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All sourcesNASA NTRSDOE OSTI
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 OSTI2025

Mitigating cosmic-ray-like correlated events with a modular quantum processor

Quantum processors based on superconducting qubits are being scaled to larger qubit numbers, enabling the implementation of small-scale quantum error-correction codes. However, catastrophic chip-scale correlated errors have been observed in these processors, attributed to, e.g., cosmic ray impacts, which challenge conventional error-correction codes such as the surface code. These events are characterized by a temporary but pronounced suppression of the qubit-energy relaxation times. Here, in this study, we explore the potential for modular quantum computing architectures to mitigate such correlated energy decay events. We measure cosmic-ray-like events in a quantum processor comprising a motherboard and two flip-chip bonded daughterboard modules, each module containing two superconducting qubits. We monitor the appearance of correlated qubit decay events within a single module and across the physically separated modules. We find that while decay events within one module are strongly correlated (over 85%), events in separate modules only display approximately 2% correlations. We also report coincident decay events in the motherboard and in either of the two daughterboard modules, providing further insight into the nature of these decay events. These results suggest that modular architectures, combined with bespoke errorcorrection codes, offer a promising approach for protecting future quantum processors from chip-scale correlated errors.

Wu, Xuntao [Univ. of Chicago, IL (United States)] ↗
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 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↗
DOE OSTI2024

Single-shot quantum error correction in intertwined toric codes

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

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Dynamical logical qubits in the Bacon-Shor code

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

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE 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

Quantum-classical embedding via ghost Gutzwiller approximation for enhanced simulations of correlated electron systems

Simulating correlated materials on present-day quantum hardware remains challenging due to limited quantum resources. Quantum embedding methods offer a promising route by reducing computational complexity through the mapping of bulk systems onto effective impurity models, allowing more feasible simulations on pre- and early-fault-tolerant quantum devices. Here, this work develops a quantum-classical embedding framework based on the ghost Gutzwiller approximation to enable quantum-enhanced simulations of ground-state properties and spectral functions of correlated electron systems. Circuit complexity is analyzed using an adaptive variational quantum algorithm on a statevector simulator, applied to the infinite-dimensional Hubbard model with increasing ghost mode numbers from 3 to 5, resulting in circuit depths growing from 16 to 104. Noise effects are examined using a realistic error model, revealing significant impact on the spectral weight of the Hubbard bands. To mitigate these effects, the Iceberg quantum error detection code is employed, achieving up to 40% error reduction in simulations. Finally, the accuracy of the density matrix estimation and the derived spectral function is benchmarked on IBM and Quantinuum quantum hardware, featuring distinct qubit-connectivity and employing multiple levels of error mitigation techniques.

Chen, I-Chi [Ames Laboratory (AMES), Ames, IA (Uni↗
DOE OSTI2025

Performance and Achievable Rates of the Gottesman-Kitaev-Preskill Code for Pure-Loss and Amplification Channels

Quantum error-correction codes protect information from realistic noisy channels and lie at the heart of quantum computation and communication tasks. Understanding the optimal performance and other information-theoretic properties, such as the achievable rates, of a given code is crucial, as these factors determine the fundamental limits imposed by the encoding in conjunction with the noise channel. Here, we use the transpose channel to analytically obtain the near-optimal performance of any Gottesman-Kitaev-Preskill (GKP) code under pure loss and pure amplification. We present rigorous connections between GKP code’s near-optimal performance and its dual lattice geometry and average input energy. With no energy constraint, we show that when |𝜏/(1−𝜏)| is an integer, specific families of GKP codes simultaneously achieve the loss and amplification capacity. 𝜏 is the transmissivity (gain) for loss (amplification). Our results establish GKP code as the first structured bosonic code family that achieves the capacity of loss and amplification.

Zheng, Guo [Univ. of Chicago, IL (United States)] ↗
DOE OSTI2025

Synchronous detection of cosmic rays and correlated errors in superconducting qubit arrays

Quantum information processing at scale will require sufficiently stable and long-lived qubits, likely enabled by error-correction codes. Several recent superconducting-qubit experiments, however, reported observing intermittent spatiotemporally correlated errors that would be problematic for conventional codes, with ionizing radiation being a likely cause. Here, we directly measured the cosmic-ray contribution to spatiotemporally correlated qubit errors. We accomplished this by synchronously monitoring cosmic-ray detectors and qubit energy-relaxation dynamics of 10 transmon qubits distributed across a 5 × 5 × 0.35 mm 3 silicon chip. Cosmic rays caused correlated errors at a rate of $1/\left(592\begin{array}{c}+48\\ -41\end{array}\,{\rm{s}}\right)$, accounting for 17.1 ± 1.3% of all such events. Our qubits responded to essentially all of the cosmic rays and their secondary particles incident on the chip, consistent with the independently measured arrival flux. Moreover, we observed that the landscape of the superconducting gap in proximity to the Josephson junctions dramatically impacts the qubit response to cosmic rays. Given the practical difficulties associated with shielding cosmic rays, our results indicate the importance of radiation hardening—for example, superconducting gap engineering—to the realization of robust quantum error correction.

