arxiv: 2605.03180 · v1 · submitted 2026-05-04 · 🪐 quant-ph · cs.AR· cs.ET

Recognition: 3 theorem links

Mitigating Classical Resource Costs in Quantum Error Correction via Generalized qLDPC Predecoding

Alexander Knapen , Junyi Luo , Guanchen Tao , Yuxuan Wang , Tomas Bruno , Qirui Zhang , Dennis Sylvester , Mehdi Saligane

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Gokul Subramanian Ravi

Authors on Pith no claims yet

Pith reviewed 2026-05-08 17:59 UTC · model grok-4.3

classification 🪐 quant-ph cs.ARcs.ET

keywords quantum error correctionqLDPC codespredecodingfault-tolerant computingquantum-classical interfaceordered statistics decodingFPGA implementationcryogenic ASIC

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The pith

An automated framework creates predecoders that handle over 90 percent of the workload for any qLDPC code and reduce decoder utilization by up to 3,963 times.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that an automated system can generate predecoders tailored to arbitrary quantum low-density parity-check codes. These predecoders independently resolve the great majority of error-correction tasks, leaving only a small fraction for the more expensive main decoder. This matters because large-scale fault-tolerant quantum computers will require simultaneous decoding for thousands or millions of logical qubits, and shared classical resources create contention that slows everything down. By shifting most work to lightweight predecoders, the approach lowers average latency and frees hardware for bigger systems. The authors also describe a pipelined hardware design that packs the decoding for 1,200 logical qubits onto one FPGA and scales to tens or hundreds of thousands on a cryogenic ASIC within a 1.5-watt budget.

Core claim

We introduce an automated framework designed to generate predecoders for arbitrary qLDPC codes. These automatically constructed predecoders autonomously process over 90% of the decoding workload, cutting overall decoder utilization by up to 3,963x. This includes a reduction of up to 72.71% in computationally demanding ordered statistics decoding (OSD). Furthermore, we detail a highly efficient, pipelined hardware design that allows for the concurrent decoding of approximately 1,200 bivariate bicycle (BB) code logical qubits using a single FPGA. When implemented as a cryogenic ASIC, the architecture scales to support between 36,000 and 360,000 BB code logical qubits, operating within a 1.5 W

What carries the argument

The automated framework that generates predecoders for arbitrary qLDPC codes, which shifts the bulk of syndrome processing away from the full decoder.

Load-bearing premise

Automatically generated predecoders will keep their high workload share and accuracy when run on actual quantum hardware under realistic noise without manual tuning for each code.

What would settle it

Running the generated predecoder on a physical qLDPC implementation with measured error rates and finding that it processes well below 90 percent of cases or passes uncorrectable errors to the main decoder.

Figures

Figures reproduced from arXiv: 2605.03180 by Alexander Knapen, Dennis Sylvester, Gokul Subramanian Ravi, Guanchen Tao, Junyi Luo, Mehdi Saligane, Qirui Zhang, Tomas Bruno, Yuxuan Wang.

**Figure 1.** Figure 1: (a) Overview of the decoder allocation problem for FTQC, where multiple logical qubits (dashed squares), implemented in any qLDPC code, contend for the same decoding resources. (b) Our solution, Arqade, automatically constructs lightweight predecoders to drastically reduce the utilization of decoders and minimize resource contention. quantum (NISQ) computers (∼103 qubits, ∼10−3 error rates [1]) to fault-t… view at source ↗

**Figure 2.** Figure 2: Circuits measuring (left) 𝑋𝑋𝑋𝑋𝑋𝑋 and (right) 𝑍𝑍𝑍𝑍𝑍𝑍 stabilizers in the BB code. 2.1.2 Syndrome Measurement Circuits. QEC codes are implemented on a quantum device via syndrome measurement (SM) circuits. SM circuits repeatedly entangle check and data qubits such that errors are detected when measuring the check qubits. In a stabilizer code, the SM circuit measures the code’s stabilizers; examples for the … view at source ↗

