Barbell Codes: qLDPC Codes for Superconducting Quantum Hardware

• URL: http://arxiv.org/abs/2606.06062v1
• Date: Thu, 04 Jun 2026 12:01:24 GMT
• Title: Barbell Codes: qLDPC Codes for Superconducting Quantum Hardware
• Abstract summary: We introduce a family of qLDPC "barbell" codes accompanied by a realistic chip layout that supports all required two-qubit interactions.<n>We find that, with a modest overhead of $30$ data qubits per logical qubit, barbell codes can preserve information at a physical noise strength of $10-4$ for several trillion QEC cycles.
• Score: 2.8712862578745018
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The major challenge on the way to fault-tolerant quantum computing comes from the insufficient quality of hardware components and the difficulty of scaling their number without further compromising fidelity. Quantum Low-Density Parity-Check (qLDPC) codes offer a promising solution by encoding logical qubits with low overhead and at a comparatively high code distance. However, it remains an open question how to scalably implement efficient qLDPC codes on fixed-connectivity quantum chips without increasing hardware complexity to enable the non-local interactions in their underlying QEC cycles. We resolve this challenge for the first time by introducing a family of qLDPC "barbell" codes accompanied by a realistic chip layout that natively supports all required two-qubit interactions. Crucially, the hardware complexity required to implement barbell codes remains constant as code distance increases. We provide a detailed investigation into the feasibility of all required hardware components and simulate a specific family of barbell codes against circuit-level noise. We find that, with a modest overhead of $<30$ data qubits per logical qubit, barbell codes can preserve information at a physical noise strength of $10^{-4}$ for several trillion QEC cycles. Simulations of logical multi-Pauli measurements, performed with circuits tailored to the chip, yield similar logical performance per QEC round, indicating that entangling gates between logical qubits in barbell codes can be realized fault-tolerantly.

