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At least 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Approximate Bacon-Shor code and holography

We explicitly construct a class of holographic quantum error correction codes with non-trivial centers in the code subalgebra. Specifically, we use the Bacon-Shor codes and perfect tensors to construct a gauge code (or a stabilizer code with gauge-fixing), which we call the holographic hybrid code. This code admits a local log-depth encoding/decoding circuit, and can be represented as a holographic tensor network which satisfies an analog of the Ryu-Takayanagi formula and reproduces features of the sub-region duality. We then construct approximate versions of the holographic hybrid codes by “skewing” the code subspace, where the size of skewing is analogous to the size of the gravitational constant in holography. These approximate hybrid codes are not necessarily stabilizer codes, but they can be expressed as the superposition of holographic tensor networks that are stabilizer codes. For such constructions, different logical states, representing different bulk matter content, can “back-react” on the emergent geometry, resembling a key feature of gravity. The locality of the bulk degrees of freedom becomes subspace-dependent and approximate. Such subspace-dependence is manifest from the point of view of the “entanglement wedge” and bulk operator reconstruction from the boundary. Exact complementary error correction breaks down for certain bipartition of the boundary degrees of freedom; however, a limited, state-dependent form is preserved for particular subspaces. We also construct an example where the connected two-point correlation functions can have a power-law decay. Coupled with known constraints from holography, a weakly back-reacting bulk also forces these skewed tensor network models to the “large N limit” where they are built by concatenating a large N number of copies.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Dynamical logical qubits in the Bacon-Shor code

The Bacon-Shor code is a quantum error correcting subsystem code composed of weight-2 check operators that admits a single logical qubit, and has distance 𝑑 on a 𝑑×𝑑 square lattice. We show that when viewed as a Floquet code, by choosing an appropriate measurement schedule of the check operators, it can additionally host several dynamical logical qubits. Specifically, we identify a period-4 measurement schedule of the check operators that preserves logical information between the instantaneous stabilizer groups. Such a schedule not only measures the usual stabilizers of the Bacon-Shor code, but also measures and promotes gauge operators of the parent subsystem code to additional temporary stabilizers that protect the dynamical logical qubits against errors. We show that the code distance of these Floquet-Bacon-Shor codes scales as Θ⁢(𝑑/√𝑘) on an 𝑛=𝑑×𝑑 lattice with 𝑘 dynamical logical qubits, along with the logical qubit of the parent subsystem code. Unlike the usual Bacon-Shor code, the Floquet-Bacon-Shor code family introduced here can therefore saturate the subsystem bound 𝑘⁢𝑑=𝑂⁡(𝑛). Moreover, several errors are shown to be self-corrected purely by the measurement schedule itself. This work provides insights into the design space for dynamical codes and expands the known approaches for constructing Floquet codes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Managing code transformations for better performance portability

Code optimization is an intricate task that is getting more complex as computing systems evolve. Managing the program optimization process, including the implementation and evaluation of code variants, is tedious, inefficient, and errors are likely to be introduced in the process. Moreover, because each platform typically requires a different sequence of transformations to fully harness its computing power, the optimization process complexity grows as new platforms are adopted. To address these issues, systems and frameworks have been proposed to automate the code optimization process. They, however, have not been widely adopted and are primarily used by experts with deep knowledge about underlying architecture and compiler intricacies. This article describes the requirements that we believe necessary for making automatic performance tuning more broadly used, especially in complex, long-lived high-performance computing applications. Besides discussing limitations of current systems and strategies to overcome these, we describe the design of a system that is able to semi-automatically generate efficient platform-specific code. In the proposed system, the code optimization is programmer-guided, separately from application code, on an external file in what we call optimization programming. The language to program the optimization process is able to represent complex collections of transformations and, as a result, generate efficient platform-specific code. A database manages different optimized versions of code regions, providing a pragmatic approach to performance portability, and the framework itself has separate components, allowing the optimized code to be used on systems without installing all of the modules required for the code generation. We present experiments on two different platforms to illustrate the generation of efficient platform-specific code that performs comparable to hand-optimized, vendor-provided code.

