Accelerating adjoint variable method based photonic optimization with Schur complement domain decomposition
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36 MATERIALS SCIENCE↗
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Results for “Quantum optimization”
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Near-optimal ground state preparation
Preparing the ground state of a given Hamiltonian and estimating its ground energy are important but computationally hard tasks. However, given some additional information, these problems can be solved efficiently on a quantum computer. We assume that an initial state with non-trivial overlap with the ground state can be efficiently prepared, and the spectral gap between the ground energy and the first excited energy is bounded from below. With these assumptions we design an algorithm that prepares the ground state when an upper bound of the ground energy is known, whose runtime has a logarithmic dependence on the inverse error. When such an upper bound is not known, we propose a hybrid quantum-classical algorithm to estimate the ground energy, where the dependence of the number of queries to the initial state on the desired precision is exponentially improved compared to the current state-of-the-art algorithm proposed in [Ge et al. 2019]. These two algorithms can then be combined to prepare a ground state without knowing an upper bound of the ground energy. We also prove that our algorithms reach the complexity lower bounds by applying it to the unstructured search problem and the quantum approximate counting problem.
97 MATHEMATICS AND COMPUTING↗
Capacitive Energy Extraction by Few-Layer Graphene Electrodes
Capacitive double-layer expansion is a promising technology to harvest energy arising from the salinity difference between freshwater and seawater. Its optimal performance requires a careful selection of the operation potentials and electrode materials. While carbonaceous materials such as graphene and various forms of activated carbons are routinely used as the electrodes, there is little knowledge on how the quantum capacitance and the electric double-layer (EDL) capacitance, which are on the same order of magnitude, affect the capacitive performance. Toward understanding that from a theoretical perspective, here we study the capacitive energy extraction with graphene electrodes as a function of the number of graphene layers. The classical density functional theory is joined with the electronic density functional theory to obtain the EDL and the quantum capacitance, respectively. The theoretical results show that the quantum capacitance contribution plays a dominant role in extracting energy using the single-layer graphene, but its effect diminishes as the number of graphene layers increases. The overall extracted energy is dominated by the EDL contribution beyond about four graphene layers. Electrodes with more graphene layers are able to extract more energy at low charging potential. Here, because many porous carbons have nanopores with stacked graphene layers, our theoretical predictions are useful to identify optimal operation parameters for capacitive energy extraction with porous electrodes of different wall thickness.
36 MATERIALS SCIENCE↗
Full-dimensional vibrational calculations of five-atom molecules using a combination of Radau and Jacobi coordinates: Applications to methane and fluoromethane
Full quantum mechanical calculations of vibrational energies of methane and fluoromethane are carried out using a polyspherical description combining Radau and Jacobi coordinates. The Hamiltonian is built in a potential-optimized discrete variable representation, and vibrational energies are solved using an iterative eigensolver. This new approach can be applied to a large variety of molecules. In particular, we show that it is able to accurately and efficiently compute eigenstates for four different molecules : CH{sub 4}, CHD{sub 3}, CH{sub 2}D{sub 2}, and CH{sub 3}F. Very good agreement is obtained with the results reported previously in the literature with different approaches and with experimental data.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Convergence and Quantum Advantage of Trotterized MERA for Strongly-Correlated Systems
Strongly-correlated quantum many-body systems are difficult to study and simulate classically. We recently proposed a variational quantum eigensolver (VQE) based on the multiscale entanglement renormalization ansatz (MERA) with tensors constrained to certain Trotter circuits. Here, we determine the scaling of computation costs for various critical spin chains which substantiates a polynomial quantum advantage in comparison to classical MERA simulations based on exact energy gradients or variational Monte Carlo. Algorithmic phase diagrams suggest an even greater separation for higher-dimensional systems. Hence, the Trotterized MERA VQE is a promising route for the efficient investigation of strongly-correlated quantum many-body systems on quantum computers. Furthermore, we show how the convergence can be substantially improved by building up the MERA layer by layer in the initialization stage and by scanning through the phase diagram during optimization. For the Trotter circuits being composed of single-qubit and two-qubit rotations, it is experimentally advantageous to have small rotation angles. We find that the average angle amplitude can be reduced considerably with negligible effect on the energy accuracy. Benchmark simulations suggest that the structure of the Trotter circuits for the TMERA tensors is not decisive; in particular, brick-wall circuits and parallel random-pair circuits yield very similar energy accuracies.
