Search NASA⌕ Search

SEARCH · Search NASA

Results for “Error correction”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 379 records · Page 21
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Low-Density Parity-Check Codes as Stable Phases of Quantum Matter

Phases of matter with robust ground-state degeneracy, such as the quantum toric code, are known to be capable of robust quantum information storage. Here, we address the converse question: given a quantum error-correcting code, when does it define a stable gapped quantum phase of matter, whose ground-state degeneracy is robust against perturbations in the thermodynamic limit? We prove that a low-density parity-check (LDPC) code defines such a phase, robust against all few-body perturbations, if its code distance grows at least logarithmically in the number of degrees of freedom, and it exhibits “check soundness.” Many constant-rate quantum LDPC expander codes have such properties, and define stable phases of matter with a constant zero-temperature entropy density, violating the third law of thermodynamics. Our results also show that quantum toric-code phases are robust to spatially nonlocal few-body perturbations. Similarly, phases of matter defined by classical codes are stable against symmetric perturbations. In the classical setting, we present improved locality bounds on the quasiadiabatic evolution operator between two nearby states in the same code phase.

quantum error correction↗
DOE OSTI2026

qSIEVE: Efficient qLDPC Memory via Systolic Movement in Atom Arrays

As quantum machines have scaled up in their number of qubits, significant research has turned towards increasing their fidelity with quantum error correction codes. Although promising results have been shown with the surface code, which only requires near-neighbor connections between qubits, the high qubit overhead of such local codes promises to be problematic. Consequently, recent work has explored non-local quantum LDPC (qLDPC) codes, which have good asymptotic encoding rates. Despite theoretical progress, hardware implementations of these codes have been a longstanding challenge. At the experimental level, demonstrations of movement based communication on atom arrays suggest this is a powerful new primitive to achieve non-local connectivity. Leveraging this, we present a protocol for implementing non-local qLDPC codes in hardware. Our protocol, qSIEVE, is a co-design of such codes with movement in atom arrays. qSIEVE defines a restricted family of qLDPC codes that can be implemented efficiently with systolic movement. We then quantify the utility of qSIEVE in the context of a complete fault tolerant architecture. We compare the cost of implementing benchmark programs in a standard, surface code only architecture and a mixed architecture where data is stored in qLDPC memory with qSIEVE and loaded to surface codes for computation.

Quantum error correction↗
NASA NTRS1998

An emerging network storage management standard: Media error monitoring and reporting information (MEMRI) - to determine optical tape data integrity

Sophisticated network storage management applications are rapidly evolving to satisfy a market demand for highly reliable data storage systems with large data storage capacities and performance requirements. To preserve a high degree of data integrity, these applications must rely on intelligent data storage devices that can provide reliable indicators of data degradation. Error correction activity generally occurs within storage devices without notification to the host. Early indicators of degradation and media error monitoring 333 and reporting (MEMR) techniques implemented in data storage devices allow network storage management applications to notify system administrators of these events and to take appropriate corrective actions before catastrophic errors occur. Although MEMR techniques have been implemented in data storage devices for many years, until 1996 no MEMR standards existed. In 1996 the American National Standards Institute (ANSI) approved the only known (world-wide) industry standard specifying MEMR techniques to verify stored data on optical disks. This industry standard was developed under the auspices of the Association for Information and Image Management (AIIM). A recently formed AIIM Optical Tape Subcommittee initiated the development of another data integrity standard specifying a set of media error monitoring tools and media error monitoring information (MEMRI) to verify stored data on optical tape media. This paper discusses the need for intelligent storage devices that can provide data integrity metadata, the content of the existing data integrity standard for optical disks, and the content of the MEMRI standard being developed by the AIIM Optical Tape Subcommittee.

Podio, Fernando↗
NASA NTRS1976

Stepping optical path difference in an interferometer

Stepping method permits higher amplitude modulation of secondary mirror of Fourier interferometer. Amplitude of mirror motion is limited only by available voltage drive on error-correcting actuator. Closed-loop controller provides servo error voltage linearly proportional to offset from proper null position. Bidirectional counter serves to count number of reference laser fringes offset from null position.

Schindler, R. A.↗
NASA NTRS1981

Methodology evaluation: Effects of independent verification and intergration on one class of application

The effects of an independent verification and integration (V and I) methodology on one class of application are described. Resource profiles are discussed. The development environment is reviewed. Seven measures are presented to test the hypothesis that V and I improve the development and product. The V and I methodology provided: (1) a decrease in requirements ambiguities and misinterpretation; (2) no decrease in design errors; (3) no decrease in the cost of correcting errors; (4) a decrease in the cost of system and acceptance testing; (5) an increase in early discovery of errors; (6) no improvement in the quality of software put into operation; and (7) a decrease in productivity and an increase in cost.

