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All sources NASA NTRS DOE OSTI

DOE OSTI2024

Cross-Cap Defects and Fault-Tolerant Logical Gates in the Surface Code and the Honeycomb Floquet Code

We consider the Z 2 toric code, surface code, and Floquet code defined on a nonorientable surface, which can be considered as families of codes extending Shor’s nine-qubit code. We investigate the fault-tolerant logical gates of the Z 2 toric code in this setup, which corresponds to e ↔ m exchanging symmetry of the underlying Z 2 gauge theory. We find that nonorientable geometry provides a new way for the emergent symmetry to act on the code space, and discover the new realization of the fault-tolerant Hadamard gate of the two-dimensional surface code with a single cross cap connecting the vertices nonlocally along a slit, dubbed a nonorientable surface code. This Hadamard gate can be realized by a constant-depth local unitary circuit modulo nonlocality caused by a cross cap. Via folding, the nonorientable surface code can be turned into a bilayer local quantum code, where the folded cross cap is equivalent to a bilayer twist terminated on a gapped boundary and the logical Hadamard only contains local gates with intralayer couplings when being away from the cross cap, as opposed to the interlayer couplings on each site needed in the case of the folded surface code. We further obtain the complete logical Clifford gate set for a stack of nonorientable surface codes and similarly for codes defined on Klein-bottle geometries. We then construct the honeycomb Floquet code in the presence of a single cross cap, and find that the period of the sequential Pauli measurements acts as a H Z logical gate on the single logical qubit, where the cross cap enriches the dynamics compared with the orientable case. We find that the dynamics of the honeycomb Floquet code is precisely described by a condensation operator of the Z 2 gauge theory, and illustrate the exotic dynamics of our code in terms of a condensation operator supported at a nonorientable surface. Published by the American Physical Society 2024

Physics↗

DOE OSTI2023

TISCC: A Surface Code Compiler and Resource Estimator for Trapped-Ion Processors

We introduce the Trapped-Ion Surface Code Compiler (TISCC), a software tool that generates circuits for a universal set of surface code patch operations in terms of a native trapped-ion gate set. To accomplish this, TISCC manages an internal representation of a trapped-ion system where a repeating pattern of trapping zones and junctions is arranged in an arbitrarily large rectangular grid. Surface code operations are compiled by instantiating surface code patches on the grid and using methods to generate transversal operations over data qubits, rounds of error correction over stabilizer plaquettes, and/or lattice surgery operations between neighboring patches. Beyond the implementation of a basic surface code instruction set, TISCC contains corner movement functionality and a patch translation that is implemented using ion movement alone. Except in the latter case, all TISCC functionality is extensible to alternative grid-like hardware architectures. TISCC output has been verified using the Oak Ridge Quasi-Clifford Simulator (ORQCS).

LeBlond, Tyler↗

DOE OSTI2025

Logical error rates for the surface code under a mixed coherent and stochastic circuit-level noise model inspired by trapped ions

With fault-tolerant quantum computing (FTQC) on the horizon, it is critical to understand sources of logical errors in plausible hardware implementations of quantum error-correcting codes. Detailed error modeling of computational instructions on particular FTQC architectures will enable the better prediction of error propagation in FT-encoded quantum circuits while revealing where greater attention is needed in hardware design. In this work, we consider logical error rates for the surface code implemented on a hypothetical grid-based trapped-ion quantum charge-coupled device architecture. Specifically, we construct logical channels for the idling surface code and examine its diamond error under a mixed coherent and stochastic circuit-level noise model inspired by trapped ions. We include the coherent dephasing noise that is known to accumulate during physical qubit idling and transport in these systems, determining idling and transport durations using the time-resolved output of an open-source trapped-ion surface code compiler. To estimate expectation values of logical Pauli observables following hardware circuits containing non-Clifford sources of noise, we utilize a Monte Carlo technique to sample from an underlying quasiprobability distribution of Clifford circuits that we independently simulate in a phase-sensitive fashion. We verify error suppression up to code distance 𝑑 = 11 at coherent dephasing rates near and below those of current-generation trapped-ion quantum computers and find that logical error rates align with those of analogous fully stochastic simulations in this regime. Exploring higher dephasing rates at 𝑑 = 3−5, we find evidence for growing coherent rotations about all three logical Pauli axes, increased diagonal logical error process matrix elements relative to those of stochastic simulations, and a reduced dephasing rate threshold. Overall, our work paves a way toward realistic hardware emulation of small fault-tolerant quantum processes, e.g., members of an FTQC instruction set.