Miao, Qiang [Duke Quantum Center, Duke University,↗
Optimisation of the prism coupling of optical whispering-gallery-mode microcavities
The methods for increasing the coupling efficiency of a prism with spheroidal microcavities, aimed at exciting whispering-gallery modes, have been analytically investigated. Optimal angles of incidence and incident beam parameters are obtained for a spheroidal cavity. The cavity eigenfrequency shift caused by the presence of a prism and the introduced loss by it is calculated. (resonators)
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Creation of an Fe 3 P Schreibersite Density Functional Tight Binding Model for Astrobiological Simulations
The mineral schreibersite, e.g., Fe 3 P, is commonly found in iron-rich meteorites and could have served as an abiotic phosphorus source for prebiotic chemistry. However, atomistic calculations of its degradation chemistry generally require quantum simulation approaches, which can be too computationally cumbersome to study sufficient time and length scales for this process. In this regard, we have created a computationally efficient semiempirical quantum density functional tight binding (DFTB) model for iron and phosphorus-containing materials by adopting an existing semiautomated workflow that represents many-body interactions by linear combinations of Chebyshev polynomials. Here, we have utilized a relatively small training set to optimize a DFTB model that is accurate for schreibersite physical and chemical properties, including its bulk properties, surface energies, and water absorption. We then show that our model shows strong transferability to several iron phosphide solids as well as multiple allotropes of iron metal. Our resulting DFTB parametrization will allow us to interrogate schreibersite aqueous decomposition at longer time and length scales than standard quantum approaches, providing for more detailed investigations of its role in prebiotic chemistry on early Earth.
36 MATERIALS SCIENCE↗
Scattering Processes from Quantum Simulation Algorithms for Scalar Field Theories
We provide practical simulation methods for scalar field theories on a quantum computer that yield improved asymptotics as well as concrete gate estimates for the simulation and physical qubit estimates using the surface code. We achieve these improvements through two optimizations. First, we consider a finite volume approach for estimating the elements of the S-matrix. This approach is appropriate in general for 1+1D and for certain low-energy elastic collisions in higher dimensions. Second, we implement our approach using a series of different fault-tolerant simulation algorithms for Hamiltonians formulated both in the field occupation basis and field amplitude basis. Our algorithms are based on either second-order Trotterization or qubitization. The cost of Trotterization in occupation basis scales as O ( λ N 7 | Ω | 3 / ( M 5 / 2 ϵ 3 / 2 ) ) where λ is the coupling strength, N is the occupation cutoff, | Ω | is the volume of the spatial lattice, M is the mass of the particles and ϵ is the uncertainty in the energy calculation used for the S -matrix determination. Qubitization in the field basis scales as O ( | Ω | 2 ( k 2 Λ + k M 2 ) / ϵ ) , where k is the cutoff in the field and Λ is a scaled coupling constant. We find in both cases that the bounds suggest physically meaningful simulations can be performed using on the order of 4 × 10 6 physical qubits and 10 12 T -gates which corresponds to roughly one day on a superconducting quantum computer with surface code and a cycle time of 100 ns. This places the simulation of scalar field theory within striking distance of the gate counts for the best available chemistry simulation results.