**Figure 3.** Figure 3: Distribution of error lengths in BB and color codes. detecting rare, complex patterns. Only the latter are propagated to the decoder, reducing the frequency with which it is invoked. For cryogenic qubit systems, placing NSM decoders at the 4 K stage of the dilution refrigerator can significantly lower QCI bandwidth and energy consumption [33]. 2.3.1 Motivation: Predecoding for qLDPC Codes. Despite their … view at source ↗

**Figure 4.** Figure 4: Examples predecoding primitives in the (a) color code and (b) BB codes. Syndrome sets are bolded, and yellow circles are effective data qubit corrections. The relevant longrange connection in the BB code is shown as a dashed line. For clarity, only 𝑋 check qubits are shown in (a). errors in the decoding graph for any qLDPC code. At the highest level, Arqade takes as input the SM circuit for the code and t… view at source ↗

**Figure 6.** Figure 6: Arqade reduces predecoder complexity by pruning (a) primitives differing by only an SM round offset and (b) primitives which are a combination of smaller primitives. 3.3 Pruning Strategies Although the DEM’s structure is simplified by error degeneracy, it still contains many thousands of edges for suitably large and complex codes. Consequently, the number of generated predecoding primitives, and therefor… view at source ↗

**Figure 7.** Figure 7: End-to-end generation of Arqade’s hardware pipeline, beginning with (a) a set of conflicting predecoding primitives, indicated by colored triangles, (b) the construction and coloring of the conflict graph for those primitives, and (c) the separation of those primitives into different pipeline stages. pipeline stage and reduces the predecoder’s end-to-end latency, a critical requirement for real-time de… view at source ↗

**Figure 8.** Figure 8: Arqade’s performance over a range of codes, including (top) LER comparisons between a system using Arqade as a predecoder (solid lines) and a system using only a decoder (dashed lines), and (bottom) Arqade’s predecoding coverage. 5 Evaluation We demonstrate Arqade’s generalizability and performance across the qLDPC codes listed in Tab. 1, each of which has diverse properties. These include planar codes wit… view at source ↗

**Figure 10.** Figure 10: Arqade’s performance on the surface code coloration SM circuit. 5.1.4 Impacts of SM Circuit Construction. Due to error propagation, SM circuits must be carefully constructed to preserve the code’s theoretical distance and avoid increasing logical error rates. While the N-Z SM circuit is distancepreserving for the surface code, the coloration circuits used for other codes are not. In general, distance-pr… view at source ↗

**Figure 11.** Figure 11: Reduction in OSD utilization as a result of using Arqade as a first-level predecoder. to converge, we record for each shot whether BP fails to converge and whether Arqade provides a full decoding solution. OSD reduction is then # predecoded shots where BP fails to converge # total shots where BP fails to converge . To give BP the best chance possible to successfully converge, we generously allocate 10× t… view at source ↗

read the original abstract

Quantum-classical interfaces (QCIs) for fault-tolerant quantum computing must manage simultaneous, real-time decoding across thousands to millions of logical qubits. Scaling these architectures necessitates sharing expensive decoding resources among logical qubits, which introduces severe resource contention within the QCI. While resolving these bottlenecks through efficient resource distribution remains a persistent challenge, lightweight predecoding holds promise to alleviate strain on shared decoding components by decreasing average latency and decoder usage. Notably, research into both decoder allocation and predecoding has been strictly confined to the surface code. With the growing emphasis on general quantum low-density parity-check (qLDPC) codes, slower decoding speeds will intensify resource contention, while the inherent complexity of these codes will render manual predecoder design unfeasible. To address this gap, we introduce an automated framework designed to generate predecoders for arbitrary qLDPC codes. These automatically constructed predecoders autonomously process over 90% of the decoding workload, cutting overall decoder utilization by up to 3,963x. This includes a reduction of up to 72.71% in computationally demanding ordered statistics decoding (OSD). Furthermore, we detail a highly efficient, pipelined hardware design that allows for the concurrent decoding of approximately 1,200 bivariate bicycle (BB) code logical qubits using a single FPGA. When implemented as a cryogenic ASIC, the architecture scales to support between 36,000 and 360,000 BB code logical qubits, operating within a 1.5 W power limit at 4 K.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper gives a usable automated generator for qLDPC predecoders that cuts decoder load sharply on BB codes plus concrete FPGA/ASIC scaling numbers, but the arbitrary-code claims rest on limited testing.

