Connecting Ansatz Expressibility to Gradient Magnitudes and Barren Plateaus
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71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
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Improving Schrödinger Equation Implementations with Gray Code for Adiabatic Quantum Computers
We reformulate the continuous-space Schrödinger equation in terms of spin Hamiltonians. For the kinetic energy operator, the critical concept facilitating the reduction in model complexity is the idea of position encoding. A binary encoding of position produces a spin-1/2 Heisenberg-like model and yields exponential improvement in space complexity when compared to classical computing. Encoding with a binary reflected Gray code (BRGC), and a Hamming-distance-2 Gray code (H2GC) reduces the model complexity down to the 𝑋𝑍 and transverse Ising model, respectively. For 𝐴 qubits BRGC yields 2 𝐴 positions and is reduced to its 2-local form with O(𝐴) ancillary qubits. H2GC yields 2 𝐴/2+1 positions with O(𝐴 2 ) three-local penalty terms. We also identify the bijective mapping between diagonal unitaries and the Walsh series, producing the mapping of any real potential to a series of 𝑘 -local Ising models through the fast Walsh transform. Finally, in a finite volume, we provide some numerical evidence to support the claim that the total time needed for adiabatic evolution is protected by the infrared cutoff of the system. As a result, initial state preparation from a free-field wave function to an interacting system is expected to exhibit polynomial time complexity with volume and constant scaling with respect to lattice discretization for all encodings. For H2GC, if the evolution starts with the transverse Hamiltonian due to hardware restrictions, then penalties are dynamically introduced such that the low-lying spectrum reproduces the energy levels of the Laplacian. The adiabatic evolution of the penalty Hamiltonian is therefore sensitive to the ultraviolet scale. It is expected to exhibit polynomial time complexity with lattice discretization, or exponential time complexity with respect to the number of qubits given a fixed volume.
97 MATHEMATICS AND COMPUTING↗
Algorithm 1049: The Delaunay Density Diagnostic
Accurate approximation of a real-valued function depends on two aspects of the available data: the density of inputs within the domain of interest and the variation of the outputs over that domain. There are few methods for assessing whether the density of inputs is sufficient to identify the relevant variations in outputs—i.e., the “geometric scale” of the function—despite the fact that sampling density is closely tied to the success or failure of an approximation method. In this article, we introduce a general purpose, computational approach to detecting the geometric scale of real-valued functions over a fixed domain using a deterministic interpolation technique from computational geometry. The algorithm is intended to work on scalar data in moderate dimensions (2–10). Our algorithm is based on the observation that a sequence of piecewise linear interpolants will converge to a continuous function at a quadratic rate (in L 2 norm) if and only if the data are sampled densely enough to distinguish the feature from noise (assuming sufficiently regular sampling). We present numerical experiments demonstrating how our method can identify feature scale, estimate uncertainty in feature scale, and assess the sampling density for fixed (i.e., static) datasets of input–output pairs. Finally, we include analytical results in support of our numerical findings and have released lightweight code that can be adapted for use in a variety of data science settings.
97 MATHEMATICS AND COMPUTING↗
Variational Quantum Fidelity Estimation
Computing quantum state fidelity will be important to verify and characterize states prepared on a quantum computer. In this work, we propose novel lower and upper bounds for the fidelity F ( ρ , σ ) based on the ``truncated fidelity'' F ( ρ m , σ ) , which is evaluated for a state ρ m obtained by projecting ρ onto its m -largest eigenvalues. Our bounds can be refined, i.e., they tighten monotonically with m . To compute our bounds, we introduce a hybrid quantum-classical algorithm, called Variational Quantum Fidelity Estimation, that involves three steps: (1) variationally diagonalize ρ , (2) compute matrix elements of σ in the eigenbasis of ρ , and (3) combine these matrix elements to compute our bounds. Our algorithm is aimed at the case where σ is arbitrary and ρ is low rank, which we call low-rank fidelity estimation, and we prove that no classical algorithm can efficiently solve this problem under reasonable assumptions. Finally, we demonstrate that our bounds can detect quantum phase transitions and are often tighter than previously known computable bounds for realistic situations.
