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arXiv:2607.19446

Decoder Comparability Across Quantum Software Stacks: Repeated-Round Surface and Digitized-GKP Syndrome Replay

Dennis Delali Kwesi Wayo, Chinonso Onah, Rodrigo Alves Dias, Leonardo Goliatt, Zaher Mundher Yaseen Sven Groppe

quant-phSubmitted Jul 21, 2026• Announced Jul 22, 2026• 0 citations
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Abstract

We present a contract-preserving, family-aware comparison of decoder behavior across four syndrome-generation stacks (PennyLane, Qiskit, Cirq, and a LiDMaS+ reference) under a fixed replay interface. Request streams from repeated-round surface-code and digitized-GKP circuits are replayed through BP, MWPM, and UF with matched controls. The unified matrix spans 24 cells and achieves line-level integrity: $24\,000$ request lines, $24\,000$ response lines, response ratio $=1.0$ in every cell, zero parse failures, and zero decoder-name mismatches. Fifteen warning-no-syndrome events occur only in GKP-Cirq rows. Within-family ordering is stable in both families ($\mathrm{BP}<\mathrm{MWPM}<\mathrm{UF}$); source-averaged flip counts are 2.435, 4.768, and 5.870 for surface and 1.595, 2.908, and 3.681 for GKP. Relative to MWPM, BP reduces mean intervention volume by $48.9\%$ in surface and $45.1\%$ in GKP. Source-vs-reference effects are family dependent, with larger coherent shifts in GKP. Source-bootstrap ranks remain unchanged, and hidden-truth sidecars add an outer-code logical-parity error-rate check in which UF has the largest source-mean rate in both families. The comparison is stack-aware, contract-verified, and avoids raw cross-family threshold-equivalence claims.

Related papers

A Unified Hardware-to-Decoder Architecture for Hybrid Continuous-Variable and Discrete-Variable Quantum Error Correction in LiDMaS+

Dennis Delali Kwesi Wayo, Chinonso Onah, Leonardo Goliatt +1 more

We present an architecture-level hardware-to-logical-to-decoder execution stack for hybrid continuous-variable and discrete-variable quantum error correction in LiDMaS+. Provider-native records are normalized into a single decoder IO contract and replayed under fixed controls across MWPM, UF, BP, and neural-MWPM. In a Xanadu case study using fixture inputs and sampled public datasets, replay integrity was complete: 108/108 fixture and 4000/4000 real-slice request-response lines, with zero request-parse errors, zero response-parse errors, and zero decoder-name mismatches. Under matched inputs, decoder behavior is clearly regime-dependent. For weighted fixture summaries, average flip count was 1.296 (MWPM), 1.296 (UF), 0.667 (BP), and 1.296 (neural-MWPM). For weighted real-data summaries, average flip count was 0.641 (MWPM), 0.741 (UF), 0.318 (BP), and 0.641 (neural-MWPM); corresponding nonempty-flip rates were 0.490, 0.490, 0.318, and 0.490. Across fixture data, BP reduced weighted correction volume by 48.6\% versus MWPM; across real slices, BP reduced weighted correction volume by 50.4\% versus MWPM and 57.1\% versus UF. Quality controls show the central interpretability tradeoff: BP is intervention-conservative but leaves higher residual burden, while MWPM-family decoders intervene more aggressively and clear more syndrome. Warning-no-syndrome rates remained decoder-invariant and dataset-driven (fixture weighted 0.259; real weighted 0.510), confirming preserved sparsity semantics from hardware input to logical correction. Re-running analysis stages reproduced identical SHA-256 artifacts, enabling deterministic study iteration. These results establish a practical benchmarking foundation for photonic GKP-oriented hardware programs where decoder policy must be selected as a function of operating regime.

quant-pharXiv:2604.15389•Apr 17, 2026•0 citations

Decoder Dependence in Surface-Code Threshold Estimation with Native Gottesman-Kitaev-Preskill Digitization and Parallelized Sampling

