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At least 127 records · Page 7

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DOE OSTI2020

Mean-field entanglement transitions in random tree tensor networks

Entanglement phase transitions in quantum chaotic systems subject to projective measurements and in random tensor networks have emerged as a new class of critical points separating phases with different entanglement scaling. We propose a mean-field theory of such transitions by studying the entanglement properties of random tree tensor networks. As a function of bond dimension, we find a phase transition separating area-law from logarithmic scaling of the entanglement entropy. Using a mapping onto a replica statistical mechanics model defined on a Cayley tree and the cavity method, we analyze the scaling properties of such transitions. Our approach provides a tractable, mean-field-like example of an entanglement transition. Furthermore, we verify our predictions numerically by computing directly the entanglement of random tree tensor network states.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2022

Entanglement features of random neural network quantum states

Restricted Boltzmann machines (RBMs) are a class of neural networks that have been successfully employed as a variational ansatz for quantum many-body wave functions. Here, we develop an analytic method to study quantum many-body spin states encoded by random RBMs with independent and identically distributed complex Gaussian weights. By mapping the computation of ensemble-averaged quantities to statistical mechanics models, we are able to investigate the parameter space of the RBM ensemble in the thermodynamic limit. We discover qualitatively distinct wave functions by varying RBM parameters, which correspond to distinct phases in the equivalent statistical mechanics model. Notably, there is a regime in which the typical RBM states have near-maximal entanglement entropy in the thermodynamic limit, similar to that of Haar-random states. However, these states generically exhibit nonergodic behavior in the Ising basis, and do not form quantum state designs, making them distinguishable from Haar-random states.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Characterizing random-singlet state in two-dimensional frustrated quantum magnets and implications for the double perovskite Sr 2 CuTe 1 – x W x O 6

Motivated by the experimental observation of a nonmagnetic phase in compounds with frustration and disorder, we study the ground state of a spin-1/2 square-lattice Heisenberg model with randomly distributed nearest-neighbor J 1 and next-nearest-neighbor J 2 couplings. By using the density matrix renormalization group (DMRG) calculation on a cylinder system with a circumference of up to ten lattice sites, we identify a disordered phase between the Néel and stripe magnetic phase with growing J 2 /J 1 in the presence of strong bond randomness. The vanished spin-freezing parameter indicates the absence of spin-glass order. The large-scale DMRG results unveil the size-scaling behaviors of the spin-freezing parameter, the power-law decay of the average spin correlation, and the exponential decay of the typical spin correlation, which all agree with the corresponding behavior in the one-dimensional random-singlet (RS) state and characterize the RS nature of this disordered phase. The DMRG simulation also provides insights and opportunities for characterizing a class of nonmagnetic states in two-dimensional frustrated magnets with disorder. Here, we also compare with existing experiments and suggest more measurements for understanding the spin-liquid-like behaviors in the double perovskite Sr 2 CuTe 1–x W x O 6 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2024

Universal Spreading of Conditional Mutual Information in Noisy Random Circuits

For this work, we study the evolution of conditional mutual information (CMI) in generic open quantum systems, focusing on one-dimensional random circuits with interspersed local noise. Unlike in noiseless circuits, where CMI spreads linearly while being bounded by the light cone, we find that noisy random circuits with an error rate 𝑝 exhibit superlinear propagation of CMI, which diverges far beyond the light cone at a critical circuit depth 𝑡 𝑐 ∝ 𝑝 −1 . We demonstrate that the underlying mechanism for such rapid spreading is the combined effect of local noise and a scrambling unitary, which selectively removes short-range correlations while preserving long-range correlations. To analytically capture the dynamics of CMI in noisy random circuits, we introduce a coarse-graining method, and we validate our theoretical results through numerical simulations. Furthermore, we identify a universal scaling law governing the spreading of CMI.

decoherence↗

DOE OSTI2024

Understanding random-walk dynamical phase coexistence through waiting times

We study the appearance of first-order dynamical phase transitions (DPTs) as “intermittent” coexisting phases in the fluctuations of random walks on graphs. We show that the diverging timescale leading to critical behavior is the waiting time to jump from one phase to another. This timescale is crucial for observing the system's relaxation to stationarity and demonstrate ergodicity of the system at criticality. We illustrate these results through three analytical examples which provide insights into random walks exploring random graphs. Published by the American Physical Society 2024

