Efficient Characterization of Quantum Evolutions via a Recommender System

We demonstrate characterizing quantum evolutions via matrix factorization algorithm, a particular type of the recommender system (RS). A system undergoing a quantum evolution can be characterized in several ways. Here we choose (i) quantum correlations quantified by measures such as entropy, negativity, or discord, and (ii) state-fidelity. Using quantum registers with up to 10 qubits, we demonstrate that an RS can efficiently characterize both unitary and nonunitary evolutions. After carrying out a detailed performance analysis of the RS in two qubits, we show that it can be used to distinguish a clean database of quantum correlations from a noisy or a fake one. Moreover, we find that the RS brings about a significant computational advantage for building a large database of quantum discord, for which no simple closed-form expression exists. Also, RS can efficiently characterize systems undergoing nonunitary evolutions in terms of quantum discord reduction as well as state-fidelity. Finally, we utilize RS for the construction of discord phase space in a nonlinear quantum system.

Nonlinear Quantum Phenomena During the Polarization of Nanometer Layers of Proton Semiconductors and Dielectrics

This paper investigates the influence of the structure and parameters of the degenerate quasi-discrete energy spectrum of relaxers (protons) on the mechanism of nonlinear quantum diffusion polarization in nanoscale layers of hydrogen bonded crystals (HBC) in a wide range of parameters of fields (100 kV/m - 1000 MV/m) and temperatures (0-1550 K). The temperature dependence of the quantum transparency of the parabolic potential barrier for protons in HBC is calculated using the Gibbs quantum canonical distribution for the ensemble of non-interacting protons (ideal proton gas balanced with the ions of anion sub-lattice) moving in an onedimensional potential field of a crystalline lattice (in the field of hydrogen bonds) with a zone structure distributed by energy levels. The influence of "zero" oscillations of protons on the temperature dependences of the proton subsystem kinetic coefficients in HBC is considered. It is revealed that proton tunneling influences the nonlinear space-charge polarization kinetics in HBC at high (150-550 K) and ultrahigh (550-1550 K) temperatures when crystalline layer thickness ranges from 1 to 10 nm. The results of theoretical studies (based on earlier experiments) are bound to be prospective for the prediction of HBC-class (KDP, DKDP) ferroelectrics properties, studying the second-order nonlinear optical effects of femtosecond lasers, and the development of memory cells for non-volatile high-speed memory devices.

Nonlinear Quantum Optimization Algorithms via Efficient Ising Model Encodings

Despite extensive research efforts, few quantum algorithms for classical optimization demonstrate realizable advantage. The utility of many quantum algorithms is limited by high requisite circuit depth and nonconvex optimization landscapes. We tackle these challenges to quantum advantage with two new variational quantum algorithms, which utilize multi-basis graph encodings and nonlinear activation functions to outperform existing methods with remarkably shallow quantum circuits. Both algorithms provide a polynomial reduction in measurement complexity and either a factor of two speedup a factor of two reduction in quantum resources. Typically, the classical simulation of such algorithms with many qubits is impossible due to the exponential scaling of traditional quantum formalism and the limitations of tensor networks. Nonetheless, the shallow circuits and moderate entanglement of our algorithms, combined with efficient tensor method-based simulation, enable us to successfully optimize the MaxCut of high-connectivity global graphs with up to 512 nodes (qubits) on a single GPU.

Population transfer in a nonlinear three-level Λ-system by Stark-shift-chirped rapid adiabatic passage

We propose the use of Stark chirped rapid-adiabatic-passage (SCRAP) method to induce a complete population transfer in a nonlinear three-level Λ-type system (nl-SCRAP). We also use the nl-SCRAP method for creating stable diatomic ground molecular Bose-Einstein condensates (BECs) from atomic BECs. In this three-laser technique the pump and Stokes pulses are slightly detuned from transition frequencies, and a third strong hyperbolic-tangent laser pulse induces dynamic Stark shifts of the relevant transitions and compensates third order nonlinearities. If the timing of the three pulses is appropriately chosen, the nonlinear quantum system is prepared to almost complete population inversion between the two lower states in the Λ-like scheme. The paper shows that the efficiency of the nl-SCRAP is higher than the nonlinear stimulated Raman adiabatic passage (nl-STIRAP) technique, and this method can be used in one-photon as well as multi-photon transitions. The transfer process is robust concerning fluctuations of experimental parameters, such as peak Rabi frequencies, the time delay between pulses, and static detunings.

Quantum Implications of Non-Extensive Statistics

Exploring the analogy between quantum mechanics and statistical mechanics, we formulate an integrated version of the Quantropy functional. With this prescription, we compute the propagator associated to Boltzmann–Gibbs statistics in the semiclassical approximation as K=F(T)exp(iScl/ℏ). We determine also propagators associated to different nonadditive statistics; those are the entropies depending only on the probability S± and Tsallis entropy Sq. For S±, we obtain a power series solution for the probability vs. the energy, which can be analytically continued to the complex plane and employed to obtain the propagators. Our work is motivated by the work of Nobre et al. where a modified q-Schrödinger equation is obtained that provides the wave function for the free particle as a q-exponential. The modified q-propagator obtained with our method leads to the same q-wave function for that case. The procedure presented in this work allows to calculate q-wave functions in problems with interactions determining nonlinear quantum implications of nonadditive statistics. In a similar manner, the corresponding generalized wave functions associated to S± can also be constructed. The corrections to the original propagator are explicitly determined in the case of a free particle and the harmonic oscillator for which the semiclassical approximation is exact, and also the case of a particle with an infinite potential barrier is discussed.