Hardy, Andrew [Toronto U.] (ORCID:0000000235817382↗
Coherence area profiling in multi-spatial-mode squeezed states
The presence of multiple bipartite entangled modes in squeezed states generated by four-wave mixing enables ultra-trace sensing, imaging, and metrology applications that are impossible to achieve with single-spatial-mode squeezed states. For Gaussian seed beams, the spatial distribution of these bipartite entangled modes, or coherence areas, across each beam is largely dependent on the spatial modes present in the pump beam, but it has proven difficult to map the distribution of these coherence areas in frequency and space. We demonstrate an accessible method to map the distribution of the coherence areas within these twin beams. In addition, we also show that the pump shape can impart different noise properties to each coherence area, and that it is possible to select and detect coherence areas with optimal squeezing with this approach.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
A general theory of interference fringes in x-ray phase grating imaging
Purpose: The authors note that the concept of the Talbot self-image distance in x-ray phase grating interferometry is indeed not well defined for polychromatic x-rays, because both the grating phase shift and the fractional Talbot distances are all x-ray wavelength-dependent. For x-ray interferometry optimization, there is a need for a quantitative theory that is able to predict if a good intensity modulation is attainable at a given grating-to-detector distance. In this work, the authors set out to meet this need. Methods: In order to apply Fourier analysis directly to the intensity fringe patterns of two-dimensional and one-dimensional phase grating interferometers, the authors start their derivation from a general phase space theory of x-ray phase-contrast imaging. Unlike previous Fourier analyses, the authors evolved the Wigner distribution to obtain closed-form expressions of the Fourier coefficients of the intensity fringes for any grating-to-detector distance, even if it is not a fractional Talbot distance. Results: The developed theory determines the visibility of any diffraction order as a function of the grating-to-detector distance, the phase shift of the grating, and the x-ray spectrum. The authors demonstrate that the visibilities of diffraction orders can serve as the indicators of the underlying interference intensity modulation. Applying the theory to the conventional and inverse geometry configurations of single-grating interferometers, the authors demonstrated that the proposed theory provides a quantitative tool for the grating interferometer optimization with or without the Talbot-distance constraints. Conclusions: In this work, the authors developed a novel theory of the interference intensity fringes in phase grating x-ray interferometry. This theory provides a quantitative tool in design optimization of phase grating x-ray interferometers.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Structures and magnetic properties of Co-Zr-B magnets studied by first-principles calculations
The structures and magnetic properties of Co-Zr-B alloys near the composition of Co{sub 5}Zr with B at. % ≤6% were studied using adaptive genetic algorithm and first-principles calculations. The energy and magnetic moment contour maps as a function of chemical composition were constructed for the Co-Zr-B magnet alloys through extensive structure searches and calculations. We found that Co-Zr-B system exhibits the same structure motif as the “Co{sub 11}Zr{sub 2}” polymorphs, and such motif plays a key role in achieving strong magnetic anisotropy. Boron atoms were found to be able to substitute cobalt atoms or occupy the “interruption” sites. First-principles calculations showed that the magnetocrystalline anisotropy energies of the boron-doped alloys are close to that of the high-temperature rhombohedral Co{sub 5}Zr phase and larger than that of the low-temperature Co{sub 5.25}Zr phase. Our calculations provide useful guidelines for further experimental optimization of the magnetic performances of these alloys.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Constructing diabatic representations using adiabatic and approximate diabatic data – Coping with diabolical singularities
We have recently introduced a diabatization scheme, which simultaneously fits and diabatizes adiabatic ab initio electronic wave functions, Zhu and Yarkony J. Chem. Phys. 140, 024112 (2014). The algorithm uses derivative couplings in the defining equations for the diabatic Hamiltonian, H{sup d}, and fits all its matrix elements simultaneously to adiabatic state data. This procedure ultimately provides an accurate, quantifiably diabatic, representation of the adiabatic electronic structure data. However, optimizing the large number of nonlinear parameters in the basis functions and adjusting the number and kind of basis functions from which the fit is built, which provide the essential flexibility, has proved challenging. In this work, we introduce a procedure that combines adiabatic state and diabatic state data to efficiently optimize the nonlinear parameters