Dennis Delali Kwesi Wayo, Chinonso Onah, Leonardo Goliatt +1 more

We quantify decoder dependence in surface-code threshold studies under two matched regimes: Pauli noise and native GKP-style Gaussian displacement digitization. Using LiDMaS+ v1.1.0, we benchmark MWPM, Union-Find (UF), Belief Propagation (BP), and neural-guided MWPM with fixed seeds, identical sweep grids, and unified reporting across runs 06--14. At $d=5$ and $σ=0.20$, MWPM and UF define the Pareto frontier, with (runtime, LER) = (1.341 s, 0.2273) and (1.332 s, 0.2303); neural-guided MWPM is slower and less accurate (1.396 s, 0.3730), and BP is dominated (7.640 s, 0.6107). Crossing-bootstrap diagnostics are stable only for MWPM, with median $σ^\star_{3,5}=0.10$ (1911/2000 valid) and $σ^\star_{5,7}=0.1375$ (1941/2000 valid), while other decoders show no valid crossing samples. Dense-window scanning over $σ\in [0.08,0.24]$ returns NaN crossings for all decoders, confirming estimator- and window-sensitive threshold localization. Rank-stability and effect-size bootstrap analyses reinforce ordering robustness: BP remains rank 4, neural-guided MWPM rank 3, and MWPM-UF differences are small ($Δ_{\mathrm{MWPM-UF}}=-0.00383$, 95\% interval $[-0.0104,0.00329]$) across $σ\in [0.05,0.35]$. Threaded execution preserves statistical fidelity while improving throughput: $1.34\times$ speedup in Pauli mode and $1.94\times$ in native GKP mode, with mean $|Δ\mathrm{LER}|$ $6.07\times10^{-3}$ and $5.20\times10^{-3}$, respectively. We therefore recommend estimator-conditional threshold reporting coupled to runtime-fidelity checks for reproducible hardware-facing practical future decoder benchmarking workflows.

quant-pharXiv:2603.25757•Mar 27, 2026•0 citations

Auditing Syndrome-to-Decoder Mappings for Repetition, Surface, CSS, and Digitized-GKP Interfaces

Dennis Delali Kwesi Wayo, Chinonso Onah, Rodrigo Alves Dias +2 more

Quantum error-correction experiments increasingly require a verified interface between measured syndrome bits and decoder-native correction requests. We report a four-branch syndrome-to-decoder mapping audit spanning a five-data-qubit repetition code, a distance-five surface Z-check interface, a compact Steane CSS benchmark, and a digitized-GKP proxy. For the surface interface, an independent noiseless interpreter verifies 40/40 single-X syndrome columns and data-bit round trips, while a reversed-register negative control fails for all 40 targets. Sampled hardware and local-noise streams are then analyzed with exact binary minimum-weight representatives to separate mapping validity from noisy localization. The results establish a narrow interface-conformance claim, not a decoder benchmark, threshold estimate, or logical-QEC demonstration.

quant-pharXiv:2607.19447•Jul 22, 2026•0 citations

When to Skip Syndrome Extraction in Surface-GKP Codes

Vaughn Sohn, Changhun Oh

Fault-tolerant quantum error correction requires repeated syndrome extraction to address errors induced by the syndrome-extraction circuit itself. However, repeated syndrome extraction incurs significant overhead in terms of gate count and ancilla consumption (e.g., Gottesman-Kitaev-Preskill (GKP) states). Moreover, noisy syndrome extraction can itself inject additional errors into the data qubits. To address these issues, we propose a concrete adaptive skipping scheme for the surface-GKP code, a representative GKP-concatenated architecture, that uses analog information naturally generated during inner GKP correction. At each round, the scheme selects one of four actions: measuring both Z-type and X-type surface-code stabilizers, measuring only one type, or skipping both types and reusing previous syndromes. The decision is based on a reliability comparison between reusing the previous syndrome value and performing a new noisy syndrome extraction. Using circuit-level simulations, we show that the adaptive skipping scheme can reduce the number of surface-code stabilizer measurements while maintaining logical error rates comparable to or lower than those of the full-measurement baseline. The improvement is most pronounced when gate and measurement noise are larger than idle noise, so that avoiding unnecessary syndrome extraction reduces the noise injected into the code. These results indicate that analog information from inner GKP correction can be used not only to improve decoding but also to reduce the measurement overhead of outer-code syndrome extraction.

quant-pharXiv:2606.24469•Jun 24, 2026•0 citations

Very low overhead fault-tolerant quantum error correction with the surface-GKP code

