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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

On the convergence of the fixed point method for solving neutron transport alpha eigenvalue problems

It was shown that the Fixed Point Method (also known as the Rayleigh Quotient Method) is several times faster than the Critical Search Method for solving neutron transport alpha eigenvalue problems. It was also shown that the Fixed Point Method is able to determine the alpha eigenvalues of sub-critical systems that are beyond the reach of the Critical Search Method. Despite these significant advances, the Fixed Point Method remains an unproven algorithm. Here, this report provides a proof.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

A Quantum Approach for Implementing Fixed-Point Arithmetic in Solving Ordinary Differential Equations

Differential equations (DEs) serve as fundamental tools in mathematical modeling across scientific disciplines, yet classical numerical solvers face limitations with large-scale or computationally intensive problems. This study explores a quantum-inspired approach to solving DEs, combining quantum- inspired techniques with classical methods. It focuses on fixed- point arithmetic on quantum circuits, utilizing basic quantum gates to manipulate DE solutions. We expand upon the techniques introduced by Zanger et al. [Quantum, 5, 502 (2021)] by offering a precise computation for a fixed-point signed multiplication scheme, while also presenting a quantum circuit capable of executing the fixed-point division algorithm. We demonstrate the feasibility of our approach through the simulation of a linear Ordinary Differential Equation (ODE), where initial conditions and parameters are encoded into quantum circuits using fixed- point representation. By executing sequences of quantum gates mimicking numerical integration steps, we obtain approximate solutions to the ODE with specified fixed-point precision.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

A Quantum Approach for Implementing Fixed-Point Arithmetic in Solving Ordinary Differential Equations

Differential equations (DEs) serve as fundamental tools in mathematical modeling across scientific disciplines, yet classical numerical solvers face limitations with large-scale or computationally intensive problems. This study explores a quantum-inspired approach to solving DEs, combining quantum-inspired techniques with classical methods. It focuses on fixed-point arithmetic on quantum circuits, utilizing basic quantum gates to manipulate DE solutions. We expand upon the techniques introduced by Zanger et al. [Quantum, 5, 502 (2021)] by offering a precise computation for a fixed-point signed multiplication scheme, while also presenting a quantum circuit capable of executing the fixed-point division algorithm. We demonstrate the feasibility of our approach through the simulation of a linear Ordinary Differential Equation (ODE), where initial conditions and parameters are encoded into quantum circuits using fixed-point representation. By executing sequences of quantum gates mimicking numerical integration steps, we obtain approximate solutions to the ODE with specified fixed-point precision.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2026

Coarse-grained fixed-point tensor networks and holographic reflected entropy in 3D gravity

We use the framework of fixed-point BCFT tensor networks to present a microscopic CFT derivation of the correspondence between reflected entropy (RE) and entanglement wedge cross section (EW) in AdS 3 /CFT 2 , for both bipartite and multipartite settings. These fixed-point tensor networks, obtained by triangulating Euclidean CFT path integrals, allow us to explicitly construct the canonical purification via cutting-and-gluing CFT path integrals. Employing modular flow in the large-c limit, we demonstrate that these intrinsic CFT manipulations reproduce bulk geometric prescriptions, without assuming the AdS/CFT dictionary. The emergence of bulk geometry is traced to coarse-graining over heavy states in the large-c limit. Universal coarse-grained BCFT data for compact 2D CFTs, through the relation to Liouville theory with ZZ boundary conditions, yields hyperbolic geometry on the Cauchy slice. The corresponding averaged replica partition functions reproduce all candidate EWs, arising from different averaging patterns, with the dominant one providing the correct RE and EW. In this way, many heuristic tensor-network intuitions in toy models are made precise and established directly from intrinsic CFT data.