Quantum benchmarking↗

DOE OSTI2024

Surf-Deformer: Mitigating Dynamic Defects on Surface Code via Adaptive Deformation

In this paper, we introduce Surf-Deformer, a code deformation framework that seamlessly integrates adaptive defect mitigation functionality into the current surface code workflow. It crafts several basic deformation instructions based on fundamental gauge transformations, which can be combined to explore a larger design space than previous methods. This enables more optimized deformation processes tailored to specific defect situations, restoring the QEC capability of deformed codes more efficiently with minimal qubit resources. Additionally, we design an adaptive code layout that accommodates our defect mitigation strategy while ensuring efficient execution of logical operations. Our evaluation shows that Surf-Deformer outperforms previous methods by significantly reducing the end-to-end failure rate of various quantum programs by 35× to 70×, while requiring only about 50% of the qubit resources compared to the previous method to achieve the same level of failure rate. Ablation studies show that Surf-Deformer surpasses previous defect removal methods in preserving QEC capability and facilitates surface code communication by achieving nearly optimal throughput.

Yin, Keyi↗

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↗

DOE OSTI2025

CaliQEC: In-situ Qubit Calibration for Surface Code Quantum Error Correction

Quantum Error Correction (QEC) is essential for fault-tolerant, large-scale quantum computation. However, error drift in qubits undermines QEC performance during long computations, necessitating frequent calibration. Conventional calibration methods disrupt quantum states, requiring system downtime and rendering in situ calibration impractical. To address this challenge, we propose QECali, a novel framework that enables in situ calibration for surface codes. Our evaluation demonstrates that QECali introduces modest qubit overhead and negligible increases in execution time, offering the first practical solution for in situ calibration in surface code based quantum computation.

Fang, Xiang [University of California, Santa Barba↗

NASA NTRS1995

Impact of differences in the solar irradiance spectrum on surface reflectance retrieval with different radiative transfer codes

Surface reflectance retrieval from imaging spectrometer data as acquired with the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) has become important for quantitative analysis. In order to calculate surface reflectance from remotely measured radiance, radiative transfer codes such as 5S and MODTRAN2 play an increasing role for removal of scattering and absorption effects of the atmosphere. Accurate knowledge of the exo-atmospheric solar irradiance (E(sub 0)) spectrum at the spectral resolution of the sensor is important for this purpose. The present study investigates the impact of differences in the solar irradiance function, as implemented in a modified version of 5S (M5S), 6S, and MODTRAN2, and as proposed by Green and Gao, on the surface reflectance retrieved from AVIRIS data. Reflectance measured in situ is used as a basis of comparison.

Staenz, K.↗

DOE OSTI2025

Hierarchical memories: Simulating quantum LDPC codes with local gates

Constant-rate low-density parity-check (LDPC) codes are promising candidates for constructing efficient fault-tolerant quantum memories. However, if physical gates are subject to geometric-locality constraints, it becomes challenging to realize these codes. In this paper, we construct a new family of [[N,K,D]] codes, referred to as hierarchical codes, that encode a number of logical qubits K=Ω(N/log(N) 2 ). The N th element of this code family is obtained by concatenating a constant-rate quantum LDPC code with a surface code; nearest-neighbor gates in two dimensions are sufficient to implement the corresponding syndrome-extraction circuit and achieve a threshold. Below threshold the logical failure rate vanishes superpolynomially as a function of the distance D(N). We present a bilayer architecture for implementing the syndrome-extraction circuit, and estimate the logical failure rate for this architecture. Under conservative assumptions, we find that the hierarchical code outperforms the basic encoding where all logical qubits are encoded in the surface code.

