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DOE OSTI2026

Resilience of the surface code to error bursts

Quantum error correction works effectively only if the error rate of gate operations is sufficiently low. However, some rare physical mechanisms can cause a temporary increase in the error rate that affects many qubits; examples include ionizing radiation in superconducting hardware and large deviations in the global control of atomic systems. We refer to such rare transient spikes in the gate error rate as error bursts. In this work, we investigate the resilience of the rotated surface code to generic error bursts. We assume that, after appropriate mitigation strategies, the spike in the error rate lasts for only a single syndrome-extraction cycle; we also assume that the enhanced error rate is uniform across the code block. Under these assumptions, and for a circuit-level depolarizing noise model, we perform Monte Carlo simulations to determine the regime in burst error rate and background error rate for which the memory time becomes arbitrarily long as the code block size grows. Our results indicate that suitable hardware mitigation methods combined with standard decoding methods may suffice to protect against transient error bursts in the rotated surface code.

Quantum error correction↗

NASA NTRS1978

A decoding procedure for the Reed-Solomon codes

A decoding procedure is described for the (n,k) t-error-correcting Reed-Solomon (RS) code, and an implementation of the (31,15) RS code for the I4-TENEX central system. This code can be used for error correction in large archival memory systems. The principal features of the decoder are a Galois field arithmetic unit implemented by microprogramming a microprocessor, and syndrome calculation by using the g(x) encoding shift register. Complete decoding of the (31,15) code is expected to take less than 500 microsecs. The syndrome calculation is performed by hardware using the encoding shift register and a modified Chien search. The error location polynomial is computed by using Lin's table, which is an interpretation of Berlekamp's iterative algorithm. The error location numbers are calculated by using the Chien search. Finally, the error values are computed by using Forney's method.

Lim, R. S.↗

NASA NTRS1990

Performance of concatenated Reed-Solomon trellis-coded modulation over Rician fading channels

A concatenated coding scheme for providing very reliable data over mobile-satellite channels at power levels similar to those used for vocoded speech is described. The outer code is a shorter Reed-Solomon code which provides error detection as well as error correction capabilities. The inner code is a 1-D 8-state trellis code applied independently to both the inphase and quadrature channels. To achieve the full error correction potential of this inner code, the code symbols are multiplexed with a pilot sequence which is used to provide dynamic channel estimation and coherent detection. The implementation structure of this scheme is discussed and its performance is estimated.

Moher, Michael L.↗

NASA NTRS2005

Optimizing Parameters for Deep-Space Optical Communication

A paper discusses the optimization of the parameters of a high-rate, deep-space optical communication link that utilizes pulse-position modulation (PPM) and an error-correcting code (ECC). The parameters in question include the PPM order (number of pulse time slots in one symbol period), the ECC rate, and the uncoded symbol error rate. In simple terms, the optimization problem is to choose the combination of these parameters that maximizes the throughput data rate at a given bit-error-rate (BER), subject to several constraints, including limits on the average and peak power and possibly a limit on the uncoded symbol error rate. This is a complex, multidimensional optimization problem, the solution of which involves computation of channel capacities for various combinations of the parameters. The paper presents extensive theoretical analyses and numerical predictions that elucidate the many facets of the optimization problem. It shows how a nearly optimum solution can be obtained by choosing the optimum PPM order for the desired number of bits per slot and concatenating the PPM mapping with an error-correction code so that the decoded bits satisfy some BER threshold.

Moison, Bruce↗

NASA NTRS2015

The Use of Field Programmable Gate Arrays (FPGA) in Small Satellite Communication Systems

This paper will describe the use of digital Field Programmable Gate Arrays (FPGA) to contribute to advancing the state-of-the-art in software defined radio (SDR) transponder design for the emerging SmallSat and CubeSat industry and to provide advances for NASA as described in the TAO5 Communication and Navigation Roadmap (Ref 4). The use of software defined radios (SDR) has been around for a long time. A typical implementation of the SDR is to use a processor and write software to implement all the functions of filtering, carrier recovery, error correction, framing etc. Even with modern high speed and low power digital signal processors, high speed memories, and efficient coding, the compute intensive nature of digital filters, error correcting and other algorithms is too much for modern processors to get efficient use of the available bandwidth to the ground. By using FPGAs, these compute intensive tasks can be done in parallel, pipelined fashion and more efficiently use every clock cycle to significantly increase throughput while maintaining low power. These methods will implement digital radios with significant data rates in the X and Ka bands. Using these state-of-the-art technologies, unprecedented uplink and downlink capabilities can be achieved in a 1/2 U sized telemetry system. Additionally, modern FPGAs have embedded processing systems, such as ARM cores, integrated inside the FPGA allowing mundane tasks such as parameter commanding to occur easily and flexibly. Potential partners include other NASA centers, industry and the DOD. These assets are associated with small satellite demonstration flights, LEO and deep space applications. MSFC currently has an SDR transponder test-bed using Hardware-in-the-Loop techniques to evaluate and improve SDR technologies.