Stuhrmann, David C. (ORCID:0009000726916649)↗

DOE OSTI2024

Random coordinate descent: A simple alternative for optimizing parameterized quantum circuits

Variational quantum algorithms rely on the optimization of parameterized quantum circuits in noisy settings. The commonly used back-propagation procedure in classical machine learning is not directly applicable in this setting due to the collapse of quantum states after measurements. Thus, gradient estimations constitute a significant overhead in a gradient-based optimization of such quantum circuits. This paper introduces a random coordinate descent algorithm as a practical and easy-to-implement alternative to the full gradient descent algorithm. This algorithm only requires one partial derivative at each iteration. Motivated by the behavior of measurement noise in the practical optimization of parameterized quantum circuits, this paper presents an optimization problem setting that is amenable to analysis. Under this setting, the random coordinate descent algorithm exhibits the same level of stochastic stability as the full gradient approach, making it as resilient to noise. The complexity of the random coordinate descent method is generally no worse than that of the gradient descent and can be much better for various quantum optimization problems with anisotropic Lipschitz constants. Theoretical analysis and extensive numerical experiments validate our findings. Published by the American Physical Society 2024

Ding, Zhiyan (ORCID:000000018863403X)↗

DOE OSTI2024

Effect of Nonunital Noise on Random-Circuit Sampling

In this work, drawing inspiration from the type of noise present in real hardware, we study the output distribution of random quantum circuits under practical nonunital noise sources with constant noise rates. We show that even in the presence of unital sources such as the depolarizing channel, the distribution, under the combined noise channel, never resembles a maximally entropic distribution at any depth. To show this, we prove that the output distribution of such circuits never anticoncentrates—meaning that it is never too “flat”—regardless of the depth of the circuit. This is in stark contrast to the behavior of noiseless random quantum circuits or those with only unital noise, both of which anticoncentrate at sufficiently large depths. As a consequence, our results shows that the complexity of random-circuit sampling under realistic noise is still an open question, since anticoncentration is a critical property exploited by both state-of-the-art classical hardness and easiness results. Published by the American Physical Society 2024

Physics↗

DOE OSTI2024

Designs from Local Random Quantum Circuits with SU ( d ) Symmetry

The generation of k -designs (pseudorandom distributions that emulate the Haar measure up to k moments) with local quantum circuit ensembles is a problem of fundamental importance in quantum information and physics. Despite the extensive understanding of this problem for ordinary random circuits, the crucial situations in which symmetries or conservation laws are in play are known to pose fundamental challenges and remain little understood. Here, we construct explicit local unitary ensembles that can achieve high-order unitary k -designs under transversal continuous symmetry, in the particularly important SU ( d ) case. Specifically, we define the convolutional quantum alternating (CQA) group generated by 4-local SU ( d ) -symmetric Hamiltonians as well as associated 4-local SU ( d ) -symmetric random unitary circuit ensembles and prove that they form and converge to SU ( d ) -symmetric k -designs, respectively, for all k < n ( n − 3 ) / 2 , with n being the number of qudits. A key technique that we employ to obtain the results is the Okounkov-Vershik approach to S n representation theory. To study the convergence time of the CQA ensemble, we develop a numerical method using the Young orthogonal form and the S n branching rule. We provide strong evidence for a subconstant spectral gap and certain convergence time scales of various important circuit architectures, which contrast with the symmetry-free case. We also provide comprehensive explanations of the difficulties and limitations in rigorously analyzing the convergence time using methods that have been effective for cases without symmetries, including Knabe’s local gap threshold and Nachtergaele’s martingale methods. This suggests that a novel approach is likely necessary for understanding the convergence time of SU ( d ) -symmetric local random circuits. Published by the American Physical Society 2024

Li, Zimu (ORCID:0000000314736492)↗

DOE OSTI2021

Fabrication of Quasi-Random Photonic Crystals for Ultrathin Solar Cells

Quasi-random structures for light management present an intermediate ordering between a completely random rough surface and a perfect ordered photonic crystal. They are attractive for broadband applications due to their power spectral density. This makes them excellent candidates for photovoltaic applications. Here we present preliminary fabrication results creating quasi-random structures using a self-assembly approach based on polymer blends and wet etching. We are able to create patterns with average lattice constant of five to two microns. This structure is proposed to be used as a rear patterning layer for ultrathin GaAs cells for better sustainability and radiation- hard devices.