97 MATHEMATICS AND COMPUTING↗
Impact Studies and Cooperative Voltage Control for High PV Penetration
The drastically increasing penetration of photovoltaic (PV) has posed tremendous challenges in operation, control, and protection in distribution networks. The over-voltage issue is one of major concerns for extremely high PV penetration (e.g. 100%). It is critical to identify the most sensitive locations to high PV penetration and apply effective methods to mitigate the over-voltage issue. This paper introduced a novel greedy search algorithm to locate worst-case scenarios of over-voltage in both distributed and centralized PV configurations, as well as a cooperative voltage control method to mitigate over-voltage. The search algorithm has the computational advantage over existing stochastic approach and provides more insights in impact studies. The cooperative control method relies upon reactive power compensation to converge system voltage to a predefined value within standard limits. Moreover, a clustering strategy is applied to divide the network into several clusters, within which all nodes share information with neighboring nodes following a scalable communication architecture. The control algorithms and communication hierarchies presented in this paper have been implemented into OpenDSS to form the Multi Agent (MA) OpenDSS package, which has been made available to the reader. The effectiveness of developed methods are demonstrated through simulation studies on the IEEE 123-node test feeder under four different load levels.
Cooperative control↗
Hierarchical Distributed Optimal Power Flow of HV and MV Distribution Networks With Continuous and Discrete Devices
With large-scale distributed photovoltaics (PVs) being integrated into distribution networks (DNs), coordinated optimal power flow (OPF) of high voltage (HV) and medium voltage (MV) DNs should be investigated to optimally dispatch the distributed PVs and other network devices. Here, this paper presents a hierarchical distributed OPF method for HV and MV DNs with on-load tap changers, reactive power compensators, feeder switches and distributed PVs. A hierarchical master-slave control architecture is applied to implement coordinated OPF of two-layer DNs. The HV master problem and MV subproblems are transformed into mixed-integer convex problems respectively with second order cone programming and LinDistFlow approximation. Since there is no efficient distributed algorithm to solve such OPF models with integer subproblems, a novel distributed algorithm is proposed in this paper to efficiently solve the hierarchical coordinated OPF model with integer subproblems in a distributed manner. In the proposed algorithm, the coordinated OPF model is solved in a branch-and-bound framework, where in each branch node generalized Benders decomposition (GBD) algorithm is applied to decompose the coordinated OPF model into a master problem and relaxed subproblems and solves them iteratively to get optimal solution. The GBD optimal and feasible cutting planes generated in a branch node are proved to be valid for its descendants. Moreover, three acceleration techniques are introduced into the proposed algorithm to improve computational efficiency. Finally, the effectiveness and accuracy of the proposed method are verified via simulation tests in Jinzhai DNs of China.
42 ENGINEERING↗
Large-scale harmonic balance simulations with Krylov subspace and preconditioner recycling
The multi-harmonic balance method combined with numerical continuation provides an efficient framework to compute a family of time-periodic solutions, or response curves, for large-scale, nonlinear mechanical systems. The predictor and corrector steps repeatedly solve a sequence of linear systems that scale by the model size and number of harmonics in the assumed Fourier series approximation. In this paper, a novel Newton–Krylov iterative method is embedded within the multi-harmonic balance and continuation algorithm to efficiently compute the approximate solutions from the sequence of linear systems that arise during the prediction and correction steps. Further, the method recycles, or reuses, both the preconditioner and the Krylov subspace generated by previous linear systems in the solution sequence. A delayed frequency preconditioner refactorizes the preconditioner only when the performance of the iterative solver deteriorates. The GCRO-DR iterative solver recycles a subset of harmonic Ritz vectors to initialize the solution subspace for the next linear system in the sequence. The performance of the iterative solver is demonstrated on two exemplars with contact-type nonlinearities and benchmarked against a direct solver with traditional Newton–Raphson iterations.
97 MATHEMATICS AND COMPUTING↗
Determination of Parameters Assigned to an Anti-Surge Controller in a Turbocompressor Automation System
An algorithm that describes the operation of a dynamic compressor control system with anti-surge valve is presented. A technique for the use of the certified gaseodynamic characteristics of a compressor and the equations of state of actual gases for determining the parameters assigned to an anti-surge controller is presented. Through the use of the algorithm and the computation technique in the design of an anti-surge compressor control system, the occurrence of surge and the stagnation regimes in the gas flow may be prevented.
42 ENGINEERING↗
Partitioning and Communication Strategies for Sparse Non-negative Matrix Factorization
Non-negative matrix factorization (NMF), the problem of finding two non-negative low-rank factors whose product approximates an input matrix, is a useful tool for many data mining and scientific applications such as topic modeling in text mining and unmixing in microscopy. In this paper, we focus on scaling algorithms for NMF to very large sparse datasets and massively parallel machines by employing effective algorithms, communication patterns, and partitioning schemes that leverage the sparsity of the input matrix. We consider two previous works developed for related problems, one that uses a fine-grained partitioning strategy using a point-to-point communication pattern and one that uses a Cartesian, or checkerboard, partitioning strategy using a collective-based communication pattern. We show that a combination of the previous approaches balances the demands of the various computations within NMF algorithms and achieves high efficiency and scalability. From the experiments, we see that our proposed strategy runs up to 10x faster than the state of the art on real-world datasets.