Kyungjoo Noh, Christopher Chamberland, Fernando G. S. L. Brandão

Fault-tolerant quantum error correction is essential for implementing quantum algorithms of significant practical importance. In this work, we propose a highly effective use of the surface-GKP code, i.e., the surface code consisting of bosonic GKP qubits instead of bare two-dimensional qubits. In our proposal, we use error-corrected two-qubit gates between GKP qubits and introduce a maximum likelihood decoding strategy for correcting shift errors in the two-GKP-qubit gates. Our proposed decoding reduces the total CNOT failure rate of the GKP qubits, e.g., from $0.87\%$ to $0.36\%$ at a GKP squeezing of $12$dB, compared to the case where the simple closest-integer decoding is used. Then, by concatenating the GKP code with the surface code, we find that the threshold GKP squeezing is given by $9.9$dB under the the assumption that finite-squeezing of the GKP states is the dominant noise source. More importantly, we show that a low logical failure rate $p_{L} < 10^{-7}$ can be achieved with moderate hardware requirements, e.g., $291$ modes and $97$ qubits at a GKP squeezing of $12$dB as opposed to $1457$ bare qubits for the standard rotated surface code at an equivalent noise level (i.e., $p=0.36\%$). Such a low failure rate of our surface-GKP code is possible through the use of space-time correlated edges in the matching graphs of the surface code decoder. Further, all edge weights in the matching graphs are computed dynamically based on analog information from the GKP error correction using the full history of all syndrome measurement rounds. We also show that a highly-squeezed GKP state of GKP squeezing $\gtrsim 12$dB can be experimentally realized by using a dissipative stabilization method, namely, the Big-small-Big method, with fairly conservative experimental parameters. Lastly, we introduce a three-level ancilla scheme to mitigate ancilla decay errors during a GKP state preparation.

•Mar 11, 2021•9 citations

Circuit-level benchmarks of GKP-concatenated qLDPC Codes

Yuan Yao, Ruipeng Xing, Jianshuo Gao +1 more

Scalable fault-tolerant quantum error correction based on Gottesman-Kitaev-Preskill (GKP) codes requires finite-rate outer codes that can exploit analog GKP information under realistic circuit noise. However, quantum low-density parity-check (qLDPC) outer codes have not been systematically compared as candidates for circuit-level GKP concatenation. Here, we benchmark BB and tricycle codes using a unified simulation framework that progresses from code-capacity noise to repeated noisy syndrome extraction and schedule-resolved displacement propagation. Across all three noise models, analog-informed belief-propagation with ordered-statistics decoding (BP-OSD) yields higher finite-size crossing estimates than hard-decision decoding. In the full circuit model, the analog-informed crossings are \(σ_{\mathrm{th}}\simeq0.212\) for the selected BB sequence and \(0.142\) for the tricycle sequence, corresponding to squeezing requirements of approximately \(10.46\,\mathrm{dB}\) and \(13.94\,\mathrm{dB}\), respectively. These results show that analog GKP information continues to improve decoding under circuit-level noise. Under the common simulation assumptions used here, the selected BB sequence also yields a higher finite-size crossing estimate than the selected tricycle sequence.