Page, J.↗
DOE OSTI2021

Leveraging Randomized Compiling for the QITE Algorithm

The success of the current generation of Noisy Intermediate-Scale Quantum (NISQ) hardware shows that quantum hardware may be able to tackle complex problems even without error correction. One outstanding issue is that of coherent errors arising from the increased complexity of these devices. These errors can accumulate through a circuit, making their impact on algorithms hard to predict and mitigate. Iterative algorithms like Quantum Imaginary Time Evolution are susceptible to these errors. This article presents the combination of both noise tailoring using Randomized Compiling and error mitigation with a purification. We also show that Cycle Benchmarking gives an estimate of the reliability of the purification. We apply this method to the Quantum Imaginary Time Evolution of a Transverse Field Ising Model and report an energy estimation and a ground state infidelity both below 1\%. Our methodology is general and can be used for other algorithms and platforms. We show how combining noise tailoring and error mitigation will push forward the performance of NISQ devices.

Ville, Jean-Loup↗
DOE OSTI2023

Dual-rail encoding with superconducting cavities

The design of quantum hardware that reduces and mitigates errors is essential for practical quantum error correction (QEC) and useful quantum computation. To this end, we introduce the circuit-Quantum Electrodynamics (QED) dual-rail qubit in which our physical qubit is encoded in the single-photon subspace, { | 01 〉 , | 10 〉 } , of two superconducting microwave cavities. The dominant photon loss errors can be detected and converted into erasure errors, which are in general much easier to correct. In contrast to linear optics, a circuit-QED implementation of the dual-rail code offers unique capabilities. Using just one additional transmon ancilla per dual-rail qubit, we describe how to perform a gate-based set of universal operations that includes state preparation, logical readout, and parametrizable single and two-qubit gates. Moreover, first-order hardware errors in the cavities and the transmon can be detected and converted to erasure errors in all operations, leaving background Pauli errors that are orders of magnitude smaller. Hence, the dual-rail cavity qubit exhibits a favorable hierarchy of error rates and is expected to perform well below the relevant QEC thresholds with today’s coherence times.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Benchmarking quantum logic operations relative to thresholds for fault tolerance

Contemporary methods for benchmarking noisy quantum processors typically measure average error rates or process infidelities. However, thresholds for fault-tolerant quantum error correction are given in terms of worst-case error rates—defined via the diamond norm—which can differ from average error rates by orders of magnitude. One method for resolving this discrepancy is to randomize the physical implementation of quantum gates, using techniques like randomized compiling (RC). In this work, we use gate set tomography to perform precision characterization of a set of two-qubit logic gates to study RC on a superconducting quantum processor. We find that, under RC, gate errors are accurately described by a stochastic Pauli noise model without coherent errors, and that spatially correlated coherent errors and non-Markovian errors are strongly suppressed. We further show that the average and worst-case error rates are equal for randomly compiled gates, and measure a maximum worst-case error of 0.0197(3) for our gate set. Our results show that randomized benchmarks are a viable route to both verifying that a quantum processor’s error rates are below a fault-tolerance threshold, and to bounding the failure rates of near-term algorithms, if—and only if—gates are implemented via randomization methods which tailor noise.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Extending the computational reach of a superconducting qutrit processor

Quantum computing with qudits is an emerging approach that exploits a larger, more connected computational space, providing advantages for many applications, including quantum simulation and quantum error correction. Nonetheless, qudits are typically afflicted by more complex errors and suffer greater noise sensitivity which renders their scaling difficult. In this work, we introduce techniques to tailor arbitrary qudit Markovian noise to stochastic Weyl–Heisenberg channels and mitigate noise that commutes with our Clifford and universal two-qudit gate in generic qudit circuits. We experimentally demonstrate these methods on a superconducting transmon qutrit processor, and benchmark their effectiveness for multipartite qutrit entanglement and random circuit sampling, obtaining up to 3× improvement in our results. To the best of our knowledge, this constitutes the first-ever error mitigation experiment performed on qutrits. Our work shows that despite the intrinsic complexity of manipulating higher-dimensional quantum systems, noise tailoring and error mitigation can significantly extend the computational reach of today’s qudit processors.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1980

Efficient program for decoding the /255, 223/ Reed-Solomon code over GF/2 to the 8th/ with both errors and erasures, using transform decoding

The paper deals with a method developed for decoding a (255, 223) Reed-Solomon code over GF(2 to the 8th) with both errors and erasures. The matrix of decoding times for correcting errors and erasures of the code using a simplified decoder is presented. It is shown that the algorithm proposed is faster by a factor of from three to seven.