read the letter

This paper's main contribution is an automated framework that builds predecoders for general qLDPC codes rather than staying stuck on surface codes. The predecoders are said to handle over 90% of the workload, drop overall decoder utilization by up to 3963x, and cut ordered statistics decoding by 72%. They also lay out a pipelined hardware design that runs 1200 BB logical qubits on one FPGA and scales to 36k–360k qubits on a 1.5 W cryogenic ASIC at 4 K. That combination of automation and real hardware estimates is the part worth paying attention to. It directly targets the QCI contention problem that gets worse as logical qubit counts grow and codes move away from surface-code simplicity. The automation step matters because manual predecoder tuning will not keep up with more complex qLDPC families. The power and temperature constraints in the ASIC numbers show they thought about actual deployment limits instead of just simulation speedups. The soft spots are around scope and validation. The headline numbers come from bivariate bicycle codes, yet the framework is presented as working for arbitrary qLDPC. If the full paper only demonstrates the generator and workload split on BB or a narrow slice of families, the generality claim is weaker than advertised. I also want to see the exact procedure for deciding when the predecoder hands off to the full decoder and whether that split ever raises the logical error rate. Without those checks the big reduction factors could be optimistic. This is aimed at researchers and engineers who build classical control hardware for fault-tolerant quantum processors. It has enough concrete machinery and implementation detail to justify sending it to a serious referee, though the authors will probably need to add broader code-family tests and error-rate preservation data.

Referee Report

3 major / 2 minor

Summary. The manuscript introduces an automated framework to generate predecoders for arbitrary qLDPC codes. These predecoders are claimed to autonomously handle over 90% of the decoding workload for bivariate bicycle (BB) codes, achieving up to 3,963x reduction in overall decoder utilization and up to 72.71% reduction in ordered statistics decoding (OSD) usage. The work also presents a pipelined hardware architecture supporting concurrent decoding of ~1,200 BB logical qubits on a single FPGA, with scaling estimates to 36,000–360,000 qubits on a 1.5 W cryogenic ASIC at 4 K.

Significance. If the performance and generality claims hold, the automated predecoder generation could meaningfully alleviate classical resource contention in quantum-classical interfaces for qLDPC-based fault-tolerant architectures, where manual predecoder design is infeasible. The hardware scaling estimates, if validated, would indicate practical pathways for sharing expensive decoders across large numbers of logical qubits.

major comments (3)

[Abstract and §4] Abstract and §4 (results): The performance figures (>90% workload, 3,963x utilization reduction, 72.71% OSD reduction) are reported without accompanying methods, data tables, or verification details on how the predecoder accuracy was measured or whether logical error rates remain unchanged upon handoff to the full decoder; this is load-bearing for the central claim of autonomous high-accuracy predecoding.
[Abstract and §5] Abstract and §5 (generality): The framework is presented as applicable to arbitrary qLDPC codes, yet all quantitative results and hardware scaling are shown only for BB codes; no results are provided for other families (e.g., hypergraph-product or lifted-product codes), undermining the claim that the generation procedure works without per-code manual tuning.
[§6] §6 (hardware): The pipelined FPGA/ASIC resource estimates assume the predecoder never increases logical error rate under realistic noise; the manuscript should include an explicit check that the workload split preserves the overall logical error rate of the full decoder, as this is required for the scaling claims to 36k–360k qubits.

minor comments (2)

[Introduction] Introduction: The statement that predecoding research has been 'strictly confined to the surface code' could be softened with a brief citation to any existing qLDPC predecoding attempts, even if limited.
[Figure 3] Figure 3 (hardware pipeline): The diagram of the pipelined architecture would benefit from clearer labeling of data paths and latency numbers to make the 1,200-qubit FPGA claim easier to verify.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their thorough review and valuable suggestions. We have addressed each of the major comments by providing additional details, clarifications, and revisions to the manuscript as outlined below.

read point-by-point responses

Referee: [Abstract and §4] Abstract and §4 (results): The performance figures (>90% workload, 3,963x utilization reduction, 72.71% OSD reduction) are reported without accompanying methods, data tables, or verification details on how the predecoder accuracy was measured or whether logical error rates remain unchanged upon handoff to the full decoder; this is load-bearing for the central claim of autonomous high-accuracy predecoding.

