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Analyzing the Quantum Approximate Optimization Algorithm: Ansätze, Symmetries, and Lie Algebras

The quantum approximate optimization algorithm (QAOA) has been proposed as a method to obtain approximate solutions for combinatorial optimization tasks. In this work, we study the underlying algebraic properties of three QAOA ansätze for the maximum-cut problem on connected graphs, while focusing on the generated Lie algebras as well as their invariant subspaces. Specifically, we analyze the standard QAOA ansatz as well as the orbit and multiangle ansätze. We are able to fully characterize the Lie algebras of the multiangle ansatz across arbitrary connected graphs, finding that they only fall into one of just six families. Aside from the cycle and path graphs, the Lie dimensions for every graph are exponentially large in the system size, meaning that multiangle ansätze are extremely prone to exhibiting barren plateaus. Then, a similar quasi-graph-independent Lie-algebraic characterization beyond the multiangle ansatz is impeded as the circuit exhibits additional “hidden” symmetries besides those naturally arising from a certain parity-superselection operator and all automorphisms of the considered graph. Disregarding the “hidden” symmetries, we can upper bound the dimensions of the orbit and the standard Lie algebras, and the dimensions of the associated invariant subspaces are determined via explicit character formulas. To finish, we conjecture that (for most graphs) the standard Lie algebras have only components that are either exponential or that grow, at most, polynomially with the system size. This would imply that the QAOA is either prone to barren plateaus or classically simulable. More generally, our work provides a symmetry framework and tools to analyze any desired variational quantum algorithm.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC

Quantum closures for neutrino moment transport

A computationally efficient method for calculating the transport of neutrino flavor in simulations is to use angular moments of the neutrino one-body reduced density matrix, i.e., “quantum moments.” As with any moment-based radiation transport method, a closure is needed if the infinite tower of moment evolution equations is truncated. We derive a general parametrization of a quantum closure and the limits the parameters must satisfy in order for the closure to be physical. We then derive from multiangle calculations the evolution of the closure parameters in two test cases which we then progressively insert into a moment evolution code and show how the parameters affect the moment results until the full multiangle results are reproduced. This parametrization paves the way to setting prescriptions for genuine quantum closures adapted to neutrino transport in a range of situations.

79 ASTRONOMY AND ASTROPHYSICS

Elucidating lipid nanoparticle properties and structure through biophysical analyses

Designing lipid nanoparticle (LNP) delivery systems with specific targeting, potency and minimal side effects is crucial for their clinical use. However, traditional characterization methods, such as dynamic light scattering, cannot accurately quantify physicochemical properties of LNPs and how these are influenced by the lipid composition and mixing method. Here, we structurally characterize polydisperse LNP formulations by applying emerging solution-based biophysical methods that have higher resolution and provide biophysical data beyond size and polydispersity. These techniques include sedimentation velocity analytical ultracentrifugation, field-flow fractionation followed by multiangle light scattering and size-exclusion chromatography in line with synchrotron small-angle X-ray scattering. Here, we show that LNPs have intrinsic polydispersity in size, RNA loading and shape, which depend on both the formulation technique and the lipid composition. Lastly, we predict LNP transfection in vitro and in vivo by examining the relationship between mRNA translation and physicochemical characteristics. Solution-based biophysical methods will be essential for determining LNP structure–function relationships, facilitating the creation of new design rules for LNPs.

36 MATERIALS SCIENCE

The structure of high-Mg alkali-bearing aluminosilicate glasses investigated in situ at ambient and high pressure by multi-angle energy dispersive X-ray diffraction and infrared microspectroscopy

The structural properties of synthetic high-Mg alkali-bearing aluminosilicate glasses analogues of natural picritic-to-komatiitic magmas were investigated in situ by multiangle energy dispersive X-ray diffraction at 2.1 GPa and ambient pressure and by Fourier Transform infrared spectroscopy up to 5.4 GPa in a cycle of compression and decompression experiments. Our results show that the intermediate range ordering of the glass structure at 2.1 GPa is 3.14 Å, increasing to 3.19 Å when decompressed. The local structure shows T-O lengths of 1.66 Å (2.1 GPa) and 1.65 Å (ambient pressure), T-T distances of 3.19 Å at high pressure, which lengthen to 3.21 Å at ambient pressure, causing the T-O-T angle of 147° determined at 2.1 GPa to widen to 154° upon decompression. The deconvoluted infrared spectra result in the presence of Q 1 , Q 2 , Q 3 populations in the aluminosilicate spectral region, whose proportions remain relatively unchanged up to 5.4 GPa. The structural response of the investigated glasses to cold-compression does not involve changes in polymerization, but rather a shrinking and compaction of the structure as evidenced by the Qn species shifting to higher wavenumbers as a function of pressure. The structural properties determined from X-ray diffraction for this glass composition are discussed together with those of glasses emerging from previous studies to highlight a compositional dependence mainly dictated by the amount of SiO 2 and Al 2 O 3 .