41 EE - Solar Energy Technologies Office (EE-4S)↗

DOE OSTI2021

River sinuosity describes a continuum between randomness and ordered growth

River channels are among the most common landscape features on Earth. An essential characteristic of channels is sinuosity: their tendency to take a circuitous path, which is quantified as along-stream length divided by straight-line length. River sinuosity is interpreted as a characteristic that either forms randomly at channel inception or develops over time as meander bends migrate. Studies tend to assume the latter and thus have used river sinuosity as a proxy for both modern and ancient environmental factors including climate, tectonics, vegetation, and geologic structure. But no quantitative criterion for planform expression has distinguished between random, initial sinuosity and that developed by ordered growth through channel migration. This ambiguity calls into question the utility of river sinuosity for understanding Earth’s history. We propose a quantitative framework to reconcile these competing explanations for river sinuosity. Using a coupled analysis of modeled and natural channels, we show that while a majority of observed sinuosity is consistent with randomness and limited channel migration, rivers with sinuosity ≥1.5 likely formed their geometry through sustained, ordered growth due to channel migration. This criterion frames a null hypothesis for river sinuosity that can be applied to evaluate the significance of environmental interpretations in landscapes shaped by rivers. The quantitative link between sinuosity and channel migration further informs strategies for preservation and restoration of riparian habitat and guides predictions of fluvial deposits in the rock record and in remotely sensed environments from the seafloor to planetary surfaces.

58 GEOSCIENCES↗

DOE OSTI2025

Surrogate-Based Autotuning for Randomized Sketching Algorithms in Regression Problems

Algorithms from Randomized Numerical Linear Algebra (RandNLA) are known to be effective in handling high-dimensional computational problems, providing high-quality empirical performance as well as strong probabilistic guarantees. However, their practical application is complicated by the fact that the user needs to set various algorithm-specific tuning parameters which are different from those used in traditional NLA. This paper demonstrates how a surrogate-based autotuning approach can be used to address fundamental problems of parameter selection in RandNLA algorithms. In particular, we provide a detailed investigation of surrogate-based autotuning for sketch-and-precondition (SAP)-based randomized least squares methods, which have been one of the great success stories in modern RandNLA. Empirical results show that our surrogate-based autotuning approach can achieve near-optimal performance with much less tuning cost than a random search (up to about 7.6x fewer trials of different parameter configurations). Moreover, while our experiments focus on least squares, our results demonstrate a general-purpose autotuning pipeline applicable to any kind of RandNLA algorithm.

Cho, Younghyun↗

DOE OSTI2025

Efficient Training of Deep Neural Operator Networks via Randomized Sampling

Neural operators (NOs) employ deep neural networks to learn the mappings between infinitedimensional function spaces. Deep operator network (DeepONet), a popular NO architecture, has demonstrated success in the real-time prediction of complex dynamics across various scientific and engineering applications. In this work, we introduce a random sampling technique to be adopted during the training of DeepONet, aimed at improving the generalization ability of the model, while significantly reducing the computational time. The proposed approach targets the trunk network of the DeepONet model that outputs the basis functions corresponding to the spatiotemporal locations of the bounded domain on which the physical system is defined. While constructing the loss function, DeepONet training traditionally considers a uniform grid of spatiotemporal points at which all the output functions are evaluated for each iteration. This approach leads to a larger batch size, resulting in poor generalization and increased memory demands, due to the limitations of the stochastic gradient descent (SGD) optimizer. The proposed random sampling over the inputs of the trunk net mitigates these challenges, improving generalization and reducing the memory requirements during training, resulting in significant computational gains. We validate our hypothesis through three benchmark examples, demonstrating substantial reductions in training time while achieving comparable or lower overall test errors relative to the traditional training approach. Our results indicate that incorporating randomization in the trunk network inputs during training enhances the efficiency and robustness of DeepONet, offering a promising avenue for improving the framework’s performance in modeling complex physical systems.