Varnavas, Kosta↗

NASA NTRS2011

Coded Modulation in C and MATLAB

This software, written separately in C and MATLAB as stand-alone packages with equivalent functionality, implements encoders and decoders for a set of nine error-correcting codes and modulators and demodulators for five modulation types. The software can be used as a single program to simulate the performance of such coded modulation. The error-correcting codes implemented are the nine accumulate repeat-4 jagged accumulate (AR4JA) low-density parity-check (LDPC) codes, which have been approved for international standardization by the Consultative Committee for Space Data Systems, and which are scheduled to fly on a series of NASA missions in the Constellation Program. The software implements the encoder and decoder functions, and contains compressed versions of generator and parity-check matrices used in these operations.

Hamkins, Jon↗

DOE OSTI2024

Approximate Quantum Codes From Long Wormholes

We discuss families of approximate quantum error correcting codes which arise as the nearly-degenerate ground states of certain quantum many-body Hamiltonians composed of non-commuting terms. For exact codes, the conditions for error correction can be formulated in terms of the vanishing of a two-sided mutual information in a low-temperature thermofield double state. We consider a notion of distance for approximate codes obtained by demanding that this mutual information instead be small, and we evaluate this mutual information for the SYK model and for a family of low-rank SYK models. After an extrapolation to nearly zero temperature, we find that both kinds of models produce fermionic codes with constant rate as the number, N , of fermions goes to infinity. For SYK, the distance scales as N 1 / 2 , and for low-rank SYK, the distance can be arbitrarily close to linear scaling, e.g. N .99 , while maintaining a constant rate. We also consider an analog of the no low-energy trivial states property which we dub the no low-energy adiabatically accessible states property and show that these models do have low-energy states that can be prepared adiabatically in a time that does not scale with system size N . We discuss a holographic model of these codes in which the large code distance is a consequence of the emergence of a long wormhole geometry in a simple model of quantum gravity.

Physics↗

NASA NTRS2003

VLSI design of turbo decoder for integrated communication system on a chip applications

A high-throughput low-power turbo decoder core has been developed for integrated communication system applications such as satellite communications, wireless LAN, digital TV, cable modem, Digital Video Broadcast (DVB), and xDSL systems. The turbo decoder is based on convolutional constituent codes, which outperform all other Forward Error Correction techniques. This turbo decoder core is parameterizable and can be modified easily to fit any size for advanced communication system-on-chip products. The turbo decoder core provides Forward Error Correction of up to 15 Mbits/sec on a 0.13-micron CMOS FPGA prototyping chip at a power of 0.1 watts.

turbo decoder↗

DOE OSTI2021

VirION2: a short- and long-read sequencing and informatics workflow to study the genomic diversity of viruses in nature

Microbes play fundamental roles in shaping natural ecosystem properties and functions, but do so under constraints imposed by their viral predators. However, studying viruses in nature can be challenging due to low biomass and the lack of universal gene markers. Though metagenomic short-read sequencing has greatly improved our virus ecology toolkit—and revealed many critical ecosystem roles for viruses—microdiverse populations and fine-scale genomic traits are missed. Some of these microdiverse populations are abundant and the missed regions may be of interest for identifying selection pressures that underpin evolutionary constraints associated with hosts and environments. Though long-read sequencing promises complete virus genomes on single reads, it currently suffers from high DNA requirements and sequencing errors that limit accurate gene prediction. Here we introduce VirION2, an integrated short- and long-read metagenomic wet-lab and informatics pipeline that updates our previous method (VirION) to further enhance the utility of long-read viral metagenomics. Using a viral mock community, we first optimized laboratory protocols (polymerase choice, DNA shearing size, PCR cycling) to enable 76% longer reads (now median length of 6,965 bp) from 100-fold less input DNA (now 1 nanogram). Using a virome from a natural seawater sample, we compared viromes generated with VirION2 against other library preparation options (unamplified, original VirION, and short-read), and optimized downstream informatics for improved long-read error correction and assembly. VirION2 assemblies combined with short-read based data (‘enhanced’ viromes), provided significant improvements over VirION libraries in the recovery of longer and more complete viral genomes, and our optimized error-correction strategy using long- and short-read data achieved 99.97% accuracy. In the seawater virome, VirION2 assemblies captured 5,161 viral populations (including all of the virus populations observed in the other assemblies), 30% of which were uniquely assembled through inclusion of long-reads, and 22% of the top 10% most abundant virus populations derived from assembly of long-reads. Viral populations unique to VirION2 assemblies had significantly higher microdiversity means, which may explain why short-read virome approaches failed to capture them. These findings suggest the VirION2 sample prep and workflow can help researchers better investigate the virosphere, even from challenging low-biomass samples. Our new protocols are available to the research community on protocols.io as a ‘living document’ to facilitate dissemination of updates to keep pace with the rapid evolution of long-read sequencing technology.

