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At least 1,297 records · Page 72

Power and Limitations of Linear Programming Decoder for Quantum LDPC Codes

Decoding quantum error-correcting codes is a key challenge in enabling fault-tolerant quantum computation. In the classical setting, linear programming (LP) decoders offer provable performance guarantees and can leverage fast practical optimization algorithms. Although LP decoders have been proposed for quantum codes, their performance and limitations remain relatively underexplored. In this work, we uncover a key limitation of LP decoding for quantum low-density parity-check (LDPC) codes: certain constant-weight error patterns lead to ambiguous fractional solutions that cannot be resolved through independent rounding. To address this issue, we incorporate a post-processing technique known as ordered statistics decoding (OSD), which significantly enhances LP decoding performance in practice. Our results show that LP decoding, when augmented with OSD, can outperform belief propagation with the same post-processing for intermediate code sizes of up to hundreds of qubits. These findings suggest that LP-based decoders, equipped with effective post-processing, offer a promising approach for decoding near-term quantum LDPC codes.

Gu, Shouzhen [Yale U.]↗

Power and Limitations of Linear Programming Decoder for Quantum LDPC Codes

Decoding quantum error-correcting codes is a key challenge in enabling fault-tolerant quantum computation. In the classical setting, linear programming (LP) decoders offer provable performance guarantees and can leverage fast practical optimization algorithms. Although LP decoders have been proposed for quantum codes, their performance and limitations remain relatively underexplored. In this work, we uncover a key limitation of LP decoding for quantum low-density parity-check (LDPC) codes: certain constant-weight error patterns lead to ambiguous fractional solutions that cannot be resolved through independent rounding. To address this issue, we incorporate a post-processing technique known as ordered statistics decoding (OSD), which significantly enhances LP decoding performance in practice. Our results show that LP decoding, when augmented with OSD, can outperform belief propagation with the same post-processing for intermediate code sizes of up to hundreds of qubits. These findings suggest that LP-based decoders, equipped with effective post-processing, offer a promising approach for decoding near-term quantum LDPC codes.

Gu, Shouzhen [Yale U.]↗

Power and Limitations of Linear Programming Decoder for Quantum LDPC Codes

Decoding quantum error-correcting codes is a key challenge in enabling fault-tolerant quantum computation. In the classical setting, linear programming (LP) decoders offer provable performance guarantees and can leverage fast practical optimization algorithms. Although LP decoders have been proposed for quantum codes, their performance and limitations remain relatively underexplored. In this work, we uncover a key limitation of LP decoding for quantum low-density parity-check (LDPC) codes: certain constant-weight error patterns lead to ambiguous fractional solutions that cannot be resolved through independent rounding. To address this issue, we incorporate a post-processing technique known as ordered statistics decoding (OSD), which significantly enhances LP decoding performance in practice. Our results show that LP decoding, when augmented with OSD, can outperform belief propagation with the same post-processing for intermediate code sizes of up to hundreds of qubits. These findings suggest that LP-based decoders, equipped with effective post-processing, offer a promising approach for decoding near-term quantum LDPC codes.

Gu, Shouzhen [Yale U.]↗

Monte Carlo simulation based study of a proposed multileaf collimator for a telecobalt machine