AdS-CFT correspondence↗
DOE OSTI2025

Convergence Analysis of the Alternating Anderson–Picard Method for Nonlinear Fixed-Point Problems

Anderson acceleration (AA) has been widely used to solve nonlinear fixed-point problems due to its rapid convergence. This work focuses on a variant of AA in which multiple Picard iterations are performed between each AA step, referred to as the Alternating Anderson–Picard (AAP) method. Furthermore, despite introducing more “slow” Picard iterations, this method has been shown to be efficient and even more robust in both linear and nonlinear cases. However, there is a lack of theoretical analysis for AAP in the nonlinear case. In this paper, we address this gap by establishing the equivalence between AAP and a multisecant-GMRES method that uses GMRES to solve a multisecant linear system at each iteration. From this perspective, we show that AAP “converges” to the Newton-GMRES method. Specifically, as the residual approaches zero, the multisecant matrix, the approximate Jacobian inverse, the search direction, and the optimization gain of AAP converge to their counterparts in the Newton-GMRES method. These connections provide insights for analyzing the asymptotic convergence properties of AAP. Consequently, we show that AAP is locally 𝑞-linear convergent and provide an upper bound for the convergence factor of AAP. To validate the theoretical results, numerical examples are provided.

Anderson acceleration↗
DOE OSTI2025

MLBS Halo scanning Lidar / Reviewed Data / Fixed-point vertical scans

This dataset contains high-frequency vertical velocity recorded by fixed-point vertical scans done by the University of Virginia Halo Streamline scanning lidar at the MLBS station. The quality control is performed according to the algorithm of Goring & Nikora (2002).

17 WIND ENERGY↗
DOE OSTI2024

Infrared fixed point in the massless twelve-flavor SU(3) gauge-fermion system

We present strong numerical evidence for the existence of an infrared fixed point in the renormalization group flow of the SU(3) gauge-fermion system with twelve massless fermions in the fundamental representation. Our numerical simulations using nHYP-smeared staggered fermions with Pauli-Villars improvement do not exhibit any first-order bulk phase transition in the investigated parameter region. We utilize an infinite volume renormalization scheme based on the gradient flow transformation to determine the renormalization group β function. The gradient flow β function exhibits a zero at g GF ⋆ 2 = 6.60 ( 62 ) , implying that the system is infrared conformal. We calculate the leading irrelevant critical exponent γ g ⋆ = 0.199 ( 32 ) . Our prediction for γ g ⋆ is consistent with available literature at the 1 − 2 σ level. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Precision Reconstruction of Rational Conformal Field Theory from Exact Fixed-Point Tensor Network

The novel concept of entanglement renormalization and its corresponding tensor network renormalization technique have been highly successful in developing a controlled real-space renormalization group (RG) scheme. Numerically approximate fixed-point (FP) tensors are widely used to extract the conformal data of the underlying conformal field theory (CFT) describing critical phenomena. In this paper, we present an explicit analytical construction of the FP tensor for 2D rational CFT. We define it as a correlation function between the “boundary-changing operators” (BCO) on triangles. Our construction fully captures all the real-space RG conditions. We also provide concrete examples, such as Ising, Yang-Lee, and tricritical Ising models, to compute the scaling dimensions explicitly based on the corresponding FP tensor. The BCO descendants turn out to be an optimal basis such that truncation in bond dimensions naturally produces comparable accuracies with the leading existing FP algorithms. Interestingly, our construction of FP tensors is closely related to a strange correlator, where the holographic picture naturally emerges. Our results also open a new door toward understanding CFT in higher dimensions. Published by the American Physical Society 2025

Cheng, Gong (ORCID:0009000891587404)↗
DOE OSTI2026

Exact and Fixed-Point Grover Search with Qudits

Grover's algorithm provides a quadratic speedup for searching unstructured databases and is traditionally implemented with qubits in Hilbert spaces whose dimensions are powers of two. With the advent of quantum platforms utilizing qudits---quantum systems with more than two levels---there is a need to generalize Grover search to these architectures, including heterogeneous systems with qudits of varying dimensions. Here, we present a unified framework for qudit-based Grover search, detailing the construction of oracles and diffusion operators with and without ancilla qubits and generalizing deterministic and fixed-point search variants that ensure exact or bounded success probabilities. We analyze phase-matching techniques and provide explicit circuit decompositions suitable for diverse hardware platforms. We also compare the corresponding trajectories on the Bloch sphere to provide an intuitive visualization of how the different phase choices amplify the target state. These results facilitate flexible, hardware-oriented protocols for implementing Grover search on qudit processors, potentially reducing circuit depth and enhancing success probabilities, thereby offering a practical toolkit for quantum computation and sensing applications leveraging multilevel quantum systems.

