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All sourcesNASA NTRSDOE OSTI
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↗
DOE OSTI2025

Superselection rules, quantum error correction, and quantum chromodynamics

We investigate the relationship between superselection rules and quantum error correcting codes. We demonstrate that the existence of a superselection rule implies the Knill-Laflamme condition in quantum error correction. As an example, we examine the code built from quantum chromodynamics, where the proton and neutron states in the model are explored as different superselection sectors that protect logical information. Finally we comment on topological quantum error correcting codes and supersymmetric quantum field theory within this framework.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Universal Optimization and Tighter Fidelity Bounds for Approximate Quantum Error Correction

Approximate quantum error correction (AQEC) not only dictates the performance of discrete- and continuous-variable quantum error correction codes but also serves as a unifying framework across various physical disciplines. Identifying the optimal recovery channel to maximize the entanglement fidelity via standard semidefinite programming is computationally bottlenecked by the exponentially growing number of Kraus operators with system size, rendering large-scale optimization prohibitive. While analytical near-optimal maps exist, they typically work only when the Knill-Laflamme conditions are nearly satisfied. In this Letter, we establish an efficient framework by leveraging the duality between recovery and environment decoupling. This framework yields a tighter analytical lower bound on entanglement fidelity than the conventional limit set by the transpose channel. Furthermore, by exploiting the decayed weights of noise Kraus operators, we introduce a framework based on principal component analysis to reduce the dimension. In thermal loss channels where the weights decay exponentially, our approach achieves a 33-fold computational speedup while maintaining rigorous accuracy. Our approach enables high-precision optimization for AQEC codes that were previously intractable due to the curse of dimensionality.

Wu, Jing [Fermilab] (ORCID:0000000249460732)↗
DOE OSTI2025

Rare events and Griffiths phases in topological quantum error correction

The performance of quantum error correcting (QEC) codes is often studied under the assumption of spatiotemporally uniform error rates. On the other hand, experimental implementations almost always produce heterogeneous error rates, in either space or time, as a result of effects such as imperfect fabrication and/or cosmic rays. It is therefore important to understand if and how their presence can affect the performance of QEC in qualitative ways. Here, in this work, we study the effects of nonuniform error rates in the representative examples of the 1D repetition code and the 2D toric code, focusing on when they have extended spatiotemporal correlations; these may arise, for instance, from rare events (such as cosmic rays) that temporarily elevate error rates over the entire code patch. These effects can be described in the corresponding statistical mechanics models for decoding, where long-range correlations in the error rates lead to extended rare regions of weaker coupling. For the 1D repetition code where the rare regions are linear, we find two distinct decodable phases: a conventional ordered phase in which logical failure rates decay exponentially with the code distance, and a rare-region dominated Griffiths phase in which failure rates are parametrically larger and decay as a stretched exponential. In particular, the latter phase is present when the error rates in the rare regions are above the bulk threshold. For the 2D toric code where the rare regions are planar, we find no decodable Griffiths phase: rare events which boost error rates above the bulk threshold lead to an asymptotic loss of threshold and failure to decode. Unpacking the failure mechanism implies that techniques for suppressing extended sequences of repeated rare events (which, without intervention, will be statistically present with high probability) will be crucial for QEC with the toric code.

classical statistical mechanics↗
DOE OSTI2025

QECC-Synth: A Layout Synthesizer for Quantum Error Correction Codes on Sparse Architectures

Quantum Error Correction (QEC) codes are essential for achieving fault-tolerant quantum computing (FTQC). However, their implementation faces significant challenges due to disparity between required dense qubit connectivity and sparse hardware architectures. Current approaches often either underutilize QEC circuit features or focus on manual designs tailored to specific codes and architectures, limiting their capability and generality. In response, we introduce QECC-Synth, an automated compiler for QEC code implementation that addresses these challenges. We leverage the ancilla bridge technique tailored to the requirements of QEC circuits and introduces a systematic classification of its design space flexibilities. We then formalize this problem using the MaxSAT framework to optimize these flexibilities. Evaluation shows that our method significantly outperforms existing methods while demonstrating broader applicability across diverse QEC codes and hardware architectures.