Long-reads↗

NASA NTRS1992

Bandwidth efficient CCSDS coding standard proposals

The basic concatenated coding system for the space telemetry channel consists of a Reed-Solomon (RS) outer code, a symbol interleaver/deinterleaver, and a bandwidth efficient trellis inner code. A block diagram of this configuration is shown. The system may operate with or without the outer code and interleaver. In this recommendation, the outer code remains the (255,223) RS code over GF(2 exp 8) with an error correcting capability of t = 16 eight bit symbols. This code's excellent performance and the existence of fast, cost effective, decoders justify its continued use. The purpose of the interleaver/deinterleaver is to distribute burst errors out of the inner decoder over multiple codewords of the outer code. This utilizes the error correcting capability of the outer code more efficiently and reduces the probability of an RS decoder failure. Since the space telemetry channel is not considered bursty, the required interleaving depth is primarily a function of the inner decoding method. A diagram of an interleaver with depth 4 that is compatible with the (255,223) RS code is shown. Specific interleaver requirements are discussed after the inner code recommendations.

Costello, Daniel J., Jr.↗

DOE OSTI2024

Autonomous Anomaly Detection for MPC Forecasts of HVAC Systems in Residential Communities

The use of residential heating, ventilation, and air conditioning (HVAC) to shift peak demand or provide ancillary services is a potential solution in the presence of older grids and distributed renewables. However, to ensure the efficient use of devices, utilities need to accurately forecast the load and adopt error correction schemes when necessary. While significant theoretical research exists in the area of predictive control of HVAC, little experimental evidence exists. The lack of experimental data in turn causes researchers to be unprepared for unsystematic errors which emerge due to the higher complexity of the data generating process. This study offers an anomaly detection methodology that uses unsupervised machine learning algorithms to detect and isolate these errors with different forecast error ranges. The results of anomaly detection procedure can then be used for error correction and would eventually help develop better predictive controllers. The methodology is tested using real world data from a smart neighborhood that currently operates in Atlanta. GA.

Lebakula, Viswadeep↗

DOE OSTI2023

High-fidelity parallel entangling gates on a neutral-atom quantum computer

The ability to perform entangling quantum operations with low error rates in a scalable fashion is a central element of useful quantum information processing. Neutral-atom arrays have recently emerged as a promising quantum computing platform, featuring coherent control over hundreds of qubits and any-to-any gate connectivity in a flexible, dynamically reconfigurable architecture. The main outstanding challenge has been to reduce errors in entangling operations mediated through Rydberg interactions. Here we report the realization of two-qubit entangling gates with 99.5% fidelity on up to 60 atoms in parallel, surpassing the surface-code threshold for error correction. Our method uses fast, single-pulse gates based on optimal control, atomic dark states to reduce scattering and improvements to Rydberg excitation and atom cooling. We benchmark fidelity using several methods based on repeated gate applications, characterize the physical error sources and outline future improvements. Finally, we generalize our method to design entangling gates involving a higher number of qubits, which we demonstrate by realizing low-error three-qubit gates. By enabling high-fidelity operation in a scalable, highly connected system, these advances lay the groundwork for large-scale implementation of quantum algorithms, error-corrected circuits and digital simulations.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Opportunities in full-stack design of low-overhead fault-tolerant quantum computation

Quantum error correction provides a route to realizing large-scale quantum computation but incurs substantial resource overheads. Here, in this work, we highlight recent advances that reduce these overheads by co-designing different levels of the computational stack, including algorithms, quantum-error-correction strategies and hardware architecture. We then discuss opportunities for further optimization such as leveraging flexible qubit connectivity and quantum low-density parity check codes. These strategies can bring useful quantum computation closer to reality as experiments advance in the coming years.

quantum information↗

NASA NTRS1988

Nested neural networks

Nested neural networks, consisting of small interconnected subnetworks, allow for the storage and retrieval of neural state patterns of different sizes. The subnetworks are naturally categorized by layers of corresponding to spatial frequencies in the pattern field. The storage capacity and the error correction capability of the subnetworks generally increase with the degree of connectivity between layers (the nesting degree). Storage of only few subpatterns in each subnetworks results in a vast storage capacity of patterns and subpatterns in the nested network, maintaining high stability and error correction capability.