Related papers

• Routing Codes: High-Rate Quantum LDPC Codes with Short, Parallel Non-Local Connectivity [10.45558661301465]
  Quantum low-density parity-check (qLDPC) codes are promising candidates for realizing large-scale fault-tolerant quantum computing.<n>For mainstream quantum platforms such as superconductors and neutral atoms, the connectivity, the length of non-local couplings, and the complexity of wiring or atom rearrangement are key factors that dictate the difficulty of hardware realization.
  arXiv  Detail & Related papers  (2026-06-24T02:50:51Z)
• Breakeven demonstration of quantum low-density parity-check codes [0.8910173568215413]
  We leverage the flexibility of a trapped-ion quantum computer to demonstrate nine quantum error-correcting codes.<n>With a qLDPC code encoding 4 logical qubits into 18 physical qubits, we achieve a logical error rate up to $9times$ better than a previous demonstration.<n>Our implementation exhibits breakeven performance, with some instances achieving qubit lifetimes comparable to or slightly exceeding that of our trapped-ion qubits.
  arXiv  Detail & Related papers  (2026-06-04T17:49:27Z)
• Placing and routing quantum LDPC codes in multilayer superconducting hardware [0.6713975160553138]
  We develop Hardware-Aware Layout, HAL: a robust, efficient runtime algorithm.<n> HAL generates around 150 explicit layouts of quantum low-density parity-check (qLDPC) codes.<n>We lay out highly nonlocal qLDPC code families that achieve competitive tradeoffs between hardware complexity and logical efficiency.
  arXiv  Detail & Related papers  (2025-07-30T18:19:44Z)
• Directional Codes: a new family of quantum LDPC codes on hexagonal- and square-grid connectivity hardware [0.0]
  Utility-scale quantum computing requires quantum error correction (QEC) to protect quantum information against noise.<n>Currently, superconducting hardware is a promising candidate for achieving fault tolerance due to its fast gate times and feasible scalability.<n>We construct a new family of qLDPC codes, which outperforms the rotated planar code (RPC)<n>We numerically evaluate the performance of directional codes, encoding four, six and twelve logical qubits.
  arXiv  Detail & Related papers  (2025-07-25T16:57:21Z)
• Quantum Compiling with Reinforcement Learning on a Superconducting Processor [55.135709564322624]
  We develop a reinforcement learning-based quantum compiler for a superconducting processor. We demonstrate its capability of discovering novel and hardware-amenable circuits with short lengths. Our study exemplifies the codesign of the software with hardware for efficient quantum compilation.
  arXiv  Detail & Related papers  (2024-06-18T01:49:48Z)
• Constant-Overhead Fault-Tolerant Quantum Computation with Reconfigurable Atom Arrays [5.542275446319411]
  We propose a hardware-efficient scheme to perform fault-tolerant quantum computation with high-rate qLDPC codes on reconfigurable atom arrays. Our work paves the way for explorations of low-overhead quantum computing with qLDPC codes at a practical scale.
  arXiv  Detail & Related papers  (2023-08-16T19:47:17Z)
• Quaternary Neural Belief Propagation Decoding of Quantum LDPC Codes with Overcomplete Check Matrices [45.997444794696676]
  Quantum low-density parity-check (QLDPC) codes are promising candidates for error correction in quantum computers.<n>One of the major challenges in implementing QLDPC codes in quantum computers is the lack of a universal decoder.<n>We first propose to decode QLDPC codes with a belief propagation (BP) decoder operating on overcomplete check matrices.<n>We extend the neural BP (NBP) decoder, which was originally studied for suboptimal binary BP decoding of QLPDC codes, to quaternary BP decoders.
  arXiv  Detail & Related papers  (2023-08-16T08:24:06Z)
• Single-shot decoding of good quantum LDPC codes [38.12919328528587]
  We prove that quantum Tanner codes facilitate single-shot quantum error correction (QEC) of adversarial noise. We show that in order to suppress errors over multiple repeated rounds of QEC, it suffices to run the parallel decoding algorithm for constant time in each round.
  arXiv  Detail & Related papers  (2023-06-21T18:00:01Z)
• Modular decoding: parallelizable real-time decoding for quantum computers [55.41644538483948]
  Real-time quantum computation will require decoding algorithms capable of extracting logical outcomes from a stream of data generated by noisy quantum hardware. We propose modular decoding, an approach capable of addressing this challenge with minimal additional communication and without sacrificing decoding accuracy. We introduce the edge-vertex decomposition, a concrete instance of modular decoding for lattice-surgery style fault-tolerant blocks.
  arXiv  Detail & Related papers  (2023-03-08T19:26:10Z)
• Neural Belief Propagation Decoding of Quantum LDPC Codes Using Overcomplete Check Matrices [60.02503434201552]
  We propose to decode QLDPC codes based on a check matrix with redundant rows, generated from linear combinations of the rows in the original check matrix. This approach yields a significant improvement in decoding performance with the additional advantage of very low decoding latency.
  arXiv  Detail & Related papers  (2022-12-20T13:41:27Z)
• Finding the disjointness of stabilizer codes is NP-complete [77.34726150561087]
  We show that the problem of calculating the $c-disjointness, or even approximating it to within a constant multiplicative factor, is NP-complete. We provide bounds on the disjointness for various code families, including the CSS codes,$d codes and hypergraph codes. Our results indicate that finding fault-tolerant logical gates for generic quantum error-correcting codes is a computationally challenging task.
  arXiv  Detail & Related papers  (2021-08-10T15:00:20Z)
• Building a fault-tolerant quantum computer using concatenated cat codes [44.03171880260564]
  We present a proposed fault-tolerant quantum computer based on cat codes with outer quantum error-correcting codes. We numerically simulate quantum error correction when the outer code is either a repetition code or a thin rectangular surface code. We find that with around 1,000 superconducting circuit components, one could construct a fault-tolerant quantum computer.
  arXiv  Detail & Related papers  (2020-12-07T23:22:40Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.