Pattison, Christopher A. [California Institute of ↗

DOE OSTI2025

Low-overhead transversal fault tolerance for universal quantum computation

Fast, reliable logical operations are essential for realizing useful quantum computers. By redundantly encoding logical qubits into many physical qubits and using syndrome measurements to detect and correct errors, we can achieve low logical error rates. However, for many practical quantum error correction codes such as the surface code, owing to syndrome measurement errors, standard constructions require multiple extraction rounds—of the order of the code distance d—for fault-tolerant computation, particularly considering fault-tolerant state preparation. Here we show that logical operations can be performed fault-tolerantly with only a constant number of extraction rounds for a broad class of quantum error correction codes, including the surface code with magic state inputs and feedforward, to achieve ‘transversal algorithmic fault tolerance’. Through the combination of transversal operations7 and new strategies for correlated decoding, despite only having access to partial syndrome information, we prove that the deviation from the ideal logical measurement distribution can be made exponentially small in the distance, even if the instantaneous quantum state cannot be made close to a logical codeword because of measurement errors. We supplement this proof with circuit-level simulations in a range of relevant settings, demonstrating the fault tolerance and competitive performance of our approach. Furthermore, our work sheds new light on the theory of quantum fault tolerance and has the potential to reduce the space–time cost of practical fault-tolerant quantum computation by over an order of magnitude.

Zhou, Hengyun [QuEra Computing, Boston, MA (United↗

NASA NTRS1995

Space Debris Surfaces (Computer Code): Probability of No Penetration Versus Impact Velocity and Obliquity

A unique collection of computer codes, Space Debris Surfaces (SD_SURF), have been developed to assist in the design and analysis of space debris protection systems. SD_SURF calculates and summarizes a vehicle's vulnerability to space debris as a function of impact velocity and obliquity. An SD_SURF analysis will show which velocities and obliquities are the most probable to cause a penetration. This determination can help the analyst select a shield design that is best suited to the predominant penetration mechanism. The analysis also suggests the most suitable parameters for development or verification testing. The SD_SURF programs offer the option of either FORTRAN programs or Microsoft-EXCEL spreadsheets and macros. The FORTRAN programs work with BUMPERII. The EXCEL spreadsheets and macros can be used independently or with selected output from the SD_SURF FORTRAN programs. Examples will be presented of the interaction between space vehicle geometry, the space debris environment, and the penetration and critical damage ballistic limit surfaces of the shield under consideration.

Elfer, N.↗

DOE OSTI2024

ORNL-QCI/TISCC

LeBlond, Tyler↗

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

Optical Surface Analysis Code (OSAC)

The purpose of this modification to the Optical Surface Analysis Code (OSAC) is to upgrade the PSF program to allow the user to get proper diffracted energy normalization even when deliberately obscuring rays with internal obscurations.

Glenn, P.↗

NASA NTRS1991

A Graphically Interactive Approach to Structured and Unstructured Surface Grid Quality Analysis

A graphically interactive approach to structured and unstructured surface grid quality analysis is described. A Surface Analysis Code SurfACe) is developed to help a user analyze surface grid quality based on surface normal vectors, first and second derivatives of these vectors, normal, Gaussian, and mean curvatures, orthogonality, aspect ratio, and cell area. The results demonstrate how this approach can be used to reduce surface grid generation errors and increase the cost effectiveness of Computational Fluid Dynamics as an aircraft design tool.