quant-pharXiv:2609.35282•Sep 29, 2026•0 citations
We present a contract-preserving, family-aware comparison of decoder behavior across four syndrome-generation stacks (PennyLane, Qiskit, Cirq, and a LiDMaS+ reference) under a fixed replay interface. Request streams from repeated-round surface-code and digitized-GKP circuits are replayed through BP, MWPM, and UF with matched controls. The unified matrix spans 24 cells and achieves line-level integrity: 24 00024\,00024000 request lines, 24 00024\,00024000 response lines, response ratio =1.0=1.0=1.0 in every cell, zero parse failures, and zero decoder-name mismatches. Fifteen warning-no-syndrome events occur only in GKP-Cirq rows. Within-family ordering is stable in both families (BP<MWPM<UF\mathrm{BP}<\mathrm{MWPM}<\mathrm{UF}BP<MWPM<UF); source-averaged flip counts are 2.435, 4.768, and 5.870 for surface and 1.595, 2.908, and 3.681 for GKP. Relative to MWPM, BP reduces mean intervention volume by 48.9%48.9\%48.9% in surface and 45.1%45.1\%45.1% in GKP. Source-vs-reference effects are family dependent, with larger coherent shifts in GKP. Source-bootstrap ranks remain unchanged, and hidden-truth sidecars add an outer-code logical-parity error-rate check in which UF has the largest source-mean rate in both families. The comparison is stack-aware, contract-verified, and avoids raw cross-family threshold-equivalence claims.
We present an architecture-level hardware-to-logical-to-decoder execution stack for hybrid continuous-variable and discrete-variable quantum error correction in LiDMaS+. Provider-native records are normalized into a single decoder IO contract and replayed under fixed controls across MWPM, UF, BP, and neural-MWPM. In a Xanadu case study using fixture inputs and sampled public datasets, replay integrity was complete: 108/108 fixture and 4000/4000 real-slice request-response lines, with zero request-parse errors, zero response-parse errors, and zero decoder-name mismatches. Under matched inputs, decoder behavior is clearly regime-dependent. For weighted fixture summaries, average flip count was 1.296 (MWPM), 1.296 (UF), 0.667 (BP), and 1.296 (neural-MWPM). For weighted real-data summaries, average flip count was 0.641 (MWPM), 0.741 (UF), 0.318 (BP), and 0.641 (neural-MWPM); corresponding nonempty-flip rates were 0.490, 0.490, 0.318, and 0.490. Across fixture data, BP reduced weighted correction volume by 48.6\% versus MWPM; across real slices, BP reduced weighted correction volume by 50.4\% versus MWPM and 57.1\% versus UF. Quality controls show the central interpretability tradeoff: BP is intervention-conservative but leaves higher residual burden, while MWPM-family decoders intervene more aggressively and clear more syndrome. Warning-no-syndrome rates remained decoder-invariant and dataset-driven (fixture weighted 0.259; real weighted 0.510), confirming preserved sparsity semantics from hardware input to logical correction. Re-running analysis stages reproduced identical SHA-256 artifacts, enabling deterministic study iteration. These results establish a practical benchmarking foundation for photonic GKP-oriented hardware programs where decoder policy must be selected as a function of operating regime.
We quantify decoder dependence in surface-code threshold studies under two matched regimes: Pauli noise and native GKP-style Gaussian displacement digitization. Using LiDMaS+ v1.1.0, we benchmark MWPM, Union-Find (UF), Belief Propagation (BP), and neural-guided MWPM with fixed seeds, identical sweep grids, and unified reporting across runs 06--14. At d=5d=5d=5 and σ=0.20σ=0.20σ=0.20, MWPM and UF define the Pareto frontier, with (runtime, LER) = (1.341 s, 0.2273) and (1.332 s, 0.2303); neural-guided MWPM is slower and less accurate (1.396 s, 0.3730), and BP is dominated (7.640 s, 0.6107). Crossing-bootstrap diagnostics are stable only for MWPM, with median σ3,5⋆=0.10σ^\star_{3,5}=0.10σ3,5⋆​=0.10 (1911/2000 valid) and σ5,7⋆=0.1375σ^\star_{5,7}=0.1375σ5,7⋆​=0.1375 (1941/2000 valid), while other decoders show no valid crossing samples. Dense-window scanning over σ∈[0.08,0.24]σ\in [0.08,0.24]σ∈[0.08,0.24] returns NaN crossings for all decoders, confirming estimator- and window-sensitive threshold localization. Rank-stability and effect-size bootstrap analyses reinforce ordering robustness: BP remains rank 4, neural-guided MWPM rank 3, and MWPM-UF differences are small (ΔMWPM−UF=−0.00383Δ_{\mathrm{MWPM-UF}}=-0.00383ΔMWPM−UF​=−0.00383, 95\% interval [−0.0104,0.00329][-0.0104,0.00329][−0.0104,0.00329]) across σ∈[0.05,0.35]σ\in [0.05,0.35]σ∈[0.05,0.35]. Threaded execution preserves statistical fidelity while improving throughput: 1.34×1.34\times1.34× speedup in Pauli mode and 1.94×1.94\times1.94× in native GKP mode, with mean ∣ΔLER∣|Δ\mathrm{LER}|∣ΔLER∣ 6.07×10−36.07\times10^{-3}6.07×10−3 and 5.20×10−35.20\times10^{-3}5.20×10−3, respectively. We therefore recommend estimator-conditional threshold reporting coupled to runtime-fidelity checks for reproducible hardware-facing practical future decoder benchmarking workflows.