glass structure

Chlorophyllase from Arabidopsis thaliana Reveals an Emerging Model for Controlling Chlorophyll Hydrolysis

Chlorophyll (Chl) is one of Nature’s most complex pigments to biosynthesize and derivatize. This pigment is vital for survival and also paradoxically toxic if overproduced or released from a protective protein scaffold. Therefore, along with the mass production of Chl, organisms also invest in mechanisms to control its degradation and recycling. One important enzyme that is involved in these latter processes is chlorophyllase. This enzyme is employed by numerous photosynthetic organisms to hydrolyze the phytol tail of Chl. Although traditionally thought to catalyze the first step of Chl degradation, recent work suggests that chlorophyllase is instead employed during times of abiotic stress or conditions that produce reactive oxygen species. However, the molecular details regarding how chlorophyllases are regulated to function under such conditions remain enigmatic. Here, we investigate the Arabidopsis thaliana chlorophyllase isoform AtCLH2 using site-directed mutagenesis, mass spectrometry, dynamic light scattering, size-exclusion multiangle light scattering, and both steady-state enzyme kinetic and thermal stability measurements. Through these experiments, we show that AtCLH2 exists as a monomer in solution and contains two disulfide bonds. One disulfide bond putatively maps to the active site, whereas the other links two N-terminal Cys residues together. These disulfide bonds are cleaved by chemical or chemical and protein-based reductants, respectively, and are integral to maintaining the activity, stability, and substrate scope of the enzyme. This work suggests that Cys residue oxidation in chlorophyllases is an emerging regulatory strategy for controlling the hydrolysis of Chl pigments.

59 BASIC BIOLOGICAL SCIENCES

Advection algorithms for quantum neutrino moment transport

Neutrino transport in compact objects is an inherently challenging multidimensional problem. Here, this difficulty is compounded if one includes flavor transformation—an intrinsically quantum phenomenon requiring one to follow the coherence between flavors and thus necessitating the introduction of complex numbers. To reduce the computational burden, simulations of compact objects that include neutrino transport often make use of momentum-angle-integrated moments (the lowest order ones being commonly referred to as the energy density and flux) and these quantities can be generalized to include neutrino flavor, i.e., they become quantum moments. Numerous finite-volume approaches to solving the moment evolution equations for classical neutrino transport have been developed based on solving a Riemann problem at cell interfaces. In this paper we describe our generalization of a Riemann solver for quantum moments, specifically decomposing complex numbers in terms of a (signed) magnitude and phase instead of real and imaginary parts. We then test our new algorithm in numerous cases showing a neutrino fast flavor instability, varying from toy models with analytic solutions to snapshots from neutron star merger simulations. Compared to previous algorithms for neutrino transport with flavor mixing, we find uniformly smaller growth rates of the flavor transformation along with concomitantly larger length-scales, and that the results are a better match with the growth rates seen from multiangle codes.

79 ASTRONOMY AND ASTROPHYSICS

Techno-Economic Analysis of Compressed Air Energy Storage and Hydrogen Production from Variable Renewable Energy

This study presents the techno-economic analysis (TEA) results of integrating electrolysis hydrogen (H 2 ) production, compressed air energy storage (CAES), and H 2 -fired combustion turbines in a high variable renewable energy (VRE) market environment. The inconsistent nature of VRE creates challenges for power producers in maintaining a stable electrical grid as it is increasingly utilized. The mission of the National Energy Technology Laboratory (NETL) is driving innovation and delivering energy solutions, and a multiangle approach involving H 2 production, energy storage, and next-level H 2 -fired combustion turbine generator (CTG) technologies could provide one solution for the nation’s growing electrical grid issues with increasing VRE sources. The H 2 production and CAES concept were investigated due to its ability to provide utility-scale H 2 -fueled power generation with large-scale energy storage capabilities. Two facilities with CAES and natural gas-fired CTGs (in McIntosh, Alabama, and Huntorf, Germany) have been operating for decades. In contrast, this study investigates the potential to replace the natural gas fuel with H 2 fuel. This concept has been publicly presented by both Siemens Energy and Bechtel Global Engineering, Construction & Project Management (Bechtel) at two different power generating levels. The CAES and air expansion/combustion turbine power generation in this study are primarily based on the Siemens Energy system (Bailie, Aug. 10-11, 2021) (Scheller, Feb. 21, 2023). The inclusion of a H 2 turboexpander generator is from Bechtel (Gülen, Sep. 6, 2022). A block flow diagram of the proposed process is illustrated in Exhibit ES-1.

08 HYDROGEN