Computer Science↗
DOE OSTI2019

Energy Storage System Safety: ESS-Related Proposed Changes to the Group B 2018 ICC International Codes. Special Briefing Paper

The goal of the DOE OE ESS Safety Roadmap is to foster confidence in the safety and reliability of energy storage systems (ESSs). Three interrelated objectives support the realization of that goal: research, codes and standards, and communication/coordination. The objective focused on codes and standards is as follows: To apply research and development (R&D) to support efforts that are focused on ensuring that codes and standards are available to enable the safe implementation of ESSs in a comprehensive, non-discriminatory and science-based manner. The following activities support that objective and realization of the goal: a. Review and assess codes and standards that affect the design, installation, and operation of ESSs. b. Identify gaps in knowledge that require research and analysis that can serve as a basis for criteria in those codes and standards. c. Identify areas in codes and standards that potentially need revision or enhancement and can benefit from activities conducted under R&D. d. Develop input for new or revisions to existing codes and standards through individual stakeholders, facilitated task forces, or through laboratory staff supporting these efforts. The purpose of this special briefing paper is to support the above objective by providing information about current and upcoming efforts being conducted by U.S. standards and model code developing organizations, specifically code changes associated with the 2018 Group B International Codes (I-Codes) of the International Code Council (100)2 that are relevant to ESSs.

25 ENERGY STORAGE↗
NASA NTRS1975

Performance of some block codes on a Gaussian channel

A technique proposed by Chase (1972) is used to evaluate the performance of several fairly long binary block codes on a wideband additive Gaussian channel. Considerations leading to the use of Chase's technique are discussed. Chase's concepts are first applied to the most powerful practical class of binary codes, the BCH codes with Berlekamp's (1972) decoding algorithm. Chase's algorithm is then described along with proposed selection of candidate codes. Results are presented of applying Chase's algorithm to four binary codes: (23, 12) Golay code, (32, 16) second-order Reed-Muller code, (63, 36) 5-error correcting BCH code, and (95, 39) 9-error correcting shortened BCH code. It is concluded that there are many block codes of length not exceeding 100 with extremely attractive maximum likelihood decoding performance on a Gaussian channel. BCH codes decoded via Berlekamp's binary decoding algorithm and Chase's idea are close to being practical competitors to short-constraint length convolutional codes with Viterbi decoding.

Baumert, L. D.↗
NASA NTRS1984

New Short Constraint Length, Rate 1/N Convolutional Codes which Minimize Required E Sub B/n Sub o for Given Bit Error Rate

Instead of using the criterion of maximum free distance, (df) or the maximum (df) with minimizing a few first distance profiles, short constraint length rate 1/N convolution codes were searched using a criterion of minimizing required bit energy-to-noise density ratio, E(b)/N(o), for a given value of desired bit error rate (BER), for the goodness of a code. The considered channel was binary antipodal signaling over additive white Gaussian noise and no quantization at the channel output. For the BER calculations, the transfer function bounding technique was used. Partial searches were performed using some known facts and a very useful idea that "good codes generate good codes.'' That is, for a given constraint length K, good rate 1/(N + 1) codes can be found by extending the code generator matrices of good rate 1/N codes. The code search results are tabulated for 3 or = K or = 7 and 2 or = N or = 8. For many pairs of K and N, the new codes are shown to save 0.1 to 0.4 dB in the required E(b)/N(o) compared to previously reported codes. Additionally, the benefits of coding bandwidth expansion are confirmed with the new codes.

Lee, P. J.↗
NASA NTRS1985

A concatenated coding scheme for error control

A concatenated coding scheme for error control in data communications is analyzed. The inner code is used for both error correction and detection, however the outer code is used only for error detection. A retransmission is requested if the outer code detects the presence of errors after the inner code decoding. The probability of undetected error of the above error control scheme is derived and upper bounded. Two specific exmaples are analyzed. In the first example, the inner code is a distance-4 shortened Hamming code with generator polynomial (X+1)(X(6)+X+1) = X(7)+X(6)+X(2)+1 and the outer code is a distance-4 shortened Hamming code with generator polynomial (X+1)X(15+X(14)+X(13)+X(12)+X(4)+X(3)+X(2)+X+1) = X(16)+X(12)+X(5)+1 which is the X.25 standard for packet-switched data network. This example is proposed for error control on NASA telecommand links. In the second example, the inner code is the same as that in the first example but the outer code is a shortened Reed-Solomon code with symbols from GF(2(8)) and generator polynomial (X+1)(X+alpha) where alpha is a primitive element in GF(z(8)).

Lin, S.↗
NASA NTRS1987

Bandwidth efficient block codes for M-ary PSK modulation

A class of bandwidth efficient block codes for M-ary PSK modulation is presented. A soft-decision decoding for this class of codes is devised. Some specific short codes for Quad Phase Shift Key (QPSK), 8-PSK and 16-PSK modulations are constructed. These codes have good minimum squared Euclidean distances and provide 2 to 5.8 dB coding gains over uncoded QPSK modulation without (or with little) bandwidth expansion. The complete weight distributions of these specific codes are determined. Based on these weight distributions, their error probabilities are evaluated. Some of these codes have simple trellis structures and hence can be decoded by Viterbi decoding algorithm with relatively simple implementation. Moreover, the codes are very suitable for use as inner codes for various cascaded coding schemes with Reed-Solomon codes as outer codes.

