Results for “Quantum error correction” — Page 4

DOE OSTI2025

Subregion-subalgebra duality: Emergence of space and time in holography

In holographic duality, a higher dimensional quantum gravity system emerges from a lower dimensional conformal field theory (CFT) with a large number of degrees of freedom. We propose a formulation of duality for a general causally complete bulk spacetime region, called subregion-subalgebra duality, which provides a framework to describe how geometric notions in the gravity system, such as spacetime subregions, different notions of times, and causal structure, emerge from the dual CFT. Subregion-subalgebra duality generalizes and brings new insights into subregion-subregion duality (or equivalently entanglement wedge reconstruction). It provides a mathematically precise definition of subregion-subregion duality and gives an independent definition of entanglement wedges without using entropy. Geometric properties of entanglement wedges, including those that play a crucial role in interpreting the bulk as a quantum error correcting code, can be understood from the duality as the geometrization of the superadditivity of certain algebras. Using general boundary subalgebras rather than those associated with geometric subregions makes it possible to find duals for general bulk spacetime regions, including those not touching the boundary. Applying subregion-subalgebra duality to a boundary state describing a single-sided black hole also provides a precise way to define mirror operators. Published by the American Physical Society 2025

Leutheusser, Sam (ORCID:0000000339228128)↗

DOE OSTI2025

Qudit Dynamical Decoupling on a Superconducting Quantum Processor

Multilevel qudit systems are increasingly being explored as alternatives to traditional qubit systems due to their denser information storage and processing potential. However, qudits are more susceptible to decoherence than qubits due to increased loss channels, noise sensitivity, and crosstalk. To address these challenges, we develop protocols for dynamical decoupling (DD) of qudit systems based on the Heisenberg-Weyl group. We implement and experimentally verify these DD protocols on a superconducting transmon processor that supports qudit operation based on qutrits (d = 3) and ququarts (d = 4). Specifically, we demonstrate single-qudit DD sequences to decouple qutrits and ququarts from system-bath-induced decoherence. Here we also introduce two-qudit DD sequences designed to suppress the detrimental cross-Kerr couplings between coupled qudits. This allows us to demonstrate a significant improvement in the fidelity of time-evolved qutrit Bell states. Our results highlight the utility of leveraging DD to enable scalable qudit-based quantum computing.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Noise Constraints on Sensitivity Scaling in Quantum Nonlinear Metrology

Quantum-enhanced metrology surpasses classical metrology by improving estimation precision scaling with a resource 𝑁 (e.g., particle number or energy) from 1/√𝑁 to 1/𝑁. Through the use of nonlinear effects, Roy and Braunstein [Exponentially enhanced quantum metrology, Phys. Rev. Lett. 100, 220501 (2008)] derived a 1/𝑁 2 scaling. However, later works argued this exponential improvement is unphysical and that even modest gains, like 1/𝑁 2 , may vanish under noise. We show that, in the presence of small errors, the nonlinear interactions enabling metrological enhancement induce emergent errors. Here, the errors propagate through the sensing protocol and are magnified proportional to any intended nonlinear enhancement. We identify a critical value of the parameter to be estimated, for a fixed error, below which the emergent errors can be avoided.

Quantum Fisher information↗

DOE OSTI2025

Constant-Overhead Fault-Tolerant Bell-Pair Distillation Using High-Rate Codes

We present a fault-tolerant Bell-pair distillation scheme achieving constant overhead through high-rate quantum low-density parity-check (qLDPC) codes. Our approach maintains a constant distillation rate equal to the code rate while requiring no additional overhead beyond the physical qubits of the code. Full circuit-level analysis demonstrates fault-tolerance for input Bell-pair infidelities below a threshold ∼10%, readily achievable with near-term capabilities. Unlike previous proposals, our scheme keeps the output Bell pairs encoded in qLDPC codes at each node, eliminating unencoding overhead and enabling direct use in distributed quantum applications through recent advances in qLDPC computation. These results establish qLDPC-based distillation as a practical route toward resource-efficient quantum networks and distributed quantum computing.