and basis function expansion. Further, we consider using direct properties based diabatizations to initialize the fitting procedure. To address this issue, we introduce a systematic method for eliminating the debilitating (diabolical) singularities in the defining equations of properties based diabatizations. We exploit the observation that if approximate diabatic data are available, the commonly used approach of fitting each matrix element of H{sup d} individually provides a starting point (seed) from which convergence of the full H{sup d} construction algorithm is rapid. The optimization of nonlinear parameters and basis functions and the elimination of debilitating singularities are, respectively, illustrated using the 1,2,3,4{sup 1}A states of phenol and the 1,2{sup 1}A states of NH{sub 3}, states which are coupled by conical intersections.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Multi-fidelity Gaussian process regression for prediction of random fields
We propose a new multi-fidelity Gaussian process regression (GPR) approach for prediction of random fields based on observations of surrogate models or hierarchies of surrogate models. Our method builds upon recent work on recursive Bayesian techniques, in particular recursive co-kriging, and extends it to vector-valued fields and various types of covariances, including separable and non-separable ones. The framework we propose is general and can be used to perform uncertainty propagation and quantification in model-based simulations, multi-fidelity data fusion, and surrogate-based optimization. We demonstrate the effectiveness of the proposed recursive GPR techniques through various examples. Specifically, we study the stochastic Burgers equation and the stochastic Oberbeck–Boussinesq equations describing natural convection within a square enclosure. In both cases we find that the standard deviation of the Gaussian predictors as well as the absolute errors relative to benchmark stochastic solutions are very small, suggesting that the proposed multi-fidelity GPR approaches can yield highly accurate results.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Thermal stability of boron nitride/silicon p-n heterojunction diodes
Heterojunctions of p-type cubic boron nitride (cBN) and n-type silicon with sp{sup 2}-bonded BN (sp{sup 2}BN) interlayers are fabricated under low-energy ion impact by plasma-enhanced chemical vapor deposition, and their rectification properties are studied at temperatures up to 573 K. The rectification ratio is increased up to the order of 10{sup 5} at room temperature by optimizing the thickness of the sp{sup 2}BN interlayer and the cBN fraction for suppressing the reverse leakage current. A highly rectifying p-type cBN/thick sp{sup 2}BN/n-type silicon junction diode shows irreversible rectification properties mainly characterized by a marked decrease in reverse current by an order of magnitude in an initial temperature ramp/down cycle. This irreversible behavior is much more reduced by conducting the cycle twice or more. The temperature-dependent properties confirm an overall increase in effective barrier heights for carrier injection and conduction by biasing at high temperatures, which consequently increases the thermal stability of the diode performance.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Hamiltonian purification
The problem of Hamiltonian purification introduced by Burgarth et al. [Nat. Commun. 5, 5173 (2014)] is formalized and discussed. Specifically, given a set of non-commuting Hamiltonians (h{sub 1}, …, h{sub m}) operating on a d-dimensional quantum system ℋ{sub d}, the problem consists in identifying a set of commuting Hamiltonians (H{sub 1}, …, H{sub m}) operating on a larger d{sub E}-dimensional system ℋ{sub d{sub E}} which embeds ℋ{sub d} as a proper subspace, such that h{sub j} = PH{sub j}P with P being the projection which allows one to recover ℋ{sub d} from ℋ{sub d{sub E}}. The notions of spanning-set purification and generator purification of an algebra are also introduced and optimal solutions for u(d) are provided.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Coupled Lindblad Pseudomode Theory for Simulating Open Quantum Systems
Coupled Lindblad pseudomode theory is a promising approach for simulating non-Markovian quantum dynamics on both classical and quantum platforms, with dynamics that can be realized as a quantum channel. We provide theoretical evidence that the number of coupled pseudomodes only needs to scale as polylog(𝑇/𝜖) in the simulation time 𝑇 and precision 𝜖. Inspired by the realization problem in control theory, we also develop a robust numerical algorithm for constructing the coupled modes that avoid the nonconvex optimization required by existing approaches. We demonstrate the effectiveness of our method by computing population dynamics and absorption spectra for the spin-boson model. Furthermore, this Letter provides a significant theoretical and computational improvement to the coupled Lindblad framework, which impacts a broad range of applications from classical simulations of quantum impurity problems to quantum simulations on near-term quantum platforms.