Yin, Keyi [University of California, San Diego]↗
DOE OSTI2025

Celestial Quantum Error Correction. Part II. From qudits to celestial CFT

A holographic CFT description of asymptotically flat spacetimes inherits vacuum degeneracies and IR divergences from its gravitational dual. We devise a Quantum Error Correcting (QEC) framework to encode both effects as correctable fluctuations on the CFT dual. The framework is physically motivated by embedding a chain of qudits in the so-called Klein spacetime and then taking a continuum 𝑁 → ∞ limit. At finite 𝑁 the qudit chain 1) enjoys a discrete version of celestial symmetries and 2) supports a Gottesman-Kitaev-Preskill (GKP) code. The limit results in hard states with quantized BMS hair in the celestial torus forming the logical subspace, robust under errors induced by soft radiation. Technically, the construction leverages the recently studied 𝑤 1+∞ hierarchy of soft currents and its realization from a sigma model in twistor space.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Concatenated dual displacement code for continuous-variable quantum error correction

The continuous-variable (CV) Gaussian no-go theorem fundamentally limits the suppression of Gaussian displacement errors using only Gaussian gates and states. Prior studies have employed Gottesman-Kitaev-Preskill (GKP) states as ancillary qumodes to suppress small Gaussian displacement errors. However, when the displacement magnitude becomes large, inevitable lattice-crossing errors arise beyond the correctable range of the GKP state. To address this issue, we concatenate the Gaussian-noise-suppression circuit with an outer analog Steane code that corrects such occasional lattice-crossing events as well as other abrupt displacement errors. Contrary to conventional concatenation, which primarily aims to reduce logical error rates, the Steane-GKP duality in encoding provides complementary protection against displacement errors at different scales: The inner GKP layer employs non-Gaussian resources to suppress continuous Gaussian noise and reduce residual variance, while the outer analog Steane code corrects discrete lattice-crossing events that exceed the GKP correctable range. It is precisely this separation of error-mitigation roles that enables CV error correction. In contrast to prior work on concatenating GKP and repetition codes to establish error correction for discrete qubit/qudit encoding, we provide correction in the continuous encoding space. Analytical studies show that, under infinite squeezing, the concatenated code suppresses the variance of Gaussian displacement errors acting on all qumodes by up to 50%, while enabling unbiased correction of lattice-crossing errors with a success probability determined by the ratio between the residual Gaussian error standard deviation and the lattice-crossing magnitude. Even with finite squeezing, the proposed architecture still provides Gaussian-error suppression and lattice-crossing correction. Moreover, the presence of the outer analog Steane code relaxes the squeezing requirement of the inner GKP states, indicating near-term experimental feasibility. This work establishes a viable route toward fault-tolerant continuous-variable quantum computation and provides insight into the design of concatenated CV error-correcting architectures.

quantum error correction↗
DOE OSTI2024

Quantum Information Encoding and Decoding for Quantum Sensi

This two-year theory project focused on theoretical investigations of novel paradigms for quantum sensing, building on information encoding and techniques from quantum error correction, quantum computing and other quantum information domains. The outcomes facilitate quantum information technology development, especially at the interface of quantum computing and quantum sensing. The results of the project show new use cases and new paradigms for quantum sensing beyond what has so far been considered. One outcome shows how quantum sensing opens new opportunities for fundamental physics such as the capability of single graviton detection. Another outcome reveals a new application of NISQ quantum computers with error correction for metrology, building on recent advances in practical quantum error correction implementation. The third outcome of the project creates new paradigms of back-action-evading sensing inspired by collective quantum information encoding, which achieves quantum sensing beyond the quantum limit without the use of entanglement.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Leveraging Qubit Loss Detection in Fault-Tolerant Quantum Algorithms

Qubit loss errors constitute a dominant source of noise in many quantum hardware systems, particularly in neutral-atom quantum computers. We develop a theoretical framework to effectively detect and correct loss errors in logical algorithms and leverage such loss information in decoding. Considering general quantum error correction codes and logical circuits, we introduce a delayed-erasure decoder for experimentally motivated error models which leverages information from delayed loss detection to accurately correct loss errors, even when the precise moment of the error is unknown. Using this decoder, we identify strategies for detecting and correcting loss errors based on the logical circuit structure. For deep circuits prior to logical measurement, we explore methods to integrate loss detection into syndrome extraction with minimal overhead, identifying optimal strategies depending on the qubit loss fraction in the noise and hardware capabilities. In contrast, we find that many key algorithmic subroutines involve frequent gate teleportation, shortening the circuit depth before logical measurement and naturally replacing qubits with no additional experimental overhead. We simulate this setting using a toy model algorithm for small-angle synthesis and find a significant performance improvement as the loss fraction increases. These results provide a path forward for advancing large-scale fault-tolerant quantum computation in systems with loss error detection.