quantum communication, protocols & technology↗

DOE OSTI2026

Solovay-Kitaev Algorithm and Randomized Compilation Data Availability

This zipped folder contains simulation notebooks, simulated data, and experimental data from the QSCOUT trapped-ion device that were used in the publication "Solovay-Kitaev Algorithm and Randomized Compilation" (https://doi.org/10.1103/ll6m-dbl7). The raw data is in the form of measurement outcomes of simple tomographic quantum circuits that were executed on the QSCOUT device and simulated using JAQALPAQ. These data are used to create plots within the jupyter notebooks that were included in the publication.

Quantum benchmarking↗

DOE OSTI2026

QEC-fidelity

Code for paper "Universal Optimization and Tighter Fidelity Bounds for Approximate Quantum Error Correction" https://doi.org/10.48550/arXiv.2607.24968

Wu, Jing [Fermi National Accelerator Laboratory (F↗

DOE OSTI2026

Leveraging Quantum Sensors for Dark Matter Detection

Recent measurements have demonstrated that superconducting qubit decoherence is affected by radiation. As a result, many groups around the world are working to better understand the relationship between different types of radiation and qubit response. This crucial to quantum error correction because radiation can cause correlated loss of information across multiple qubits on a chip, defeating error correction algorithms. Additionally, the fundamental energy scale at which superconducting qubits operate may enable their development as meV-scale detectors for HEP applications, such as the direct detection of dark matter. At Fermilab, we have two world-class underground facilities which are already being used to study this problem: NEXUS and QUIET. I will present on results from operating superconducting qubits in each of these facilities, and the potential implications towards utilizing qubits as sensors for a novel dark matter detector.

Baxter, Daniel [Texas U., Arlington]↗

DOE OSTI2026

Leveraging Quantum Sensors for Dark Matter Detection

Recent measurements have demonstrated that superconducting qubit decoherence is affected by radiation. As a result, many groups around the world are working to better understand the relationship between different types of radiation and qubit response. This crucial to quantum error correction because radiation can cause correlated loss of information across multiple qubits on a chip, defeating error correction algorithms. Additionally, the fundamental energy scale at which superconducting qubits operate may enable their development as meV-scale detectors for HEP applications, such as the direct detection of dark matter. At Fermilab, we have two world-class underground facilities which are already being used to study this problem: NEXUS and QUIET. I will present on results from operating superconducting qubits in each of these facilities, and the potential implications towards utilizing qubits as sensors for a novel dark matter detector.

Baxter, Daniel [Texas U., Arlington]↗

NASA NTRSDate not supplied

Floquet Codes on Non-Trivalent Lattices

Floquet codes are a novel form of quantum error correcting codes, where the logical degrees of freedom appear in a dynamical form. The first example of such a code was constructed by Hastings and Haah on a honeycomb lattice. Specifically, they showed how to Floquetify the Kitaev honeycomb model, which when viewed as a subsystem code, encodes no logical qubits. However, by choosing a particular measurement schedule of the check operators, this model leads to dynamically encoded logical qubits. Since this initial work, several examples of Floquet codes have been constructed, mainly on trivalent lattices. Here, we report progress on understanding when such codes can be implemented on lattices of different connectivities.

Muhammad Sohaib Alam↗

NASA NTRSDate not supplied

Tools for Quantum Algorithms, Protocols, Benchmarking, Architectural Design and Co-Design

Explore the source record for details and available documents.