Baram, Yoram↗

NASA NTRS2014

The CCSDS Next Generation Space Data Link Protocol (NGSLP)

The CCSDS space link protocols i.e., Telemetry (TM), Telecommand (TC), Advanced Orbiting Systems (AOS) were developed in the early growth period of the space program. They were designed to meet the needs of the early missions, be compatible with the available technology and focused on the specific link environments. Digital technology was in its infancy and spacecraft power and mass issues enforced severe constraints on flight implementations. Therefore the Telecommand protocol was designed around a simple Bose, Hocquenghem, Chaudhuri (BCH) code that provided little coding gain and limited error detection but was relatively simple to decode on board. The infusion of the concatenated Convolutional and Reed-Solomon codes5 for telemetry was a major milestone and transformed telemetry applications by providing them the ability to more efficiently utilize the telemetry link and its ability to deliver user data. The ability to significantly lower the error rates on the telemetry links enabled the use of packet telemetry and data compression. The infusion of the high performance codes for telemetry was enabled by the advent of digital processing, but it was limited to earth based systems supporting telemetry. The latest CCSDS space link protocol, Proximity-1 was developed in early 2000 to meet the needs of short-range, bi-directional, fixed or mobile radio links characterized by short time delays, moderate but not weak signals, and short independent sessions. Proximity-1 has been successfully deployed on both NASA and ESA missions at Mars and is planned to be utilized by all Mars missions in development. A new age has arisen, one that now provides the means to perform advanced digital processing in spacecraft systems enabling the use of improved transponders, digital correlators, and high performance forward error correcting codes for all communications links. Flight transponders utilizing digital technology have emerged and can efficiently provide the means to make the next leap in performance for space link communications. Field Programmable Gate Arrays (FPGAs) provide the capability to incorporate high performance forward error correcting codes implemented within software transponders providing improved performance in data transfer, ranging, link security, and time correlation. Given these synergistic technological breakthroughs, the time has come to take advantage of them in applying them to both on going (e.g., command, telemetry) and emerging (e.g., space link security, optical communication) space link applications. However one of the constraining factors within the Data Link Layer in realizing these performance gains is the lack of a generic transfer frame format and common supporting services amongst the existing CCSDS link layer protocols. Currently each of the four CCSDS link layer protocols (TM, TC, AOS, and Proximity-1) have unique formats and services which prohibits their reuse across the totality of all space link applications of CCSDS member space agencies. For example, Mars missions. These missions implement their proximity data link layer using the Proximity-1 frame format and the services it supports but is still required to support the direct from Earth (TC) protocols and the Direct To Earth (AOS/TM) protocols. The prime purpose of this paper, is to describe a new general purpose CCSDS Data Link layer protocol, the NGSLP that will provide the required services along with a common transfer frame format for all the CCSDS space links (ground to/from space and space to space links) targeted for emerging missions after a CCSDS agency-wide coordinated date. This paper will also describe related options that can be included for the Coding and Synchronization sub-layer of the Data Link layer to extend the capacities of the link and additionally provide an independence of the transfer frame sub-layer from the coding sublayer. This feature will provide missions the option of running either the currently performed synchronous coding and transfer frame data link or an asynchronous coding/frame data link, in which the transfer frame length is independent of the block size of the code. The benefits from the elimination of this constraint (frame synchronized to the code block) will simplify the interface between the transponder and the data handling equipment and reduce implementation costs and complexities. The benefits include: inclusion of encoders/decoders into transmitters and receivers without regard to data link protocols, providing the ability to insert latency sensitive messages into the link to support launch, landing/docking, telerobotics. and Variable Coded Modulation (VCM). In addition the ability to transfer different sized frames can provide a backup for delivering stored anomaly engineering data simultaneously with real time data, or relaying of frames from various sources onto a trunk line for delivery to Earth.