atoms↗
DOE OSTI2025

Perturbative Stability and Error-Correction Thresholds of Quantum Codes

Topologically ordered phases are stable to local perturbations, and topological quantum error-correcting codes enjoy thresholds to local errors. We connect the two notions of stability by constructing classical statistical mechanics models for decoding general Calderbank-Shor-Steane codes and classical linear codes. Our construction encodes correction success probabilities under uncorrelated bit-flip and phase-flip errors, and simultaneously describes a generalized ℤ 2 lattice-gauge theory with quenched disorder. We observe that the clean limit of the latter is precisely the discretized imaginary-time path integral of the corresponding quantum code Hamiltonian when the errors are turned into a perturbative 𝑋 or 𝑍 magnetic field. Motivated by error-correction considerations, we define general order parameters for all such generalized ℤ 2 lattice-gauge theories, and show that they are generally lower bounded by success probabilities of error correction. For CSS codes satisfying the low-density parity-check condition and with a sufficiently large code distance, we prove the existence of a low-temperature ordered phase of the corresponding lattice-gauge theories, particularly for those lacking Euclidean spatial locality and/or when there is a nonzero code rate. We further argue that these results provide evidence for stable phases in the corresponding perturbed quantum Hamiltonians, obtained in the limit of continuous imaginary time. To do so, we distinguish space- and timelike defects in the lattice-gauge theory. A high free-energy cost of spacelike defects corresponds to a successful “memory experiment” and suppresses the energy splitting among the ground states, while a high free-energy cost of timelike defects corresponds to a successful “stability experiment” and points to a nonzero gap to local excitations.

quantum error correction↗
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

Covariant Quantum Error-Correcting Codes with Metrological Entanglement Advantage

Here, we show that a subset of the basis for the irreducible representations of a tensor-product SU(2) rotation forms a covariant approximate quantum error-correcting code with transversal U(1) logical gates. Generalizing previous work on “thermodynamic codes” to general local spin and different irreducible representations using only properties of the angular momentum algebra, we obtain bounds on the code inaccuracy under generic noise on any known 𝑑 sites, under independent and identically distributed noise, and under heralded 𝑑-local erasures. We demonstrate that this family of codes protects a probe state with quantum Fisher information surpassing the standard quantum limit when the sensing parameter couples to the generator of the U(1) logical gate.

quantum error correction↗
DOE OSTI2025

An Early Investigation of the HHL Quantum Linear Solver for Scientific Applications

In this paper, we explore using the Harrow–Hassidim–Lloyd (HHL) algorithm to address scientific and engineering problems through quantum computing, utilizing the NWQSim simulation package on a high-performance computing platform. Focusing on domains such as power-grid management and climate projection, we demonstrate the correlations of the accuracy of quantum phase estimation, along with various properties of coefficient matrices, on the final solution and quantum resource cost in iterative and non-iterative numerical methods such as the Newton–Raphson method and finite difference method, as well as their impacts on quantum error correction costs using the Microsoft Azure Quantum resource estimator. We summarize the exponential resource cost from quantum phase estimation before and after quantum error correction and illustrate a potential way to reduce the demands on physical qubits. This work lays down a preliminary step for future investigations, urging a closer examination of quantum algorithms’ scalability and efficiency in domain applications.

hybrid software for QC-HPC↗
DOE OSTI2025

Enhancing quantum memory lifetime with measurement-free local error correction and reinforcement learning

Reliable quantum computation requires systematic identification and correction of errors that occur and accumulate in quantum hardware. To diagnose and correct such errors, standard quantum error-correcting protocols utilize global error information across the system obtained by mid-circuit readout of ancillary qubits. We investigate circuit-level error-correcting protocols that are measurement-free and based on local error information. Such a local error correction (LEC) circuit consists of faulty multi-qubit gates to perform both syndrome extraction and ancilla-controlled error removal. We develop and implement a reinforcement learning framework that takes a fixed set of faulty gates as inputs and outputs an optimized LEC circuit. To evaluate this approach, we quantitatively characterize an extension of logical qubit lifetime by a noisy LEC circuit. For the two-dimensional (2D) classical Ising model and four-dimensional toric code, our optimized LEC circuit performs better at extending a memory lifetime compared with a conventional LEC circuit based on Toom's rule in a subthreshold gate error regime. We further show that such circuits can be used to reduce the rate of mid-circuit readouts to preserve a 2D toric code memory. Lastly, we discuss the application of the LEC protocol on dissipative preparation of quantum states with topological phases.

74 ATOMIC AND MOLECULAR PHYSICS↗
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↗
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↗
DOE OSTI2026

Noninvasive mid-circuit measurement and reset on atomic qubits

Mid-circuit measurement and reset of subsets of qubits are crucial ingredients of quantum error correction and many quantum information applications. Measurement of atomic qubits is accomplished through resonant fluorescence, which typically disturbs neighboring atoms due to photon scattering. We propose and prototype a scheme for measurement and reset that provides both spatial and spectral isolation by using tightly focused laser beams and narrow atomic transitions. The unique advantage of this scheme is that all operations are applied exclusively to the read-out qubit, with little overhead and negligible disturbance to the other qubits of the same species. In this paper, we pave the way for noninvasive and high-fidelity mid-circuit measurement and demonstrate all key building blocks on a single trapped barium ion.

atomic systems↗