Purpose: The objective of the present work was to propose a design of a secondary multileaf collimator (MLC) for a telecobalt machine and optimize its design features through Monte Carlo simulation. Methods: The proposed MLC design consists of 72 leaves (36 leaf pairs) with additional jaws perpendicular to leaf motion having the capability of shaping a maximum square field size of 35 Multiplication-Sign 35 cm{sup 2}. The projected widths at isocenter of each of the central 34 leaf pairs and 2 peripheral leaf pairs are 10 and 5 mm, respectively. The ends of the leaves and the x-jaws were optimized to obtain acceptable values of dosimetric and leakage parameters. Monte Carlo N-Particle code was used for generating beam profiles and depth dose curves and estimating the leakage radiation through the MLC. A water phantom of dimension 50 Multiplication-Sign 50 Multiplication-Sign 40 cm{sup 3} with an array of voxels (4 Multiplication-Sign 0.3 Multiplication-Sign 0.6 cm{sup 3}= 0.72 cm{sup 3}) was used for the study of dosimetric and leakage characteristics of the MLC. Output files generated for beam profiles were exported to the PTW radiation field analyzer software through locally developed software for analysis of beam profiles in order to evaluate radiation field width, beam flatness, symmetry, and beam penumbra. Results: The optimized version of the MLC can define radiation fields of up to 35 Multiplication-Sign 35 cm{sup 2} within the prescribed tolerance values of 2 mm. The flatness and symmetry were found to be well within the acceptable tolerance value of 3%. The penumbra for a 10 Multiplication-Sign 10 cm{sup 2} field size is 10.7 mm which is less than the generally acceptable value of 12 mm for a telecobalt machine. The maximum and average radiation leakage through the MLC were found to be 0.74% and 0.41% which are well below the International Electrotechnical Commission recommended tolerance values of 2% and 0.75%, respectively. The maximum leakage through the leaf ends in closed condition was observed to be 8.6% which is less than the values reported for other MLCs designed for medical linear accelerators. Conclusions: It is concluded that dosimetric parameters and the leakage radiation of the optimized secondary MLC design are well below their recommended tolerance values. The optimized design of the proposed MLC can be integrated into a telecobalt machine by replacing the existing adjustable secondary collimator for conformal radiotherapy treatment of cancer patients.

60 APPLIED LIFE SCIENCES↗

Automating Discovery of Physics-Informed Neural State Space Models via Learning and Evolution

Recent works exploring deep learning application to dynamical systems modeling have demonstrated that embedding physical priors into neural networks can yield more effective, physically-realistic, and data-efficient models. However, in the absence of complete prior knowledge of a dynamical system's physical characteristics, determining the optimal structure and optimization strategy for these models can be difficult. In this work, we explore methods for discovering neural state space dynamics models for system identification. Starting with a design space of block-oriented state space models and structured linear maps with strong physical priors, we encode these components into a model genome alongside network structure, penalty constraints, and optimization hyperparameters. Demonstrating the overall utility of the design space, we employ an asynchronous genetic search algorithm that alternates between model selection and optimization and obtains accurate physically consistent models of three physical systems: an aerodynamics body, a continuous stirred tank reactor, and a two tank interacting system.

genetic algorithms, neural architecture search, ne↗

Gradient process parameter optimization in additive friction stir deposition of aluminum alloys

As one of the most novel additive manufacturing methods, currently selection and optimization of processing parameters in additive friction stir deposition (AFSD) have mainly relied on experiments and subsequent characterization of microstructural and mechanical properties. Such approaches are both time- and resource-consuming. Therefore, an ultrasound elastography enhanced gradient process parameter optimization method was applied in the present work to obtain a window of optimized processing parameters for AFSD processing of aluminum alloy by varying both rotational and linear deposition speeds. Further, the quality of AFSD processed layer was investigated for physical nature of surface, dynamic elastic modulus, and microstructural aspects in cross-sections of the deposited layer. The efficiency in exploring process parameters was significantly enhanced by implementing a high-throughput screening experimental design based on application of gradient process parameters and continuous ultrasound elastographs. In addition, the applied ultrasonic elastography technique assisted in evaluating the homogeneity in microstructure and mechanical properties of AFSD sample over the entire gradients of the process parameters. The techniques adopted in current work can be further extended to identify suitable parameters for AFSD fabrication of components with desired mechanical properties such as hardness, fatigue, etc.

36 MATERIALS SCIENCE↗

Dispatch optimization of concentrating solar power with utility-scale photovoltaics