Kaya, Oguz↗
Analysis of the VERA Core Physics Benchmark Problems using cosRMC Code
In reactor physics, two kinds of numerical methods are generally employed to solve the neutron transport equations, one of which is the deterministic method and the other one is the Monte Carlo method. Monte Carlo is widely used to provide reference solution because of its ability to deal with continuous energy cross sections and complex geometry. Just like any statistical process, the Monte Carlo method requires repetition to achieve a small relative uncertainty, and therefore may inevitably have larger simulation times than deterministic method. Fortunately, the great advancements of computer technology make it possible to apply Monte Carlo method in reactor core analysis. To promote nuclear power plant system design and simulation software self-reliance development, a Monte Carlo neutron/photon transport code cosRMC has been developed jointly by State Nuclear Power Software Development Center (SNPSDC) and Tsinghua University. The cosRMC is aimed at achieving full core calculations and analysis with high fidelity and efficiency by means of advanced methodologies and algorithms as well as high performance computing techniques. The cosRMC has many functions as criticality calculation, fixed-source calculation, burnup calculation, etc. In order to ensure its reliability, several types of verification and validation (V and V) work have been and are being carried out for cosRMC. The simulation results of cosRMC based on Problem 1 to 3 of VERA Core Physics Benchmark showed its good capability of 2D lattice and 3D assembly modeling. In this paper, some progressive verification results of multi-assembly and full core problems are presented.
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
AI-enhanced Codesign for Next-Generation Neuromorphic Circuits and Systems
This report details work that was completed to address the Fiscal Year 2022 Advanced Science and Technology (AS&T) Laboratory Directed Research and Development (LDRD) call for “AI-enhanced Co-Design of Next Generation Microelectronics.” This project required concurrent contributions from the fields of 1) materials science, 2) devices and circuits, 3) physics of computing, and 4) algorithms and system architectures. During this project, we developed AI-enhanced circuit design methods that relied on reinforcement learning and evolutionary algorithms. The AI-enhanced design methods were tested on neuromorphic circuit design problems that have real-world applications related to Sandia’s mission needs. The developed methods enable the design of circuits, including circuits that are built from emerging devices, and they were also extended to enable novel device discovery. We expect that these AI-enhanced design methods will accelerate progress towards developing next-generation, high-performance neuromorphic computing systems.
42 ENGINEERING↗
QUCODE: End-to-End Qubit Co-Design
The design of a quantum computer can be broken down into different steps, e.g., the material science aspect of designing qubits and devices, considerations of controlling the state of the qubits and their environment, the computer science aspects of mapping algorithms to the available primitives of the quantum computer, and the programming of an application in terms of the available algorithms. Research in these areas is currently fairly isolated, and there is framework for an end-to-end design approach where a desired application informs the choice of materials for the qubits and their environment, and vice versa.We identify knowledge gaps and opportunities for research that builds on existing PNNL capabilities.
36 MATERIALS SCIENCE↗
Process optimization of complex geometries using feed forward control for laser powder bed fusion additive manufacturing
Additive manufacturing (AM) enables the fabrication of complex designs that are difficult to create by other means. Metal parts manufactured by laser powder bed fusion (LPBF) can incorporate intricate design features and demonstrate desirable mechanical properties. However, printing a part that is qualified for its intended application often involves reprinting and discarding many parts to eliminate defects, improve dimensional accuracy, and increase repeatability. The process of iteratively converging on the appropriate build parameters increases the time and cost of creating functional LPBF manufactured parts. This work describes a fast, scalable method for part-scale process optimization of arbitrary geometries. Additionally, the computational approach uses feature extraction to identify scan vectors in need of parameter adaptation and applies results from simulation-based feed forward control models. This method provides a framework to quickly optimize complex parts through the targeted application of models with a range of fidelity and by automating the transfer of optimization strategies to new part designs. The computational approach and algorithmic framework are described, a software package is implemented, the method is applied to parts with complex features, and parts are printed on a customized open architecture LPBF machine.