Lin, Shu↗
NASA NTRS1989

The weight distribution and randomness of linear codes

Finding the weight distributions of block codes is a problem of theoretical and practical interest. Yet the weight distributions of most block codes are still unknown except for a few classes of block codes. Here, by using the inclusion and exclusion principle, an explicit formula is derived which enumerates the complete weight distribution of an (n,k,d) linear code using a partially known weight distribution. This expression is analogous to the Pless power-moment identities - a system of equations relating the weight distribution of a linear code to the weight distribution of its dual code. Also, an approximate formula for the weight distribution of most linear (n,k,d) codes is derived. It is shown that for a given linear (n,k,d) code over GF(q), the ratio of the number of codewords of weight u to the number of words of weight u approaches the constant Q = q(-)(n-k) as u becomes large. A relationship between the randomness of a linear block code and the minimum distance of its dual code is given, and it is shown that most linear block codes with rigid algebraic and combinatorial structure also display certain random properties which make them similar to random codes with no structure at all.

Cheung, K.-M.↗
NASA NTRS1990

Multi-level modulation codes and multi-stage decoding

Multi-level method is a powerful technique for constructing bandwidth efficient modulation codes. It allows the construction of modulation codes systematically with arbitrary large minimum squared Euclidean distance from component codes in conjunction with proper bits-to-signal mapping. If the component codes are chosen properly, the resultant modulation code not only has good minimum squared Euclidean distance but is also rich in structural properties such as: linear structure, phase invariant property, and trellis structure. A modulation code with linear structure has invariant distance distribution. Phase invariant property is useful in resolving carrier-phase ambiguity and ensuring rapid carrier-phase resynchronization after temporary loss of synchronization. It the component codes have trellis structure, the resultant multi-level modulation code also has trellis structure. Trellis structure allows decoding of a multi-level modulation code with the soft-decision Viterbi decoding algorithm. Furthermore, the multi-level structure allows decoding of a multi-level modulation code with the multi-stage decoding. This type of decoding reduces the decoding complexity. Multi-stage decoding is not optimum even though the decoding of each component is optimum. Based on the analysis and simulation results, the difference in error performance between the optimum decoding of the overall multi-level modulation code and the suboptimum multi-stage decoding of the code is very little, a fraction of dB loss.

Lin, Shu↗
NASA NTRS2002

CEM2k and LAQGSM Codes as Event-Generators for Space Radiation Shield and Cosmic Rays Propagation Applications

Space radiation shield applications and studies of cosmic ray propagation in the Galaxy require reliable cross sections to calculate spectra of secondary particles and yields of the isotopes produced in nuclear reactions induced both by particles and nuclei at energies from threshold to hundreds of GeV per nucleon. Since the data often exist in a very limited energy range or sometimes not at all, the only way to obtain an estimate of the production cross sections is to use theoretical models and codes. Recently, we have developed improved versions of the Cascade-Exciton Model (CEM) of nuclear reactions: the codes CEM97 and CEM2k for description of particle-nucleus reactions at energies up to about 5 GeV. In addition, we have developed a LANL version of the Quark-Gluon String Model (LAQGSM) to describe reactions induced both by particles and nuclei at energies up to hundreds of GeVhucleon. We have tested and benchmarked the CEM and LAQGSM codes against a large variety of experimental data and have compared their results with predictions by other currently available models and codes. Our benchmarks show that CEM and LAQGSM codes have predictive powers no worse than other currently used codes and describe many reactions better than other codes; therefore both our codes can be used as reliable event-generators for space radiation shield and cosmic ray propagation applications. The CEM2k code is being incorporated into the transport code MCNPX (and several other transport codes), and we plan to incorporate LAQGSM into MCNPX in the near future. Here, we present the current status of the CEM2k and LAQGSM codes, and show results and applications to studies of cosmic ray propagation in the Galaxy.