Concentrating solar power (CSP) tower technologies capture thermal radiation from the sun utilizing a field of solar-tracking heliostats. When paired with inexpensive thermal energy storage (TES), CSP technologies can dispatch electricity during peak-market-priced hours, day or night. The cost of utility-scale photovoltaic (PV) systems has dropped significantly in the last decade, resulting in inexpensive energy production during daylight hours. The hybridization of PV and CSP with TES systems has the potential to provide continuous and stable energy production at a lower cost than a PV or CSP system alone. Hybrid systems are gaining popularity in international markets as a means to increase renewable energy portfolios across the world. Typically, CSP-PV hybrid systems have been evaluated using either monthly averages of hourly PV production or scheduling algorithms that neglect the time-of-production value of electricity in the market. To more accurately evaluate a CSP-PV-battery hybrid design, we develop a profit-maximizing mixed-integer linear program ($\mathcal{H}$) that determines a dispatch schedule for the individual sub-systems with a sub-hourly time fidelity. We introduce the mathematical formulation of such a model and show that it is computationally expensive to solve. To improve model tractability and reduce solution times, we offer techniques that: (1) reduce the problem size, (2) tighten the linear programming relaxation of ($\mathcal{H}$) via reformulation and the introduction of cuts, and (3) implement an optimization-based heuristic (that can yield initial feasible solutions for (($\mathcal{H}$) and, at any rate, yields near-optimal solutions). Applying these solution techniques results in a 79% improvement in solve time, on average, for our 48-h instances of (($\mathcal{H}$); corresponding solution times for an annual model run decrease by as much as 93%, where such a run consists of solving 365 instances of (($\mathcal{H}$), retaining only the first 24 h' worth of the solution, and sliding the time window forward 24 h. We present annual system metrics for two locations and two markets that inform design practices for hybrid systems and lay the groundwork for a more exhaustive policy analysis. A comparison of alternative hybrid systems to the CSP-only system reflects that hybrid models can almost double capacity factors while resulting in a 30% improvement related to various economic metrics.

14 SOLAR ENERGY↗

Random circuit block-encoded matrix and a proposal of quantum LINPACK benchmark

The LINPACK benchmark reports the performance of a computer for solving a system of linear equations with dense random matrices. Although this task was not designed with a real application directly in mind, the LINPACK benchmark has been used to define the list of TOP500 supercomputers since the debut of the list in 1993. We propose that a similar benchmark, called the quantum LINPACK benchmark, could be used to measure the whole machine performance of quantum computers. The success of the quantum LINPACK benchmark should be viewed as the minimal requirement for a quantum computer to perform a useful task of solving linear algebra problems, such as linear systems of equations. We propose an input model called the Random Circuit Block-Encoded Matrix (RACBEM), which is a proper generalization of a dense random matrix in the quantum setting. The RACBEM model is efficient to be implemented on a quantum computer and can be designed to optimally adapt to any given quantum architecture, with relying on a black-box quantum compiler. Besides solving linear systems, the RACBEM model can be used to perform a variety of linear algebra tasks relevant to many physical applications, such as computing spectral measures, time series generated by a Hamiltonian simulation, and thermal averages of the energy. We implement these linear algebra operations on IBM Q quantum devices as well as quantum virtual machines, and demonstrate their performance in solving scientific computing problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Comparison of Fickian and temporally nonlocal transport theories over many scales in an exhaustively sampled sandstone slab

It is not a compelling argument, solely on the basis of a better fit to solute breakthrough curve (BTC) data, that a temporally nonlocal model is necessary to simulate transport in an advection-dominated system. One may counter that the classical advection-dispersion equation (ADE) is a valid model at some small scale and that the detailed hydraulic conductivity (K) data must be well-represented: then the nonlocality is only a result of upscaling and loss of information. But is the nonlocal model demonstrably necessary at all scales? We examine the experiment conducted by Klise et al. (2008) in which a 30.5 by 30.5 cm slab of relatively homogeneous, cross-bedded sandstone was exhaustively sampled for K. The slab was sealed, saturated with potassium iodide, and X-rayed 10 times while being flushed with fresh water. The 8,649 air-permeameter measurements were down- and upscaled to make finer and coarser grids on which the velocity field was solved and the ADE applied. The optimized parameters in the ADE were found to scale predictably, most notably the longitudinal dispersivity (α L ), which grew linearly with upscaling. But at all levels of up- and downscaling, including the original K measurement scale of 0.33 cm, the ADE did not adequately represent the late-time tails. The temporally nonlocal, time- fractional ADE (t-FADE) was applied and the optimized parameters (α L and the immobile capacity beta) did not depend on scale. The better fit provided by the t-FADE in the late BTC tails did not bring about a sacrificed fit elsewhere in the BTC. Furthermore, the optimized ADE and t-FADE solutions do not converge at the smallest scale, directly implying that the temporal nonlocality is a necessary model component. We conclude that the logical inference if the ADE is valid in heterogeneous material, then there is tailing in the BTC'' is not a proof that the reverse is true. We provide a clear counterexample. A corollary is that a mismatch between data and a discretized solution to the ADE does not imply that more data will improve fits or predictive ability.

