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Lower bounds on circuit depth of the quantum approximate optimization algorithm

The quantum approximate optimization algorithm (QAOA) is a method of approximately solving combinatorial optimization problems. While QAOA is developed to solve a broad class of combinatorial optimization problems, it is not clear which classes of problems are best suited for it. One factor in demonstrating quantum advantage is the relationship between a problem instance and the circuit depth required to implement the QAOA method. As errors in noisy intermediate-scale quantum (NISQ) devices increase exponentially with circuit depth, identifying lower bounds on circuit depth can provide insights into when quantum advantage could be feasible. In this work, we identify how the structure of problem instances can be used to identify lower bounds for circuit depth for each iteration of QAOA and examine the relationship between problem structure and the circuit depth for a variety of combinatorial optimization problems including MaxCut and MaxIndSet. Specifically, we show how to derive a graph, G, that describes a general combinatorial optimization problem and show that the depth of circuit is at least the chromatic index of G. By looking at the scaling of circuit depth, we argue that MaxCut, MaxIndSet, and some instances of vertex covering and Boolean satisfiability problems are suitable for QAOA approaches while knapsack and traveling salesperson problems are not.

97 MATHEMATICS AND COMPUTING↗

Direct laser writing of volumetric gradient index lenses and waveguides

Abstract Direct laser writing (DLW) has been shown to render 3D polymeric optical components, including lenses, beam expanders, and mirrors, with submicrometer precision. However, these printed structures are limited to the refractive index and dispersive properties of the photopolymer. Here, we present the subsurface controllable refractive index via beam exposure (SCRIBE) method, a lithographic approach that enables the tuning of the refractive index over a range of greater than 0.3 by performing DLW inside photoresist-filled nanoporous silicon and silica scaffolds. Adjusting the laser exposure during printing enables 3D submicron control of the polymer infilling and thus the refractive index and chromatic dispersion. Combining SCRIBE’s unprecedented index range and 3D writing accuracy has realized the world’s smallest (15 µm diameter) spherical Luneburg lens operating at visible wavelengths. SCRIBE’s ability to tune the chromatic dispersion alongside the refractive index was leveraged to render achromatic doublets in a single printing step, eliminating the need for multiple photoresins and writing sequences. SCRIBE also has the potential to form multicomponent optics by cascading optical elements within a scaffold. As a demonstration, stacked focusing structures that generate photonic nanojets were fabricated inside porous silicon. Finally, an all-pass ring resonator was coupled to a subsurface 3D waveguide. The measured quality factor of 4600 at 1550 nm suggests the possibility of compact photonic systems with optical interconnects that traverse multiple planes. SCRIBE is uniquely suited for constructing such photonic integrated circuits due to its ability to integrate multiple optical components, including lenses and waveguides, without additional printed supports.

36 MATERIALS SCIENCE↗

Design of a neutron microscope based on Wolter mirrors

The predominant geometry for a neutron imaging experiment is that of a pinhole camera. Here, this is primarily due to the difficulty in focusing neutrons due to the weak refractive index, which is also strongly chromatic. Proof of concept experiments demonstrated that neutron image forming lenses based on reflective Wolter mirrors can produce quantitative, high spatial resolution neutron images while also increasing the time resolution compared to the conventional pinhole camera geometry. Motivated by these results, we report the design of a neutron microscope where two Wolter mirrors replace condensing and objective lenses, in direct analogy with typical visible light microscopes. Ray tracing results indicate that this system will yield 3 µm spatial resolution images with an acquisition time of order <1 s (10 4 faster than currently possible at this spatial resolution) with a field of view of about 5 mm in diameter.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Lens Design Using Group Indices of Refraction

An approach to lens design is described in which the ratio of the group velocity to the speed of light (the group index) in glass is used, in conjunction with the more familiar phase index of refraction, to control certain chromatic properties of a system of thin lenses in contact. The first-order design of thin-lens systems is illustrated by examples incorporating the methods described.