Mashnik, S. G.↗
NASA NTRS2005

Convergence Acceleration and Documentation of CFD Codes for Turbomachinery Applications

The development and analysis of turbomachinery components for industrial and aerospace applications has been greatly enhanced in recent years through the advent of computational fluid dynamics (CFD) codes and techniques. Although the use of this technology has greatly reduced the time required to perform analysis and design, there still remains much room for improvement in the process. In particular, there is a steep learning curve associated with most turbomachinery CFD codes, and the computation times need to be reduced in order to facilitate their integration into standard work processes. Two turbomachinery codes have recently been developed by Dr. Daniel Dorney (MSFC) and Dr. Douglas Sondak (Boston University). These codes are entitled Aardvark (for 2-D and quasi 3-D simulations) and Phantom (for 3-D simulations). The codes utilize the General Equation Set (GES), structured grid methodology, and overset O- and H-grids. The codes have been used with success by Drs. Dorney and Sondak, as well as others within the turbomachinery community, to analyze engine components and other geometries. One of the primary objectives of this study was to establish a set of parametric input values which will enhance convergence rates for steady state simulations, as well as reduce the runtime required for unsteady cases. The goal is to reduce the turnaround time for CFD simulations, thus permitting more design parametrics to be run within a given time period. In addition, other code enhancements to reduce runtimes were investigated and implemented. The other primary goal of the study was to develop enhanced users manuals for Aardvark and Phantom. These manuals are intended to answer most questions for new users, as well as provide valuable detailed information for the experienced user. The existence of detailed user s manuals will enable new users to become proficient with the codes, as well as reducing the dependency of new users on the code authors. In order to achieve the objectives listed, the following tasks were accomplished: 1) Parametric Study Of Preconditioning Parameters And Other Code Inputs; 2) Code Modifications To Reduce Runtimes; 3) Investigation Of Compiler Options To Reduce Code Runtime; and 4) Development/Enhancement of Users Manuals for Aardvark and Phantom

Marquart, Jed E.↗
DOE OSTI2023

Spin-squeezed Gottesman-Kitaev-Preskill codes for quantum error correction in atomic ensembles

Gottesman-Kitaev-Preskill (GKP) codes encode a qubit in displaced phase-space combs of a continuous-variable (CV) quantum system and are useful for correcting a variety of high-weight photonic errors. Here we propose atomic ensemble analogs of the single-mode CV GKP code by using the quantum central limit theorem to pull back the phase-space structure of a CV system to the compact phase space of a quantum spin system. We study the optimal recovery performance of these codes under error channels described by stochastic relaxation and isotropic ballistic dephasing processes using the diversity combining approach for calculating channel fidelity. Additionally, we find that the spin GKP codes outperform other spin system codes such as cat codes or binomial codes. Our spin GKP codes based on the two-axis countertwisting interaction and superpositions of SU(2) coherent states are direct spin analogs of the finite-energy CV GKP codes, whereas our codes based on one-axis twisting do not yet have well-studied CV analogs. A state preparation scheme for the spin GKP codes is proposed which uses the linear-combination-of-unitaries method, applicable to both the CV and spin GKP settings. Finally, we discuss a fault-tolerant approximate gate set for quantum computing with spin-GKP-encoded qubits, obtained by translating gates from the CV GKP setting using the quantum central limit theorem.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Single-shot quantum error correction in intertwined toric codes

We construct a subsystem code in three dimensions that exhibits single-shot error correction in a user-friendly and transparent way. As this code is a subsystem version of coupled toric codes, we call it the intertwined toric code (ITC). Although previous codes share the property of single-shot error correction, the ITC is distinguished by its physically motivated origin, geometrically straightforward logical operators and errors, and a simple phase diagram. The code arises from three-dimensional (3D) stabilizer toric codes in a way that emphasizes the physical origin of the single-shot property. In particular, starting with two copies of the 3D toric code, we add check operators that provide for the confinement of pointlike excitations without condensing the loop excitations. Geometrically, the bare and dressed logical operators in the ITC derive from logical operators in the underlying toric codes, creating a clear relationship between errors and measurement outcomes. The syndromes of the ITC resemble the syndromes of the single-shot code by Kubica and Vasmer, allowing us to use their decoding schemes. We also extract the phase diagram corresponding to ITC and show that it contains the phases found in the Kubica-Vasmer code. Lastly, we suggest various connections to Walker-Wang models and measurement-based quantum computation.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Error-correcting codes for fermionic quantum simulation

Utilizing the framework of \mathbb{Z}_2 ℤ 2 lattice gauge theories in the context of Pauli stabilizer codes, we present methodologies for simulating fermions via qubit systems on a two-dimensional square lattice. We investigate the symplectic automorphisms of the Pauli module over the Laurent polynomial ring. This enables us to systematically increase the code distances of stabilizer codes while fixing the rate between encoded logical fermions and physical qubits. We identify a family of stabilizer codes suitable for fermion simulation, achieving code distances of d=2,3,4,5,6,7, allowing correction of any \lfloor \frac{d-1}{2} \rfloor ⌊ d − 1 2 ⌋ -qubit error. In contrast to the traditional code concatenation approach, our method can increase the code distances without decreasing the (fermionic) code rate. In particular, we explicitly show all stabilizers and logical operators for codes with code distances of d=3,4,5. We provide syndromes for all Pauli errors and invent a syndrome-matching algorithm to compute code distances numerically.