58 GEOSCIENCES↗

Re-Analysis of DARHT Axis 2 S4 Magnet Sweep Measurements

The Dual-Axis Radiographic Hydrodynamic Test (DARHT) facility provides flash radiography capabilities using two electron Linear Induction Accelerators (LIA’s). Understanding fundamental properties of the electron beams is essential to optimizing spot size and dose for radiography. This work describes distribution measurements of a single-kicked electron beam (16.5MeV, 1.7kA, 60ns) at a location downstream at imaging station C on DARHT Axis 2. The beam at station C is focused by the S4 solenoid located upstream. The beam distribution is measured by imaging optical transition radiation (OTR) from electrons striking a 51-µm thick titanium foil. This data and analysis were originally published by Ekdahl. The results here are a re-analysis of the asymmetric halo emittance contribution as compared to the emittance resulting from the FWHM of the distribution. This is accomplished using xtr2 fits to the data which include non-linear magnetic field effects in S4. Also examined are the calculated S4 spherical aberration contributions to the emittance using xtr.

43 PARTICLE ACCELERATORS↗

A log-barrier Newton-CG method for bound constrained optimization with complexity guarantees

Abstract We describe an algorithm based on a logarithmic barrier function, Newton’s method and linear conjugate gradients that seeks an approximate minimizer of a smooth function over the non-negative orthant. We develop a bound on the complexity of the approach, stated in terms of the required accuracy and the cost of a single gradient evaluation of the objective function and/or a matrix-vector multiplication involving the Hessian of the objective. The approach can be implemented without explicit calculation or storage of the Hessian.

O’Neill, Michael↗

Optimal Wentzell Boundary Control of Parabolic Equations

This paper deals with a class of optimal control problems governed by an initial-boundary value problem of a parabolic equation. The case of semi-linear boundary control is studied where the control is applied to the system via the Wentzell boundary condition. The differentiability of the state variable with respect to the control is established and hence a necessary condition is derived for the optimal solution in the case of both unconstrained and constrained problems. The condition is also sufficient for the unconstrained convex problems. A second order condition is also derived.

97 MATHEMATICS AND COMPUTING↗

Distributed Controllers Seeking AC Optimal Power Flow Solutions Using ADMM

This paper focuses on power distribution systems with inverter-interfaced renewable energy sources (RESs), and develops a distributed control framework to steer the RES output powers to solutions of ac optimal power flow (OPF) problems. The design of the distributed control algorithm is based on suitable linear approximation of the ac power-flow equations, and leverages the so-called alternating direction method of multipliers (ADMM). Convergence of the RES-inverter output powers to solutions of the approximate ac OPF problem is established under suitable conditions on the mismatches between the commanded setpoints and actual RES output powers. Overall, since the proposed scheme can be cast as an ADMM with inexact primal and dual updates, the convergence results can be applied to more general distributed optimization settings.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Switching current reduction in magnetoresistive random access memories

We present an approach for minimizing the critical current for the magnetization switching in magnetic tunnel junctions by optimizing the spatial distribution of the current density. We show that such a minimization is possible because critical current is determined by the condition of making one of the magnetization eigenstates grow in time. The excitation of the eigenstates is enhanced when the spatial distributions of the eigenstates and current density overlap. Critical current can be viewed as a functional of the current density spatial distribution and it can be minimized by optimizing this distribution. Such an optimization results in a major reduction of the critical current and increase of the switching efficiency, viz. the ratio between the energy barrier and critical current. The minimized critical current increases approximately linearly with the magnetic tunnel junction size, which is much slower than critical current for the case of a uniform current density. The optimized efficiency can be approximately a constant with respect to the magnetic tunnel junction size, which is much higher than the efficiency for the uniform current density. Additional optimization can be achieved by spatially modulating the material parameters, e.g., the saturation magnetization. The presented approach and obtained scaling of the critical current and efficiency offers opportunities for the magnetic tunnel junction optimization.