optical glass interferometry ultrashort pulses↗

Mapping Temperate Forest Phenology Using Tower, UAV, and Ground-Based Sensors

Phenology is a distinct marker of the impacts of climate change on ecosystems. Accordingly, monitoring the spatiotemporal patterns of vegetation phenology is important to understand the changing Earth system. A wide range of sensors have been used to monitor vegetation phenology, including digital cameras with different viewing geometries mounted on various types of platforms. Sensor perspective, view-angle, and resolution can potentially impact estimates of phenology. We compared three different methods of remotely sensing vegetation phenology—an unoccupied aerial vehicle (UAV)-based, downward-facing RGB camera, a below-canopy, upward-facing hemispherical camera with blue (B), green (G), and near-infrared (NIR) bands, and a tower-based RGB PhenoCam, positioned at an oblique angle to the canopy—to estimate spring phenological transition towards canopy closure in a mixed-species temperate forest in central Virginia, USA. Our study had two objectives: (1) to compare the above- and below-canopy inference of canopy greenness (using green chromatic coordinate and normalized difference vegetation index) and canopy structural attributes (leaf area and gap fraction) by matching below-canopy hemispherical photos with high spatial resolution (0.03 m) UAV imagery, to find the appropriate spatial coverage and resolution for comparison; (2) to compare how UAV, ground-based, and tower-based imagery performed in estimating the timing of the spring phenological transition. We found that a spatial buffer of 20 m radius for UAV imagery is most closely comparable to below-canopy imagery in this system. Sensors and platforms agree within +/− 5 days of when canopy greenness stabilizes from the spring phenophase into the growing season. We show that pairing UAV imagery with tower-based observation platforms and plot-based observations for phenological studies (e.g., long-term monitoring, existing research networks, and permanent plots) has the potential to scale plot-based forest structural measures via UAV imagery, constrain uncertainty estimates around phenophases, and more robustly assess site heterogeneity.

Jeff W. Atkins↗

Aperiodic optical coatings for neutral-color semi-transparent organic photovoltaics

Semi-transparent organic photovoltaics (ST-OPVs) have the potential for integration with windows for ubiquitous power generating applications. Typically, such applications require that ST-OPVs be neutrally transparent across the visible and exhibit both a high average photopic transmittance (APT) and color rendering index, as well as iso-energetic chromaticity coordinates. In this work, we demonstrate the design and use of optical coatings to achieve ST-OPVs with a neutral visible transmittance of APT = 50%, a power conversion efficiency of 8.3%, and optical properties that are independent of a ± 30° variation in the solar angle of incidence. As a result, these simple optical coatings are rapidly designed using a genetic algorithm and transfer matrix formalism.

14 SOLAR ENERGY↗

Sensor-based phenology from snowmelt experiment gradient, East River, Colorado, 2017 to 2020

The timing of snowmelt is a critical cue for the initiation of growth in mountain meadow ecosystems and can also impact the duration and magnitude of plant production. High frequency observations of species-level phenology are time consuming and require a high degree of expertise, and publicly available remote sensing products lack the necessary temporal resolution to assess fine-scale growing season dynamics. Near-surface sensing methods provide a middle ground with high temporal frequency and tractable spatial scales (from sub-meter to hillslope scale). This data package includes csv files of Normalized Difference Vegetation Index (NDVI) timeseries (SM_NDVI_dailymax.csv) and phenological thresholds (SM_NDVI_summary.csv) for sub-plots (1m2) and Green Chromatic Coordinate (GCC) phenological thresholds (SM_GCC_summary.csv) at the plot scale (10m x 14m). Location IDs associated with this data package are: ER-LM, WG-UM, WG-LS, ER-US, and XX-AL. Related data packages include: “Microclimate observations associated with snowmelt experiment gradient sites, East River, Colorado, 2017 to 2020” and “Colorado Elevation Gradient Snowmelt Manipulation Plant Phenology 2017-2018”.