3D printing↗
Computer Modeling and Simulation: Increasing Reliability by Disentangling Verification and Validation
Verification and validation (V&V) of computer codes and models used in simulations are two aspects of the scientific practice of high importance that recently have been discussed widely by philosophers of science. While verification is predominantly associated with the correctness of the way a model is represented by a computer code or algorithm, validation more often refers to the model’s relation to the real world and its intended use. Because complex simulations are generally opaque to a practitioner, the Duhem problem can arise with verification and validation due to their entanglement; such an entanglement makes it impossible to distinguish whether a coding error or the model’s general inadequacy to its target should be blamed in the case of a failure. I argue that a clear distinction between computer modeling and simulation has to be made to disentangle verification and validation. Drawing on that distinction, I suggest to associate modeling with verification and simulation, which shares common epistemic strategies with experimentation, with validation. To explain the reasons for their entanglement in practice, I propose a Weberian ideal–typical model of modeling and simulation as roles in practice. I examine an approach to mitigate the Duhem problem for verification and validation that is generally applicable in practice and is based on differences in epistemic strategies and scopes. Based on this analysis, I suggest two strategies to increase the reliability of simulation results, namely, avoiding alterations of verified models at the validation stage as well as performing simulations of the same target system using two or more different models. In response to Winsberg’s claim that verification and validation are entangled I argue that deploying the methodology proposed in this work it is possible to mitigate inseparability of V&V in many if not all domains where modeling and simulation are used.
97 MATHEMATICS AND COMPUTING↗
Reconstruction of Charged Particle Tracks in Realistic Detector Geometry Using a Vectorized and Parallelized Kalman Filter Algorithm
One of the most computationally challenging problems expected for the High-Luminosity Large Hadron Collider (HL-LHC) is finding and fitting particle tracks during event reconstruction. Algorithms used at the LHC today rely on Kalman filtering, which builds physical trajectories incrementally while incorporating material e ects and error estimation. Recognizing the need for faster computational throughput, we have adapted Kalman-filterbased methods for highly parallel, many-core SIMD and SIMT architectures that are now prevalent in high-performance hardware. Previously we observed significant parallel speedups, with physics performance comparable to CMS standard tracking, on Intel Xeon, Intel Xeon Phi, and (to a limited extent) NVIDIA GPUs. While early tests were based on artificial events occurring inside an idealized barrel detector, we showed subsequently that our mkFit software builds tracks successfully from complex simulated events (including detector pileup) occurring inside a geometrically accurate representation of the CMS-2017 tracker. Here, we report on advances in both the computational and physics performance of mkFit, as well as progress toward integration with CMS production software. Recently we have improved the overall eciency of the algorithm by preserving short track candidates at a relatively early stage rather than attempting to extend them over many layers. Moreover, mkFit formerly produced an excess of duplicate tracks; these are now explicitly removed in an additional processing step. We demonstrate that with these enhancements, mkFit becomes a suitable choice for the first iteration of CMS tracking, and eventually for later iterations as well. We plan to test this capability in the CMS High Level Trigger during Run 3 of the LHC, with an ultimate goal of using it in both the CMS HLT and oine reconstruction for the HL-LHC CMS tracker.
Cerati, Giuseppe↗
Lockheed Martin Quantum Machine Learning
The primary goal of this collaboration is to produce an algorithm for applying a class of machine learning solutions to real world problems to be executed on a quantum annealer. FRA will utilize this algorithm to produce at least one scientific publication based on data filtering using machine learning algorithms on a quantum computer. LM's primary goal is to leverage current quantum machine learning algorithmic expertise and apply it to cosmological data.
97 MATHEMATICS AND COMPUTING↗
Resource-Efficient Quantum Simulations on NISQ Devices: Advancing the State-of-the-Art (Final Technical Report)
This is the final technical report for the project "Resource-Efficient Quantum Simulations on NISQ Devices: Advancing the State-of-the-Art". Under this effort we have devised novel resource efficient quantum dynamical simulation algorithms. The report details our progress over the course of this three-year effort.
97 MATHEMATICS AND COMPUTING↗
Feedback-based quantum algorithm inspired by counterdiabatic driving
In recent quantum algorithmic developments, a feedback-based approach has shown promise for preparing quantum many-body system ground states and solving combinatorial optimization problems. This method utilizes quantum Lyapunov control to iteratively construct quantum circuits. Here, we propose a substantial enhancement by implementing a protocol that uses ideas from quantum Lyapunov control and the counterdiabatic driving protocol, a key concept from quantum adiabaticity. Our approach introduces an additional control field inspired by counterdiabatic driving. We apply our algorithm to prepare ground states in one-dimensional quantum Ising spin chains. Comprehensive simulations demonstrate a remarkable acceleration in population transfer to low-energy states within a significantly reduced time frame compared to conventional feedback-based quantum algorithms. This acceleration translates to a reduced quantum circuit depth, a critical metric for potential quantum computer implementation. We validate our algorithm on the IBM cloud computer, highlighting its efficacy in expediting quantum computations for many-body systems and combinatorial optimization problems.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