On Quantum Entropy and Excess Entropy Production in a System-Environment Pure State

We explore a recently introduced quantum thermodynamic entropy $S^Q_{univ}$ of a pure state of a composite system-environment computational "universe" with a simple system $\mathcal{S}$ coupled to a constant temperature bath $\mathcal{E}$. The principal focus is "excess entropy production" in which the quantum entropy change is greater than expected from the classical entropy-free energy relationship. We analyze this in terms of quantum spreading of time dependent states, and its interplay with the idea of a microcanonical shell. The entropy takes a basis-dependent Shannon information definition. We argue for the zero-order $\mathcal{SE}$ energy basis as the unique choice that gives classical thermodynamic relations in the limit of weak coupling and high density of states, including an exact division into system and environment components. Entropy production takes place due to two kinds of processes. The first is classical "ergodization" that fills the full density of states within the microcanonical shell. The second is excess entropy production related to quantum spreading or "quantum ergodization" of the wavepacket that effectively increases the width of the energy shell. Lorentzian superpositions with finite microcanonical shell width lead to classical results as the limiting case, with no excess entropy. We then consider a single $\mathcal{SE}$ zero-order initial state, as the examplar of extreme excess entropy production. Systematic formal results are obtained for a unified treatment of excess entropy production for time-dependent Lorentzian superpositions, and verified computationally. It is speculated that the idea of free energy might be extended to a notion of "available energy" corresponding to the excess entropy production. A unified perspective on quantum thermodynamic entropy is thereby attained from the classical limit to extreme quantum conditions.Comment: 24+21 pages (double spaced), 6+6 figure

Second hyperpolarizability of carbon tetrachloride

Although present theories of nonlinear optics agree with observed behavior in simple atoms such as helium, more complex molecules containing many electrons, such as carbon tetrachloride (CCI4), cannot consistently be described by theory. Through experimental analysis of nonlinear materials, a new, more sophisticated model for describing their properties could be realized. The purpose of our experiment was to measure the nonlinear behavior of the second harmonic signal generated from CCI4 and to compare the results with the prediction by the CCSD(T) molecular model

Numerical analysis of oscillating flow about a circular cylinder

The numerical experiments, carried out through the use of the vorticity­ stream function equations and their finite difference form, on sinusoidally­ oscillating as well as co-existing flows (sinusoidal oscillation plus steady mean flow) at low and intermediate Keulegan-Carpenter numbers are described. A third-order in time, second-order in space, three-level predictor-corrector finite­ difference scheme has been used. The Poisson equation for the stream function was solved by a Fast Poisson Solver based on the High Order Difference Approximation with Identity Expansion (HODIE) and the Fast Fourier Transform (FFT) methods provided by the National Center for Atmospheric Research for the solution of separable elliptic partial differential equations with a non-square grid. The analysis has produced force-transfer and fluid-damping coefficients comparable to those obtained experimentally for both types of flows (i.e., with and without current) and to those obtained with a square grid through the use of the IMSL library.http://archive.org/details/numericalanalysi00lotsLieutenant Commander, United States NavyApproved for public release; distribution is unlimited

Graph decomposition techniques for solving combinatorial optimization problems with variational quantum algorithms

The quantum approximate optimization algorithm (QAOA) has the potential to approximately solve complex combinatorial optimization problems in polynomial time. However, current noisy quantum devices cannot solve large problems due to hardware constraints. In this work, we develop an algorithm that decomposes the QAOA input problem graph into a smaller problem and solves MaxCut using QAOA on the reduced graph. The algorithm requires a subroutine that can be classical or quantum--in this work, we implement the algorithm twice on each graph. One implementation uses the classical solver Gurobi in the subroutine and the other uses QAOA. We solve these reduced problems with QAOA. On average, the reduced problems require only approximately 1/10 of the number of vertices than the original MaxCut instances. Furthermore, the average approximation ratio of the original MaxCut problems is 0.75, while the approximation ratios of the decomposed graphs are on average of 0.96 for both Gurobi and QAOA. With this decomposition, we are able to measure optimal solutions for ten 100-vertex graphs by running single-layer QAOA circuits on the Quantinuum trapped-ion quantum computer H1-1, sampling each circuit only 500 times. This approach is best suited for sparse, particularly $k$-regular graphs, as $k$-regular graphs on $n$ vertices can be decomposed into a graph with at most $\frac{nk}{k+1}$ vertices in polynomial time. Further reductions can be obtained with a potential trade-off in computational time. While this paper applies the decomposition method to the MaxCut problem, it can be applied to more general classes of combinatorial optimization problems

Modelling noise in global Molmer-Sorensen interactions applied to quantum approximate optimization

Many-qubit Molmer-Sorensen (MS) interactions applied to trapped ions offer unique capabilities for quantum information processing, with applications including quantum simulation and the quantum approximate optimization algorithm (QAOA). Here, we develop a physical model to describe many-qubit MS interactions under four sources of experimental noise: vibrational mode frequency fluctuations, laser power fluctuations, thermal initial vibrational states, and state preparation and measurement errors. The model parameterizes these errors from simple experimental measurements, without free parameters. We validate the model in comparison with experiments that implement sequences of MS interactions on two and three $^{171}$Yb$^+$ ions. The model shows good agreement after several MS interactions as quantified by the reduced chi-squared statistic $\chi^2_\mathrm{red}< 2$. As an application we examine MaxCut QAOA experiments on three and six ions. The experimental performance is quantified by approximation ratios that are $91\%$ and $83\%$ of the optimal theoretical values. Our model predicts $0.93^{+0.03}_{-0.02}$ and $0.92^{+0.06}_{-0.06}$, respectively, with disagreement in the latter value attributable to secondary noise sources beyond those considered in our analysis. With realistic experimental improvements to reduce measurement error and radial trap frequency variations the model achieves approximation ratios that are 99$\%$ of the optimal. Incorporating these improvements into future experiments is expected to reveal new aspects of noise for future modeling and experimental improvements.Comment: 10+5 pages, 6+3 figure

NASA ESTO Lidar Technologies Investment Strategy: 2016 Decadal Update

The NASA Earth Science Technology Office (ESTO) recently updated its investment strategy in the area of lidar technologies as it pertains to NASA's Earth Science measurement goals in the next decade. The last ESTO lidar strategy was documented in 2006. The current (2016) report assesses the state-of-the-art in lidar technologies a decade later. Lidar technology maturation in the past decade has been evaluated, and the ESTO investment strategy is updated and laid out in this report according to current NASA Earth science measurement needs and new emerging technologies

Generation of Kerr combs centered at 4.5{\mu}m in crystalline microresonators pumped by quantum cascade lasers

We report on the generation of mid-infrared Kerr frequency combs in high-finesse CaF$_2$ and MgF$_2$ whispering-gallery mode resonators pumped with continuous wave room temperature quantum cascade lasers. The combs were centered at 4.5$\mu$m, the longest wavelength to date. A frequency comb wider than a half of an octave was demonstrated when approximately 20mW of pump power was coupled to an MgF2 resonator characterized with quality factor exceeding 10$^8$.Comment: 5 pages, 5 figure