Stewart, John E.↗

NASA NTRS1987

A user's manual for the Electromagnetic Surface Patch code: ESP version 3

This report serves as a user's manual for Version III of the Electromagnetic Surface Patch Code or ESP code. ESP is user-oriented, based on the method of moments (MM) for treating geometries consisting of an interconnection of thin wires and perfectly conducting polygonal plates. Wire/plate junctions must be about 0.1 lambda or more from any plate edge. Several plates may intersect along a common edge. Excitation may be by either a delta-gap voltage generator or by a plane wave. The thin wires may have finite conductivity and also may contain lumped loads. The code computes most of the usual quantities of interest such as current distribution, input impedance, radiation efficiency, mutual coupling, far zone gain patterns (both polarizations) and radar-cross-section (both/cross polarizations).

Newman, E. H.↗

NASA NTRS1983

Optical surface analysis code (OSAC)

A computer program for the evaluation of surface ripple effects on an optical system is discussed. The program consists of a modification of conventional ray tracing so that the effects of all roughness frequency scales on image quality can be analyzed. The code is designed to deal with image quality problems arising in connection with X-ray telescopes and near-normal incidence systems used in the infrared, visible, and near-UV parts of the spectrum. The emphasis of the program analysis is on narrow angle scattering and its effect on image quality. The intent is to provide the optical engineer with a measure of the sensitivity of image quality to various surface characteristics. The paper will highlight some of the unique modeling features of the code, and illustrate some system examples.

Noll, R. J.↗

NASA NTRS1983

A lifting surface computer code with jet-in-crossflow interference effects. Volume 1: Theoretical description

A method is proposed to combine a numerical description of a jet in a crossflow with a lifting surface panel code to calculate the jet/aerodynamic-surface interference effects on a V/STOL aircraft. An iterative technique is suggested that starts with a model for the properties of a jet/flat plate configuration and modifies these properties based on the flow field calculated for the configuration of interest. The method would estimate the pressures, forces, and moments on an aircraft out of ground effect. A first-order approximation to the method suggested is developed and applied to two simple configurations. The first-order approximation is a noniterative precedure which does not allow for interactions between multiple jets in a crossflow and also does not account for the influence of lifting surfaces on the jet properties. The jet/flat plate model utilized in the examples presented is restricted to a uniform round jet injected perpendicularly into a uniform crossflow for a range of jet-to-crossflow velocity ratios from three to ten.

Furlong, K. L.↗

DOE OSTI2025

Fault Tolerant Decoding of QLDPC-GKP Codes with Circuit Level Soft Information

Concatenated bosonic-stabilizer codes have recently gained prominence as promising candidates for achieving low-overhead fault-tolerant quantum computing in the long term. In such systems, analog information obtained from the syndrome measurements of an inner bosonic code is used to inform decoding for an outer code layer consisting of a discrete-variable stabilizer code such as a surface code. The use of Quantum Low-Density Parity Check (QLDPC) codes as an outer code is of particular interest due to the significantly higher encoding rates offered by these code families, leading to a further reduction in overhead for large-scale quantum computing. Recent works have investigated the performance of QLDPC-GKP codes in detail, and the use of analog information from the inner code significantly boosts decoder performance. However, the noise models assumed in these works are typically limited to depolarizing or phenomenological noise. In this paper, we investigate the performance of QLDPC-GKP concatenated codes under circuit-level noise, based on a model introduced by Noh et al. in the context of the surface-GKP code. To demonstrate the performance boost from analog information, we investigate three scenarios: (a) decoding without soft information, (b) decoding with precomputed error probabilities but without real-time soft information, and (c) decoding with real-time soft information obtained from round-to-round decoding of the inner GKP code. Results show minimal improvement between (a) and (b), but a significant boost in (c), indicating that real-time soft information is critical for concatenated decoding under circuit-level noise. We also study the effect of measurement schedules with varying depths and show that using a schedule with minimum depth is essential for obtaining reliable soft information from the inner code.

Borah, Shantom K. [Arizona U. (main)]↗