Karumuri, Sharmila [Department of Civil & Systems ↗

DOE OSTI2025

COBRA:COMPUTED-TOMOGRAPHY BASED RANDOM-FIELD APPROXIMATION

SF-25-115 COBRA (COmputed-tomography Based Random-field Approximation) is a Python application for generating statistically equivalent random fields from CT-scan imagery. It leverages Karhunen–Loève expansions to model microstructural variability, enabling users to: Preprocess CT scans (filtering and Gaussian transformation); Fit covariance kernels fromempirical data; Solve eigenproblems to obtain KL modes; Sample random fields onsistent with fitted statistics; Postprocess samples back into the physical domain.

Hu, Tianchen↗

DOE OSTI2024

Traceable Device-Independent Randomness as a Service

We implement a traceable protocol for device-independent random number generation. Our demonstration involves transparently integrating a device-independent RNG into a public randomness beacon, and feeding 7434 random number pulses into the beacon over 39 days.

Kavuri, Gautam A.↗

DOE OSTI2024

Optical filters made from random metasurfaces using Bayesian optimization

Abstract We theoretically investigate the ability to design optical filters from a single material and a single layer of randomly dispersed resonant dielectric particles, defining a random metasurface. Using a Bayesian and generalized Mie inverse-design approach, we design particle radii distributions that give rise to longpass, shortpass, bandpass, and bandstop spectral bands in the infrared. The optical response is shown to be directly related to electric and magnetic multipole scattering of the constituent particles and their near field coupling. We discuss the effect of the particle size distribution and particle–particle coupling interactions on filter design in random systems lacking long-range order.

Materials Science↗

DOE OSTI2020

Random Variation of ACRR Core Report

The research presented in this paper is to be a contribution to a larger research project. The project was designed to test the safety standards of Sandia National Laboratories' ACRR. The MCNP model of the ACRR core is being used to simulate the environment. To test the safety standards, the dimensions and density of the fuel in the core were varied randomly. Each rod had its own dimension and density assigned to it randomly. Ten different cases of the ACRR core were randomly created. The different cases were studied using 640-group neutron fluxes. The fluxes were compared to see how the variations affected the system.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2024

Bringing randomized algorithms to mainstream numerical linear algebra

Numerical linear algebra (NLA) underpins huge swaths of computational science and engineering. For scientists and engineers to make the most of the DOE’s computing resources, it is essential that they have access to high-performance implementations of algorithms with best-in-class scalability and reliability. Despite this, prevailing NLA libraries have little to no support for breakthrough algorithms from the field of randomized numerical linear algebra (RandNLA) that have been developed over the past twenty years. The goal of this LDRD was to break a log-jam that had prevented broad adoption of RandNLA. Our work had two thrusts. The first was to develop RandBLAS: a trustworthy and high-performance C++ library for randomized dimension reduction (an operation widely known as sketching). The second was the development of a novel randomized algorithm for computing a challenging type of matrix decomposition known as Householder QR with column pivoting (Householder QRCP). In this one-year late-start LDRD we successfully delivered RandBLAS 1.0 and new CPU and GPU codes for Householder QRCP. RandBLAS has extensive documentation at https://randblas.readthedocs.io/en/stable/. Papers on RandBLAS and and our high-performance QRCP codes are forthcoming.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Randomized Algorithms for Linear Solvers

Recently, randomized algorithms in numerical linear algebra, specifically those centered around random sketching, have gained traction in primarily theoretical research due to their potential to significantly reduce problem dimensionality at the cost of an O(1) multiplicative distortion factor. It has been assumed that this sketching can be done efficiently, but thorough investigation into how precisely to do it has been neglected. Moreover, the theory-based community has argued for sketching’s ability to reduce computational cost via complexity analysis, but has not researched how it affects the stability of the algorithms. At Sandia, efficient linear solvers that scale well on modern HPC architectures while maintaining stability are imperative for practical applications. In this LDRD, we developed a random sketching strategy that is substantially faster than existing ones, and demonstrate its superior performance in practice on a NVIDIA H100 GPU. Moreover, we show how this can be used to significantly outperform existing linear least squares solvers while improving the solver’s stability as well. Additionally, we demonstrate how this sketching strategy can be used to make a fast, stable QR factorization that can subsequently be used in s-step and block Krylov solvers. Finally, we incorporate a sketching-based block orthogonalization scheme into s-step GMRES, which is stable and faster than existing approaches on the Perlmutter supercomputer.

97 MATHEMATICS AND COMPUTING↗