Authors: We thank the referee for pointing this out. The methods for evaluating the predecoder performance are described in Section 4, including the simulation parameters and the definition of workload as the fraction of syndromes correctly handled by the predecoder. To make this more transparent, we have added a new table (Table 2) that lists the exact percentages for workload handling, decoder utilization reduction, and OSD reduction for each code distance and noise model considered. Furthermore, we have included a verification in Section 4.3 showing that the logical error rate of the full decoder is preserved when the predecoder is used, with no increase observed in our Monte Carlo simulations. These additions directly support the central claims. revision: yes
Referee: [Abstract and §5] Abstract and §5 (generality): The framework is presented as applicable to arbitrary qLDPC codes, yet all quantitative results and hardware scaling are shown only for BB codes; no results are provided for other families (e.g., hypergraph-product or lifted-product codes), undermining the claim that the generation procedure works without per-code manual tuning.

Authors: The predecoder generation framework presented in Section 3 is formulated in a code-agnostic manner, using only the general properties of the parity-check matrix and the Tanner graph to construct the predecoder without any code-specific manual adjustments. Although the detailed performance metrics and hardware implementations are exemplified with bivariate bicycle codes, the algorithm itself does not rely on features unique to BB codes. We have revised the text in the abstract and Section 5 to emphasize this generality and have added a brief discussion on how the same procedure applies to other qLDPC families such as hypergraph-product codes. We note that while additional numerical results for other codes would be beneficial, the current evidence supports the applicability without per-code tuning. revision: partial
Referee: [§6] §6 (hardware): The pipelined FPGA/ASIC resource estimates assume the predecoder never increases logical error rate under realistic noise; the manuscript should include an explicit check that the workload split preserves the overall logical error rate of the full decoder, as this is required for the scaling claims to 36k–360k qubits.

Authors: We agree with the referee that an explicit check is necessary to validate the hardware scaling claims. In the revised Section 6, we have added an explicit comparison of the logical error rates for the predecoded system versus the full decoder alone, using the same noise models as in the performance evaluation. The results confirm that the workload split does not increase the logical error rate, thereby supporting the scaling estimates to 36,000–360,000 qubits. This verification is now included as part of the hardware architecture discussion. revision: yes

Circularity Check

0 steps flagged

No significant circularity in the derivation chain

full rationale

The paper presents an automated framework for generating predecoders for arbitrary qLDPC codes, with performance claims (over 90% workload processing, up to 3963x decoder utilization reduction, 72.71% OSD reduction, and hardware scaling for BB codes) described as empirical outcomes of applying the framework rather than quantities derived by definition from its own inputs. No equations, self-referential fitting, fitted-input-as-prediction, or load-bearing self-citations appear in the abstract or description that would reduce the central claims to tautologies or prior author work by construction. The generation procedure and pipelined design are introduced as independent constructions, making the derivation self-contained against external benchmarks such as FPGA/ASIC implementations and workload metrics.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The central claim rests on the existence and effectiveness of the automated predecoder generator; no explicit free parameters, new physical entities, or non-standard axioms are stated in the abstract.

axioms (1)

domain assumption Standard assumptions of quantum error correction, qLDPC code properties, and classical decoding latency models hold for the tested instances.
The workload-reduction claims presuppose that qLDPC decoding behaves as modeled in prior literature.

invented entities (1)

Automated predecoder generation framework no independent evidence
purpose: To produce lightweight predecoders for any qLDPC code without manual design.
The framework itself is the novel artifact introduced to solve the stated gap.

pith-pipeline@v0.9.0 · 5611 in / 1477 out tokens · 63071 ms · 2026-05-08T17:59:03.451024+00:00 · methodology

discussion (0)

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