36 MATERIALS SCIENCE↗

Applications of Optimal Building Energy System Selection and Operation

Berkeley Lab has been developing the Distributed Energy Resources Customer Adoption Model (DER-CAM) for several years. Given load curves for energy services requirements in a building microgrid (u grid), fuel costs and other economic inputs, and a menu of available technologies, DER-CAM finds the optimum equipment fleet and its optimum operating schedule using a mixed integer linear programming approach. This capability is being applied using a software as a service (SaaS) model. Optimisation problems are set up on a Berkeley Lab server and clients can execute their jobs as needed, typically daily. The evolution of this approach is demonstrated by description of three ongoing projects. The first is a public access web site focused on solar photovoltaic generation and battery viability at large commercial and industrial customer sites. The second is a building CO2 emissions reduction operations problem for a University of California, Davis student dining hall for which potential investments are also considered. And the third, is both a battery selection problem and a rolling operating schedule problem for a large County Jail. Together these examples show that optimization of building u grid design and operation can be effectively achieved using SaaS.

25 ENERGY STORAGE↗

Optical Frequency Domain Visualization of Electron Beam Driven Plasma Wakefields

Bunch driven plasma wakefield accelerators (PWFA), such as the 'plasma afterburner', are a promising emerging method for significantly increasing the energy output of conventional particle accelerators. The study and optimization of this method would benefit from an experimental correlation of the drive bunch parameters and the accelerated particle parameters with the corresponding plasma wave structure. However, the plasma wave structure has not been observed directly so far. We will report ongoing development of a noninvasive optical Frequency Domain Interferometric (FDI) and Holographic (FDH) diagnostics of bunch driven plasma wakes. Both FDI and FDH have been previously demonstrated in the case of laser driven wakes. These techniques employ two laser pulses co-propagating with the drive particle bunch and the trailing plasma wave. One pulse propagates ahead of the drive bunch and serves as a reference, while the second is overlapped with the plasma wave and probes its structure. The multi-shot FDI and single-shot FDH diagnostics permit direct noninvasive observation of longitudinal and transverse structure of the plasma wakes. The experiment is being developed at the 70 MeV Linac in the Accelerator Test Facility at Brookhaven National Laboratory to visualize wakes generated by two and multi-bunch drive beams.

43 PARTICLE ACCELERATORS↗

Remarks on Hierarchic Control for a Linearized Micropolar Fluids System in Moving Domains

We study a Stackelberg strategy subject to the evolutionary linearized micropolar fluids equations in domains with moving boundaries, considering a Nash multi-objective equilibrium (non necessarily cooperative) for the “follower players” (as is called in the economy field) and an optimal problem for the leader player with approximate controllability objective. We will obtain the following main results: the existence and uniqueness of Nash equilibrium and its characterization, the approximate controllability of the linearized micropolar system with respect to the leader control and the existence and uniqueness of the Stackelberg–Nash problem, where the optimality system for the leader is given.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

An Emergent Conductivity Relationship for Water Flow Based on Minimized Dissipation: From Landscapes to Unsaturated Soils

Optimality principles have been widely used in many areas. Based on an optimality principle that a flow field will tend toward a minimum in the energy dissipation rate, this work shows that there exists a unified form of conductivity relationship for two different flow systems: landscapes and unsaturated soils. The conductivity, the ratio of water flux to water head (energy) gradient, is a power function of water flux where the exponent value is system dependent. This relationship indicates that to minimize energy dissipation rate for a whole system, water flow has a small resistance (or a large conductivity) at a location of large water flux. Empirical evidence supports validity of the relationship for landscape and unsaturated soils (under gravity dominated conditions). Especially, it is of interest that according to this relationship, hydraulic conductivity for gravity-dominated unsaturated flow, unlike that defined in the classic theories, depends on not only capillary pressure (or saturation), but also the water flux. Use of the optimality principle allows for determining useful results that may be applicable to a broad range of areas involving highly non-linear processes and may not be possible to obtain from classic theories describing water flow processes.

54 ENVIRONMENTAL SCIENCES↗