Roy, Tanay [Fermilab] (ORCID:000000019442862X)↗
DOE OSTI2026

Towards a Quintic Ginzburg-Landau Description of the (2,7) Minimal Model

We discuss dimensional continuation of the massless scalar field theory with the 𝑖⁢𝜙 5 interaction term. It preserves the so-called 𝒫⁢𝒯 symmetry, which acts by 𝜙 →−𝜙 accompanied by 𝑖 →−𝑖. Below its upper critical dimension 10/3, this theory has interacting infrared fixed points. We argue that the fixed point in 𝑑 = 2 describes the nonunitary minimal conformal model 𝑀⁡(2,7). We identify the operators 𝜙 and 𝜙 2 with the Virasoro primaries 𝜙 1,2 and 𝜙 1,3 , respectively, and 𝑖⁢𝜙 3 with a quasiprimary operator, which is a Virasoro descendant of 𝜙 1,3 . Our identifications appear to be consistent with the operator product expansions and with considerations based on integrability. Using constrained Padé extrapolations, we provide estimates of the critical exponents in 𝑑 = 3. We also comment on possible lattice descriptions of 𝑀⁡(2,7) and discuss RG flows to and from this conformal field theory (CFT). Finally, we conjecture that the minimal models 𝑀⁡(2,2⁢𝑛 +1) are described by the massless scalar field theories with the 𝑖⁢𝜙 2⁢𝑛−1 interaction terms.

Conformal field theory↗
DOE OSTI2025

Efficient Floating-Point Arithmetic on Fault-Tolerant Quantum Computers

We propose a novel floating-point encoding scheme that builds on prior work involving fixed-point encodings. We encode floating-point numbers using Two's Complement fixed-point mantissas and Two's Complement integral exponents. We used our proposed approach to develop quantum algorithms for fundamental arithmetic operations, such as bit-shifting, reciprocation, multiplication, and addition. We prototyped and investigated the performance of the floating-point encoding scheme on quantum computer simulations by performing reciprocation on randomly drawn inputs and by solving first-order ordinary differential equations, while varying the number of qubits in the encoding. We observed rapid convergence to the exact solutions as we increased the number of qubits and a significant reduction in the number of ancilla qubits required for reciprocation when compared with similar approaches.

Serrallés, José Cruz [Weill Cornell Med. Coll.]↗
DOE OSTI2026

Monitored Fluctuating Hydrodynamics

We introduce a hydrodynamic framework for describing monitored classical stochastic processes. We study the conditional ensembles for these monitored processes—i.e., we compute spacetime correlation functions conditioned on a fixed, typical measurement record. In the presence of global symmetries we show that these conditional ensembles can undergo measurement-induced “sharpening” phase transitions as a function of the monitoring rate; moreover, even weak monitoring can give rise to novel critical phases, derived entirely from a classical perspective. We give a simple hydrodynamic derivation of the known “charge-fuzzy phase” for weakly monitored diffusive many-body quantum systems. We show that although the unmonitored symmetric and asymmetric exclusion processes are in different universality classes of transport, the fluctuations in their conditional ensembles flow to the same fixed point with emergent relativistic invariance under monitoring. On the other hand, weakly monitored systems with non-Abelian symmetries enter a novel strongly coupled fixed point with nontrivial dynamical exponent, which we characterize. Our formalism naturally accounts for monitoring general observables, such as currents or density gradients, and allows for a direct calculation of information-theoretic diagnostics of sharpening transitions, including the Shannon entropy of the measurement record.

classical statistical mechanics↗
DOE OSTI2025

Landscape of 4d N = 1 SCFTs with a = c

We study a landscape of four-dimensional N = 1 superconformal field theories (SCFTs) with identical central charges. These theories are obtained by renormalization group flows triggered by supersymmetry-preserving superpotential deformations of the N = 1 gauging of the flavor symmetry of a collection of N = 2 D p ( G ) Argyres-Douglas SCFTs. In this work, we focus on the fixed points in the landscape of the S U ( 3 ) gauging of three copies of the D 2 ( S U ( 3 ) ) = H 2 theory together with an adjoint-valued chiral multiplet. We catalog the network of a = c fixed points, and, along the way, we find a variety of dualities and instances of supersymmetry enhancement. Published by the American Physical Society 2025