Science & Technology - Other Topics↗
DOE OSTI2025

Holographic codes and bulk RG flows

We consider the coarse-graining of holographic quantum error correcting codes under a generalized notion of bulk renormalization-group flow. In particular, we study the renormalization under this flow of the $A/4G$ term in the Faulkner-Lewkowycz-Maldacena formula and in its Rényi generalization. This provides a general quantum code perspective on the arguments of Susskind and Uglum. Specifically, given a 'UV' code with two-sided recovery and appropriately flat entanglement spectrum together with a set of 'seed' states in the UV code, we explicitly construct an 'IR' code with corresponding properties which contains the given seed states and is of minimal size in a sense we describe.

FOS: Physical sciences↗
DOE OSTI2025

Geometric Structure and Transversal Logic of Quantum Reed–Muller Codes

Designing efficient and noise-tolerant quantum computation protocols generally begins with an understanding of quantum error-correcting codes and their native logical operations. The simplest class of native operations are transversal gates, which are naturally fault-tolerant. Here, in this paper, we aim to characterize the transversal gates of quantum Reed–Muller (RM) codes by exploiting the well-studied properties of their classical counterparts. We start our work by establishing a new geometric characterization of quantum RM codes via the Boolean hypercube and its associated subcube complex. More specifically, a set of stabilizer generators for a quantum RM code can be described via transversal X and Z operators acting on subcubes of particular dimensions. This characterization leads us to define subcube operators composed of single-qubit π/2 k Z -rotations that act on subcubes of given dimensions. We first characterize the action of subcube operators on the code space: depending on the dimension of the subcube, these operators either (1) act as a logical identity on the code space, (2) implement non-trivial logic, or (3) rotate a state away from the code space. Second, and more remarkably, we uncover that the logic implemented by these operators corresponds to circuits of multi-controlled-Z gates that have an explicit and simple combinatorial description. Overall, this suite of results yields a comprehensive understanding of a class of natural transversal operators for quantum RM codes.

Reed–Muller (RM) codes↗
DOE OSTI2025

On infinite tensor networks, complementary recovery and type II factors

We initiate a study of local operator algebras at the boundary of infinite tensor networks, using the mathematical theory of inductive limits. In particular, we consider tensor networks in which each layer acts as a quantum code with complementary recovery, a property that features prominently in the bulk-to-boundary maps intrinsic to holographic quantum error-correcting codes. In this case, we decompose the limiting Hilbert space and the algebras of observables in a way that keeps track of the entanglement in the network. As a specific example, we describe this inductive limit for the holographic Harlow-Pastawski-Preskill-Yoshida code model and relate its algebraic and error-correction features. We find that the local algebras in this model are given by the hyperfinite type II$_\infty$ factor. Next, we discuss other networks that build upon this framework and comment on a connection between type II factors and stabilizer circuits. We conclude with a discussion of multiscale entanglement renormalization ansatz networks in which complementary recovery is broken. We argue that this breaking possibly permits a limiting type III von Neumann algebra, making them more suitable ansätze for approximating subregions of quantum field theories.

holographic dualities↗
DOE OSTI2026

Composite-dimensional topological codes with boundaries and defects

We introduce new algorithms and provide example constructions of stabilizer models for the gapped boundaries, domain walls, and 0D defects of Abelian composite-dimensional twisted quantum doubles. Using the physically intuitive concept of condensation, our algorithm explicitly describes how to construct the boundary and domain-wall stabilizers starting from the bulk model. This extends the utility of Pauli stabilizer models in describing nontranslationally invariant topological orders with gapped boundaries. To highlight this utility, we provide a series of examples, including a new family of quantum error-correcting codes where the double of ℤ4 is coupled to instances of the double semion (DS) phase. We discuss the codes' utility in the burgeoning area of quantum error correction with an emphasis on the interplay between deconfined anyons, logical operators, error rates, and decoding. We also augment our construction, built using algorithmic tools to describe the properties of explicit stabilizer layouts at the microscopic lattice level, with dimensional counting arguments and macroscopic-level constructions building on pants decompositions. The latter outlines how such codes' representation and design can be automated. Our results are validated by a series of error-correcting threshold calculations comparing our codes' performance with that of standard surface codes. To do so, we introduce a composite-dimensional belief-propagation decoder with ordered statistics that utilizes combination sweeps. Going beyond our worked-out examples, we expect our explicit step-by-step algorithms to pave the path for higher-dimensional codes to be discovered and implemented in near-future architectures that take advantage of various hardware platforms.

Mousa, Mohamad [Purdue University]↗
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

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

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 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↗