Physics↗
DOE OSTI2020

Status Report on ASME Code Development for Nonmetallic Core Components in 2020

The purpose of this report is to provide a status update on the progress and ongoing activities of the current ASME Boiler Pressure Vessel (BPV) Code Section III, Division 5, on nonmetallic core components and assemblies which includes the design rules for graphite and ceramic composite materials. Section III is concerned with the design and construction of nuclear reactor components and Division 5 focuses on high temperature reactors (HTR). The ASME Section III Committee’s function for nuclear items other than pressure-retaining components, is to establish rules of safety related to structural integrity. The term “construction” refers to the all-inclusive effort comprising of materials, design, fabrication, examination, inspection, testing, certification, and pressure relief. The Department of Energy (DOE) supports industry codes and standards development through focused research providing the technical basis for new or modified codes and standards and the participation of subject matter experts in codes and standards committees. The activities for the nonmetallic core components and assemblies committees are the pursuit of two working groups that meet quarterly during ASME BPV Code Week meetings. The two working groups are General Requirements for Graphite and Ceramic Composite Core Components and Assemblies (GR GCCCCA) and Nonmetallic Design and Materials (NDM). The rules on general requirements for nonmetallic core components are discussed in the articles of Subsection HA subpart B. Ceramic composites were recently incorporated within the rules, and the GR GCCCCA working group is now in the process of aligning the requirements with the subsections and articles of ASME BPV Code Section III NCA, the general requirements for Division 1 and 2 of the code. The NDM working group is concerned with the design rules for graphite and composite materials for core components and assemblies discussed in Subsection HH (Class SN Nonmetallic Core Components) subpart A and subpart B which reference graphite and composite materials respectively. The bulk of the progress and work is done within this working group. A significant undertaking, with discussion that started in 2015, is to gain endorsement of ASME Section III, Division 5, by the U.S. Nuclear Regulatory Commission (NRC). In June 2018, ASME formally recommended endorsement to the NRC. The NRC has since initiated the endorsement review process, which is to be concluded early in 2021. ASME task groups on metallic structures and components, as well as non-metallic core support structures, have been formed to define potential pathways and schedules for NRC endorsement of Division 5. NRC determined to perform a review on the 2017 edition of Section III Division 5 as a baseline. As a result, the use of graphite as nonmetallic core components formed part of the review, but it excluded composite materials (which were first introduced in the 2019 edition). This report documents progress in FY 2020 directed toward ASME’s efforts to develop design codes for graphite and composites. Progress includes a major code review by NRC, the first code enquiry, and its solution, an overhaul of the treatment of Weibull Statistics, and the addition of Nonmandatory Appendices to the composites code relating to carbon-carbon composite materials.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
NASA NTRS1979

A connection between block and convolutional codes

Convolutional codes of any rate and any constraint length give rise to a sequence of quasi-cyclic codes. Conversely, any quasi-cyclic code may be convolutionally encoded. Among the quasi-cyclic codes are the quadratic residue codes, Reed-Solomon codes and optimal BCH codes. The constraint length K for the convolutional encoding of many of these codes (Golay, (48, 24) QR, etc.) turns out to be surprisingly small. Thus using the soft decoding techniques for convolutional decoding, a new maximum likelihood decoding algorithm for many block codes is established. Conversely an optimal quasi-cyclic code will yield a convolutional encoding with optimal local properties and therefore with good infinite convolutional coding properties.

Solomon, G.↗
NASA NTRS1987

Constructions for finite-state codes

A class of codes called finite-state (FS) codes is defined and investigated. These codes, which generalize both block and convolutional codes, are defined by their encoders, which are finite-state machines with parallel inputs and outputs. A family of upper bounds on the free distance of a given FS code is derived from known upper bounds on the minimum distance of block codes. A general construction for FS codes is then given, based on the idea of partitioning a given linear block into cosets of one of its subcodes, and it is shown that in many cases the FS codes constructed in this way have a d sub free which is as large as possible. These codes are found without the need for lengthy computer searches, and have potential applications for future deep-space coding systems. The issue of catastropic error propagation (CEP) for FS codes is also investigated.

Pollara, F.↗