Kang, Monica Jinwoo (ORCID:0000000204542064)↗
DOE OSTI2024

Fixed lines in four fermion models in two dimensions

Motivated by conjectures about near-horizon dynamics in quantum gravity, we search for lines of perturbatively accessible fixed points emanating from models of N free fermions. Through two loops we find a new class of models, apart from the well-known Abelian Thirring models. Further study is needed to see whether these can lead to true conformal manifolds, or perhaps a new class of large- N fixed points. Published by the American Physical Society 2024

Astronomy & Astrophysics↗
DOE OSTI2025

Fully Homomorphic Encryption

This code implements a Fully Homomorphic Encryption (FHE) system, enabling secure computation on encrypted data without requiring decryption. It supports encryption, decryption, and homomorphic operations like matrix multiplication and addition. This code is adaptable for integrating FHE into linear-time invariant (LTI) systems, including digital control and filtering. With proper configuration from subject matter expertise, encrypted system parameters and signals can be manipulated to perform tasks like state updates, output calculations, and convolution in the encrypted domain. By preserving the structure of LTI systems while ensuring privacy, the framework facilitates secure applications in areas such as autonomous systems, signal processing, and industrial automation. The code initializes the encryption system using parameters provided in the env dictionary. These parameters include the ciphertext modulus, key dimension, plaintext fixed-point scaling factor, and noise bound. During initialization, a secret key is generated, which is essential for encrypting and decrypting data securely. The modular design allows users to tailor these parameters to specific use cases or security requirements. The code implements multiple cryptographic schemes. The learning with errors (LWE) encryption method encodes cleartext message to their plaintext fixed-point representation then encrypted into ciphertext space with additive noise. This noise ensures the security of the scheme, relying on the computational hardness of the LWE problem. The code also includes the Gentry-Sahai-Waters (GSW) scheme based off the LWE problem. Homomorphic matrix multiplication is performed between the LWE and GSW to encrypted data. This is achieved using a decomposition function on the LWE ciphertext during the multiplication operation. For higher-dimensional data, the code includes a method to encrypt entire matrices (GSWMat) using GSW encryption. These encrypted matrices can then be used for homomorphic matrix multiplications (MatMult). The decryption function uses the secret key to recover the original plaintext, removing the added noise and scaling that was originally applied during encryption.

Lois, Roberts [Idaho National Laboratory (INL), Id↗
DOE OSTI2025

Accuracy Guarantees and Quantum Advantage in Analog Open Quantum Simulation with and without Noise

Many-body open quantum systems, described by Lindbladian master equations, are a rich class of physical models that display complex equilibrium and out-of-equilibrium phenomena which remain to be understood. In this paper, we theoretically analyze noisy analog quantum simulation of geometrically local open quantum systems and provide evidence that this problem both is hard to simulate on classical computers and could be approximately solved on near-term quantum devices. First, given a noiseless quantum simulator, we show that the dynamics of local observables and the fixed-point expectation values of rapidly mixing local observables in geometrically local Lindbladians can be obtained to a precision of ϵ in time that is poly ( ϵ − 1 ) and uniform in system size. Furthermore, we establish that the quantum simulator would provide a superpolynomial advantage, in run-time scaling with respect to the target precision and either the evolution time (when simulating dynamics) or the Lindbladian’s decay rate (when simulating fixed points), over any classical algorithm for these problems, assuming BQP ≠ BPP . We then consider the presence of noise in the quantum simulator in the form of additional geometrically local Lindbladian terms. We show that the simulation tasks considered in this paper are stable to errors; i.e., they can be solved to a noise-limited, but system-size independent, precision. Finally, we establish that, assuming BQP ≠ BPP , there are stable geometrically local Lindbladian simulation problems such that, as the noise rate on the simulator is reduced, classical algorithms must take time superpolynomially longer in the inverse noise rate to attain the same precision as the analog quantum simulator. Published by the American Physical Society 2025

Kashyap, Vikram (ORCID:0000000208195207)↗