{12}C+^{12}C rate similar to the one explored here would have profound consequences for the physical conditions in the SNIa explosion, namely the central density, neutronization, thermal profile, mass of the convective core, location of the runaway hot spot, or time elapsed since crossing the ignition curve. For instance, with the largest resonance strength we use, the time elapsed since crossing the ignition curve to the supernova event is shorter by a factor ten than for models using the standard rate of ^{12}C+^{12}C, and the runaway temperature is reduced from \sim8.14\times10^{8} K to \sim4.26\times10^{8} K. On the other hand, a resonance at 1.5 MeV, with a strength ten thousand times smaller than the one measured at 2.14 MeV, but with an {\alpha}/p yield ratio substantially different from 1 would have a sizeable impact on the degree of neutronization of matter during carbon simmering. We conclude that a robust understanding of the links between SNIa properties and their progenitors will not be attained until the ^{12}C+^{12}C reaction rate is measured at energies \sim1.5 MeV.Comment: 15 pages, 6 tables, 10 figures, accepted for Astronomy and Astrophysic