Miller, R. L.↗
NASA NTRS1986

A cascaded coding scheme for error control and its performance analysis

A coding scheme is investigated for error control in data communication systems. The scheme is obtained by cascading two error correcting codes, called the inner and outer codes. The error performance of the scheme is analyzed for a binary symmetric channel with bit error rate epsilon <1/2. It is shown that if the inner and outer codes are chosen properly, extremely high reliability can be attained even for a high channel bit error rate. Various specific example schemes with inner codes ranging form high rates to very low rates and Reed-Solomon codes as inner codes are considered, and their error probabilities are evaluated. They all provide extremely high reliability even for very high bit error rates. Several example schemes are being considered by NASA for satellite and spacecraft down link error control.

Lin, Shu↗
NASA NTRS1988

A cascaded coding scheme for error control and its performance analysis

A coding scheme for error control in data communication systems is investigated. The scheme is obtained by cascading two error-correcting codes, called the inner and outer codes. Its error performance is analyzed for a binary symmetric channel with bit-error rate epsilon less than 1/2. It is shown that, if the inner and outer codes are chosen properly, high reliability can be attained even for a high-channel bit-error rate. Specific examples with inner codes ranging from high rates and Reed-Solomon codes as outer codes are considered, and their error probabilities evaluated. They all provide high reliability even for high bit-error rates, say 0.1-0.01. Several example schemes are being considered for satellite and spacecraft downlink error control.

Kasami, Tadao↗
NASA NTRS1996

Innovative Networking Concepts Tested on the Advanced Communications Technology Satellite

This paper describes a program of experiments conducted over the advanced communications technology satellite (ACTS) and the associated TI-VSAT (very small aperture terminal). The experiments were motivated by the commercial potential of low-cost receive only satellite terminals that can operate in a hybrid network environment, and by the desire to demonstrate frame relay technology over satellite networks. The first experiment tested highly adaptive methods of satellite bandwidth allocation in an integrated voice-data service environment. The second involved comparison of forward error correction (FEC) and automatic repeat request (ARQ) methods of error control for satellite communication with emphasis on the advantage that a hybrid architecture provides, especially in the case of multicasts. Finally, the third experiment demonstrated hybrid access to databases and compared the performance of internetworking protocols for interconnecting local area networks (LANs) via satellite. A custom unit termed frame relay access switch (FRACS) was developed by COMSAT Laboratories for these experiments; the preparation and conduct of these experiments involved a total of 20 people from the University of Maryland, the University of Colorado and COMSAT Laboratories, from late 1992 until 1995.

Friedman, Daniel↗
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↗
NASA NTRS1976

The statistical significance of error probability as determined from decoding simulations for long codes

The very low error probability obtained with long error-correcting codes results in a very small number of observed errors in simulation studies of practical size and renders the usual confidence interval techniques inapplicable to the observed error probability. A natural extension of the notion of a 'confidence interval' is made and applied to such determinations of error probability by simulation. An example is included to show the surprisingly great significance of as few as two decoding errors in a very large number of decoding trials.

Massey, J. L.↗
NASA NTRS1986

A cascaded coding scheme for error control and its performance analysis

A coding scheme for error control in data communication systems is investigated. The scheme is obtained by cascading two error correcting codes, called the inner and the outer codes. The error performance of the scheme is analyzed for a binary symmetric channel with bit error rate epsilon < 1/2. It is shown that, if the inner and outer codes are chosen properly, extremely high reliability can be attained even for a high channel bit error rate. Various specific example schemes with inner codes ranging from high rates to very low rates and Reed-Solomon codes are considered, and their probabilities are evaluated. They all provide extremely high reliability even for very high bit error rates, say 0.1 to 0.01. Several example schemes are being considered by NASA for satellite and spacecraft down link error control.

Lin, S.↗
NASA NTRS1987

Cyclic unequal error protection codes constructed from cyclic codes of composite length

The distance structure of cyclic codes of composite length was investigated. A lower bound on the minimum distance for this class of codes is derived. In many cases, the lower bound gives the true minimum distance of a code. Then the distance structure of the direct sum of two cyclic codes of composite length were investigated. It was shown that, under certain conditions, the direct-sum code provides two levels of error correcting capability, and hence is a two-level unequal error protection (UEP) code. Finally, a class of two-level UEP cyclic direct-sum codes and a decoding algorithm for a subclass of these codes are presented.

Lin, Shu↗