Anderson impurity model↗
Sputtered p-Type Cu x Zn 1– x S Back Contact to CdTe Solar Cells
As thin-film cadmium telluride (CdTe) solar cells gain prominence, one particular challenge is optimizing contacts and their interfaces to transfer charge without losses in efficiency. Back contact recombination is still significant and will prevent CdTe solar technology from reaching its full potential in device efficiency, and transparent back contacts have not been developed for bifacial solar technology or multijunction solar cells. To address these challenges, here we investigate sputtered Cu x Zn 1– x S as a p-type semi-transparent back contact material to thin-film polycrystalline CdTe solar cells at Cu concentrations x = 0.30, 0.45, and 0.60. This material is selected for its high hole conductivity (160–2120 S cm –1 ), wide optical band gap (2.25–2.75 eV), and variable ionization potential (approximately 6–7 eV) that can be aligned to that of CdTe. We report that without device optimization, CdTe solar cells with these Cu x Zn 1– x S back contacts perform as well as control cells with standard ZnTe:Cu back contacts. We observe no reduction in external quantum efficiency, low contact barrier heights of approximately 0.3 eV, and carrier lifetimes on par with those of baseline CdTe. These cells are relatively stable over one year in air, with V OC and efficiency of the x = 0.30 cell decreasing by only 1 and 3%, respectively. Using scanning electron microscopy and scanning transmission electron microscopy to investigate the Cu x Zn 1– x S/CdTe interface, we demonstrate that the Cu x Zn 1– x S layer segregates into a bilayer of Cu-Te-S and Zn-Cd-S, and thermodynamic reaction calculations support these findings. Despite its bilayer formation, the back contact still functions well. This investigation explains some of the physical mechanisms governing the device stack, inspires future work to understand interfacial chemistry and charge transfer, and elicits optimization to achieve higher-efficiency CdTe cells.
14 SOLAR ENERGY↗
Optical amplifiers for coherent lidar
We examine application of optical amplification to coherent lidar for the case of a weak return signal (a number of quanta of the return optical field close to unity). We consider the option that has been explored to date, namely, incorporation of an optical amplifier operated in a linear manner located after reception of the signal and immediately prior to heterodyning and photodetection. We also consider alternative strategies where the coherent interaction, the nonlinear processes, and the amplification are not necessarily constrained to occur in the manner investigated to date. We include the complications that occur because of mechanisms that occur at the level of a few, or one, quantum excitation. Two factors combine in the work to date that limit the value of the approach. These are: (1) the weak signal tends to require operation of the amplifier in the linear regime where the important advantages of nonlinear optical processing are not accessed, (2) the linear optical amplifier has a -3dB noise figure (SN(out)/SN(in)) that necessarily degrades the signal. Some improvement is gained because the gain provided by the optical amplifier can be used to overcome losses in the heterodyned process and photodetection. The result, however, is that introduction of an optical amplifier in a well optimized coherent lidar system results in, at best, a modest improvement in signal to noise. Some improvement may also be realized on incorporating more optical components in a coherent lidar system for purely practical reasons. For example, more compact, lighter weight, components, more robust alignment, or more rapid processing may be gained. We further find that there remain a number of potentially valuable, but unexplored options offered both by the rapidly expanding base of optical technology and the recent investigation of novel nonlinear coherent interference phenomena occurring at the single quantum excitation level. Key findings are: (1) insertion of linear optical amplifiers in well optimized conventional lidar systems offers modest improvements, at best, (2) the practical advantages of optical amplifiers, especially fiber amplifiers, such as ease of alignment, compactness, efficiency, lightweight, etc., warrant further investigation for coherent lidar, (3) the possibility of more fully optical lidar systems should be explored, (4) advantages gained by use of coherent interference of optical fields at the level of one, or a few, signal quanta should be explored, (5) amplification without inversion, population trapping, and use of electromagnetic induced transparency warrant investigation in connection with coherent lidar, (6) these new findings are probably more applicable to earth related NASA work, although applications to deep space should not be excluded, and (7) our own work in the Ultrafast Laboratory at UAH along some of the above lines of investigation, may be useful.
Fork, Richard↗