Pith. sign in

REVIEW 6 cited by

Directional Codes: a new family of quantum LDPC codes on hexagonal- and square-grid connectivity hardware

Not yet reviewed by Pith; the record is open.

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2507.19430 v3 pith:44FG6NBJ submitted 2025-07-25 quant-ph

Directional Codes: a new family of quantum LDPC codes on hexagonal- and square-grid connectivity hardware

classification quant-ph
keywords codesquantumcodedirectionalconnectivityerrorfamilygate
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
0 comments
read the original abstract

Utility-scale quantum computing requires quantum error correction (QEC) to protect quantum information against noise. Currently, superconducting hardware is a promising candidate for achieving fault tolerance due to its fast gate times and feasible scalability. However, it is often restricted to two-dimensional nearest-neighbour connectivity, and therefore the variety of quantum low-density parity-check (qLDPC) codes that can be implemented on it without sacrificing QEC performance is believed to be greatly restricted. In this paper we construct a new family of qLDPC codes, which we call ``directional codes'', that outperforms the rotated toric code (RTC) while satisfying the connectivity requirements of the widely adopted square-grid, and some even the sparser hexagonal-grid, on a torus. The key idea is to utilise the iSWAP gate -- a native gate demonstrated on superconducting qubits -- to construct circuits that measure the stabilisers of these qLDPC codes without the need for additional connections. We numerically evaluate the performance of directional codes, encoding four, six, twelve and eighteen logical qubits, using a common superconducting-inspired circuit-level Pauli noise model. We also compare them to the RTC and to the bivariate bicycle (BB) codes, currently the two most popular quantum LDPC code families. As a concrete example, when evaluated with the Tesseract decoder with short beam setting, the best directional code family investigated achieves the same logical error rate as the RTC at physical error rate $p=10^{-3}$ but requires only a quarter to a third of the number of physical qubits. Our discovery opens a novel direction in QEC code design, suggesting that complex high-connectivity hardware may not be necessary for low-overhead fault-tolerant quantum computation.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 6 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Vine Codes: Low-Overhead Quantum LDPC Codes on a Planar Square Grid

    quant-ph 2026-06 unverdicted novelty 8.0

    Vine codes generalize directional codes to open planar boundaries, delivering up to 28% fewer data/measure qubits at circuit distance 7 and better simulated performance than the surface code at 10^{-3} noise while usi...

  2. Strictly Local Tile-Code Architectures on Two-Dimensional Planar Lattices

    quant-ph 2026-07 accept novelty 7.0

    Routed tile codes on a 2D nearest-neighbor grid achieve circuit-level thresholds of 0.11%-0.13% under SI1000 noise and become more qubit-efficient than the surface code below a physical error rate of 0.08%.

  3. Nearest-neighbour gates are all you need: High-rate quantum low-density parity-check codes on a planar grid

    quant-ph 2026-06 unverdicted novelty 7.0

    Presents planar open-boundary quantum LDPC codes with nearest-neighbor iSWAP-based syndrome extraction that outperform rotated surface codes in code-efficiency and logical error rate on finite instances like [[323,14,15]].

  4. Placing and routing quantum LDPC codes in multilayer superconducting hardware

    quant-ph 2025-07 unverdicted novelty 7.0

    HAL heuristic produces explicit layouts for bivariate bicycle, tile, radial, and Tanner qLDPC codes on multilayer superconducting hardware, demonstrating that open-boundary designs reduce hardware demands with only mo...

  5. Bunny Codes: Broadening Superconducting Quantum Error Correction Capability through Advanced Control Engineering

    quant-ph 2026-06 unverdicted novelty 6.0

    Bunny codes are qLDPC codes found via exhaustive search that achieve ~3x higher code rate than toric codes (periodic) and ~2x over rotated surface codes (open) when using CNOT+CXSWAP on nearest-neighbor connectivity, ...

  6. Optimising Quantum Error Correction Using Morphing Circuits

    quant-ph 2026-04 unverdicted novelty 6.0

    Morphing circuits optimize syndrome extraction for Abelian 2BGA and other QEC codes, yielding new circuits with improved parameters, connectivity, and stability against measurement errors.