Kazz, Greg J.↗

DOE OSTI2023

Erasure conversion in a high-fidelity Rydberg quantum simulator

Minimizing and understanding errors is critical for quantum science, both in noisy intermediate scale quantum (NISQ) devices and for the quest towards fault-tolerant quantum computation. Rydberg arrays have emerged as a prominent platform in this context with impressive system sizes and proposals suggesting how error-correction thresholds could be significantly improved by detecting leakage errors with single-atom resolution, a form of erasure error conversion. However, two-qubit entanglement fidelities in Rydberg atom arrays have lagged behind competitors and this type of erasure conversion is yet to be realized for matter-based qubits in general. Here we demonstrate both erasure conversion and high-fidelity Bell state generation using a Rydberg quantum simulator. When excising data with erasure errors observed via fast imaging of alkaline-earth atoms, we achieve a Bell state fidelity of $\ge 0.997{1}_{-13}^{+10}$ , which improves to $\ge 0.998{5}_{-12}^{+7}$ when correcting for remaining state-preparation errors. We further apply erasure conversion in a quantum simulation experiment for quasi-adiabatic preparation of long-range order across a quantum phase transition, and reveal the otherwise hidden impact of these errors on the simulation outcome. Our work demonstrates the capability for Rydberg-based entanglement to reach fidelities in the 0.999 regime, with higher fidelities a question of technical improvements, and shows how erasure conversion can be utilized in NISQ devices. These techniques could be translated directly to quantum-error-correction codes with the addition of long-lived qubits.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1998

Efficient Methods to Assimilate Satellite Retrievals Based on Information Content: Suboptimal Retrieval Assimilation - Part 2

One of the outstanding problems in data assimilation has been and continues to be how best to utilize satellite data while balancing the tradeoff between accuracy and computational cost. A number of weather prediction centers have recently achieved remarkable success in improving their forecast skill by changing the method by which satellite data are assimilated into the forecast model from the traditional approach of assimilating retrievals to the direct assimilation of radiances in a variational framework. The operational implementation of such a substantial change in methodology involves a great number of technical details, e.g., pertaining to quality control procedures, systematic error correction techniques, and tuning of the statistical parameters in the analysis algorithm. Although there are clear theoretical advantages to the direct radiance assimilation approach, it is not obvious at all to what extent the improvements that have been obtained so far can be attributed to the change in methodology, or to various technical aspects of the implementation. The issue is of interest because retrieval assimilation retains many practical and logistical advantages which may become even more significant in the near future when increasingly high-volume data sources become available. The central question we address here is: how much improvement can we expect from assimilating radiances rather than retrievals, all other things being equal? We compare the two approaches in a simplified one-dimensional theoretical framework, in which problems related to quality control and systematic error correction are conveniently absent. By assuming a perfect radiative transfer model and perfect knowledge of radiance and background error covariances, we are able to formulate a nonlinear local error analysis for each assimilation method. Direct radiance assimilation is optimal in this idealized context, while the traditional method of assimilating retrievals is suboptimal because it ignores the cross-covariances between background errors and retrieval errors. We show that interactive retrieval assimilation (where the same background used for assimilation is also used in the retrieval step) is equivalent to direct assimilation of radiances with suboptimal analysis weights. We illustrate and extend these theoretical arguments with several one-dimensional assimilation experiments, where we estimate vertical atmospheric profiles using simulated data from both the High-resolution InfraRed Sounder 2 (HIRS2) and the future Atmospheric InfraRed Sounder (AIRS).

Joiner, J.↗

DOE OSTI2024

How to Build a Quantum Supercomputer: Scaling from Hundreds to Millions of Qubits

In the span of four decades, quantum computation has evolved from an intellectual curiosity to a potentially realizable technology. Today, small-scale demonstrations have become possible for quantum algorithmic primitives on hundreds of physical qubits and proof-of-principle error-correction on a single logical qubit. Nevertheless, despite significant progress and excitement, the path toward a full-stack scalable technology is largely unknown. There are significant outstanding quantum hardware, fabrication, software architecture, and algorithmic challenges that are either unresolved or overlooked. These issues could seriously undermine the arrival of utility-scale quantum computers for the foreseeable future. Here, we provide a comprehensive review of these scaling challenges. We show how the road to scaling could be paved by adopting existing semiconductor technology to build much higher-quality qubits, employing system engineering approaches, and performing distributed quantum computation within heterogeneous high-performance computing infrastructures. These opportunities for research and development could unlock certain promising applications, in particular, efficient quantum simulation/learning of quantum data generated by natural or engineered quantum systems. To estimate the true cost of such promises, we provide a detailed resource and sensitivity analysis for classically hard quantum chemistry calculations on surface-code error-corrected quantum computers given current, target, and desired hardware specifications based on superconducting qubits, accounting for a realistic distribution of errors. Furthermore, we argue that, to tackle industry-scale classical optimization and machine learning problems in a cost-effective manner, heterogeneous quantum-probabilistic computing with custom-designed accelerators should be considered as a complementary path toward scalability.

Mohseni, Masoud↗