Quantum computing↗

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

Spectral Properties and Coding Transitions of Haar-Random Quantum Codes

A quantum error-correcting code with a nonzero error threshold undergoes a mixed-state phase transition when the error rate reaches that threshold. We explore this phase transition for Haar-random quantum codes, in which the logical information is encoded in a random subspace of the physical Hilbert space. We focus on the spectrum of the encoded system density matrix as a function of the rate of uncorrelated, single-qudit errors. For low error rates, this spectrum consists of well-separated bands, representing errors of different weights. As the error rate increases, the bands for high-weight errors merge. The evolution of these bands with increasing error rate is well described by a simple analytic ansatz. Using this ansatz, as well as an explicit calculation, we show that the threshold for Haar-random quantum codes saturates the hashing bound, and thus coincides with that for random stabilizer codes. For error rates that exceed the hashing bound, typical errors are uncorrectable, but postselected error correction remains possible until a much higher detection threshold. Postselection can in principle be implemented by projecting onto subspaces corresponding to low-weight errors, which remain correctable past the hashing bound.

decoherence↗

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 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 OSTI2025

Power and Limitations of Linear Programming Decoder for Quantum LDPC Codes

Decoding quantum error-correcting codes is a key challenge in enabling fault-tolerant quantum computation. In the classical setting, linear programming (LP) decoders offer provable performance guarantees and can leverage fast practical optimization algorithms. Although LP decoders have been proposed for quantum codes, their performance and limitations remain relatively underexplored. In this work, we uncover a key limitation of LP decoding for quantum low-density parity-check (LDPC) codes: certain constant-weight error patterns lead to ambiguous fractional solutions that cannot be resolved through independent rounding. To address this issue, we incorporate a post-processing technique known as ordered statistics decoding (OSD), which significantly enhances LP decoding performance in practice. Our results show that LP decoding, when augmented with OSD, can outperform belief propagation with the same post-processing for intermediate code sizes of up to hundreds of qubits. These findings suggest that LP-based decoders, equipped with effective post-processing, offer a promising approach for decoding near-term quantum LDPC codes.

Gu, Shouzhen [Yale U.]↗

DOE OSTI2025

Power and Limitations of Linear Programming Decoder for Quantum LDPC Codes

Decoding quantum error-correcting codes is a key challenge in enabling fault-tolerant quantum computation. In the classical setting, linear programming (LP) decoders offer provable performance guarantees and can leverage fast practical optimization algorithms. Although LP decoders have been proposed for quantum codes, their performance and limitations remain relatively underexplored. In this work, we uncover a key limitation of LP decoding for quantum low-density parity-check (LDPC) codes: certain constant-weight error patterns lead to ambiguous fractional solutions that cannot be resolved through independent rounding. To address this issue, we incorporate a post-processing technique known as ordered statistics decoding (OSD), which significantly enhances LP decoding performance in practice. Our results show that LP decoding, when augmented with OSD, can outperform belief propagation with the same post-processing for intermediate code sizes of up to hundreds of qubits. These findings suggest that LP-based decoders, equipped with effective post-processing, offer a promising approach for decoding near-term quantum LDPC codes.

Gu, Shouzhen [Yale U.]↗

DOE OSTI2025

Power and Limitations of Linear Programming Decoder for Quantum LDPC Codes

Decoding quantum error-correcting codes is a key challenge in enabling fault-tolerant quantum computation. In the classical setting, linear programming (LP) decoders offer provable performance guarantees and can leverage fast practical optimization algorithms. Although LP decoders have been proposed for quantum codes, their performance and limitations remain relatively underexplored. In this work, we uncover a key limitation of LP decoding for quantum low-density parity-check (LDPC) codes: certain constant-weight error patterns lead to ambiguous fractional solutions that cannot be resolved through independent rounding. To address this issue, we incorporate a post-processing technique known as ordered statistics decoding (OSD), which significantly enhances LP decoding performance in practice. Our results show that LP decoding, when augmented with OSD, can outperform belief propagation with the same post-processing for intermediate code sizes of up to hundreds of qubits. These findings suggest that LP-based decoders, equipped with effective post-processing, offer a promising approach for decoding near-term quantum LDPC codes.

Gu, Shouzhen [Yale U.]↗

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)] ↗