54 ENVIRONMENTAL SCIENCES↗

Color-neutral, semitransparent organic photovoltaics for power window applications

Semitransparent organic photovoltaic cells (ST-OPVs) are emerging as a solution for solar energy harvesting on building facades, rooftops, and windows. However, the trade-off between power-conversion efficiency (PCE) and the average photopic transmission (APT) in color-neutral devices limits their utility as attractive, power-generating windows. A color-neutral ST-OPV is demonstrated by using a transparent indium tin oxide (ITO) anode along with a narrow energy gap nonfullerene acceptor near-infrared (NIR) absorbing cell and outcoupling (OC) coatings on the exit surface. The device exhibits PCE = 8.1 ± 0.3% and APT = 43.3 ± 1.2% that combine to achieve a light-utilization efficiency of LUE = 3.5 ± 0.1%. Commission Internationale d’eclairage chromaticity coordinates of (0.38, 0.39), a color-rendering index of 86, and a correlated color temperature of 4,143 K are obtained for simulated AM1.5 illumination transmitted through the cell. Using an ultrathin metal anode in place of ITO, we demonstrate a slightly green-tinted ST-OPV with PCE = 10.8 ± 0.5% and APT = 45.7 ± 2.1% yielding LUE = 5.0 ± 0.3% These results indicate that ST-OPVs can combine both efficiency and color neutrality in a single device.

14 SOLAR ENERGY↗

Solid-State Lighting Using Side-by-Side White Phosphorescent Organic Light-Emitting Diodes

White organic light-emitting diodes (WOLEDs) have become increasingly popular for use in solid-state illumination, where diffuse, large area light sources that achieve a high color rendering index and luminous power efficiency are desirable. Color-tunable emission, where the light source combines emission from multiple, separately addressed color elements, is conveniently provided by WOLEDs for the purpose of adapting the lighting source to a particular illumination requirement. In this work, we demonstrate a method for side-by-side positioning of monochromatic blue and yellow phosphorescent OLED stripes that are combined to create tunable white light, using a high resolution mechanical peel-off patterning method. We achieve a peak luminous power efficiency of 17.1 ± 0.3 lm W –1 and an external quantum efficiency of 11.8 ± 0.2% and demonstrate color tunability of the 1960 Commission Internationale d’Eclairage chromaticity coordinates from (u,v) = (0.33,0.36) to (0.12,0.32). This corresponds to a tuning rnge of the color rendering index from 74 ± 1 to 86 ± 1 and the correlated color temperature from 2000 to 8000 ± 500 K. Here, due to the nondestructive nature of the peel-off technique, patterned devices exhibit a lifetime comparable to conventional, shadow mask-patterned devices.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Advanced Photon Acceleration Schemes for Tunable XUV/Soft X-Ray Sources

We report on the advances made under the purview of DOE award number DE-SC0019135 that was active during the period: 09/01/2018–08/31/2021. The grant investigated the application of a “flying focus” to the problem of photon acceleration—in which a dynamic refractive index gradient is used to continuously upshift a probe beam’s frequency. Codes were written to describe the creation of ionization waves of arbitrary velocity (IWAVs) for use as a photon-accelerating medium, as well as the behavior of a witness pulse residing in said medium. Experiments first verified the spatiotemporal control over laser intensity provided by a chromatic flying focus, then used that ability to produce small-diameter IWAVs in the far-field with the expected dynamics, and finally demonstrated even further flexibility by producing large-diameter IWAVs in the laser quasi-far-field that maintained the beneficial dynamics. Multiple innovative diagnostics—spectrally resolved Schlieren and spectrally resolved interferometry—were pioneered in order to diagnose the IWAVs. For IWAV production in the laboratory, however, beam quality was identified as a key limitation in the quasi-far-field. Since the original chromatic flying focus was found to result in relatively long (ps duration) intensity peaks, which could limit some applications including photon acceleration, additional techniques were invented to provide similar spatiotemporal control while also retaining ultrashort intensity peaks. While simulations have identified several interesting regimes for photon acceleration—first predicting the upshift of a counterpropagating witness pulse from the optical to the extreme ultraviolet in less than 1 cm, and later obtaining similar shifts in less than 100 μm in a simpler self-seeded configuration—experimental demonstration is left for future work.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