Quantum error-correction experiments increasingly require a verified interface between measured syndrome bits and decoder-native correction requests. We report a four-branch syndrome-to-decoder mapping audit spanning a five-data-qubit repetition code, a distance-five surface Z-check interface, a compact Steane CSS benchmark, and a digitized-GKP proxy. For the surface interface, an independent noiseless interpreter verifies 40/40 single-X syndrome columns and data-bit round trips, while a reversed-register negative control fails for all 40 targets. Sampled hardware and local-noise streams are then analyzed with exact binary minimum-weight representatives to separate mapping validity from noisy localization. The results establish a narrow interface-conformance claim, not a decoder benchmark, threshold estimate, or logical-QEC demonstration.
Fault-tolerant quantum error correction requires repeated syndrome extraction to address errors induced by the syndrome-extraction circuit itself. However, repeated syndrome extraction incurs significant overhead in terms of gate count and ancilla consumption (e.g., Gottesman-Kitaev-Preskill (GKP) states). Moreover, noisy syndrome extraction can itself inject additional errors into the data qubits. To address these issues, we propose a concrete adaptive skipping scheme for the surface-GKP code, a representative GKP-concatenated architecture, that uses analog information naturally generated during inner GKP correction. At each round, the scheme selects one of four actions: measuring both Z-type and X-type surface-code stabilizers, measuring only one type, or skipping both types and reusing previous syndromes. The decision is based on a reliability comparison between reusing the previous syndrome value and performing a new noisy syndrome extraction. Using circuit-level simulations, we show that the adaptive skipping scheme can reduce the number of surface-code stabilizer measurements while maintaining logical error rates comparable to or lower than those of the full-measurement baseline. The improvement is most pronounced when gate and measurement noise are larger than idle noise, so that avoiding unnecessary syndrome extraction reduces the noise injected into the code. These results indicate that analog information from inner GKP correction can be used not only to improve decoding but also to reduce the measurement overhead of outer-code syndrome extraction.
Fault-tolerant quantum error correction is essential for implementing quantum algorithms of significant practical importance. In this work, we propose a highly effective use of the surface-GKP code, i.e., the surface code consisting of bosonic GKP qubits instead of bare two-dimensional qubits. In our proposal, we use error-corrected two-qubit gates between GKP qubits and introduce a maximum likelihood decoding strategy for correcting shift errors in the two-GKP-qubit gates. Our proposed decoding reduces the total CNOT failure rate of the GKP qubits, e.g., from 0.87%0.87\%0.87% to 0.36%0.36\%0.36% at a GKP squeezing of 121212dB, compared to the case where the simple closest-integer decoding is used. Then, by concatenating the GKP code with the surface code, we find that the threshold GKP squeezing is given by 9.99.99.9dB under the the assumption that finite-squeezing of the GKP states is the dominant noise source. More importantly, we show that a low logical failure rate pL<10−7p_{L} < 10^{-7}pL​<10−7 can be achieved with moderate hardware requirements, e.g., 291291291 modes and 979797 qubits at a GKP squeezing of 121212dB as opposed to 145714571457 bare qubits for the standard rotated surface code at an equivalent noise level (i.e., p=0.36%p=0.36\%p=0.36%). Such a low failure rate of our surface-GKP code is possible through the use of space-time correlated edges in the matching graphs of the surface code decoder. Further, all edge weights in the matching graphs are computed dynamically based on analog information from the GKP error correction using the full history of all syndrome measurement rounds. We also show that a highly-squeezed GKP state of GKP squeezing ≳12\gtrsim 12≳12dB can be experimentally realized by using a dissipative stabilization method, namely, the Big-small-Big method, with fairly conservative experimental parameters. Lastly, we introduce a three-level ancilla scheme to mitigate ancilla decay errors during a GKP state preparation.
Scalable fault-tolerant quantum error correction based on Gottesman-Kitaev-Preskill (GKP) codes requires finite-rate outer codes that can exploit analog GKP information under realistic circuit noise. However, quantum low-density parity-check (qLDPC) outer codes have not been systematically compared as candidates for circuit-level GKP concatenation. Here, we benchmark BB and tricycle codes using a unified simulation framework that progresses from code-capacity noise to repeated noisy syndrome extraction and schedule-resolved displacement propagation. Across all three noise models, analog-informed belief-propagation with ordered-statistics decoding (BP-OSD) yields higher finite-size crossing estimates than hard-decision decoding. In the full circuit model, the analog-informed crossings are σth≃0.212σ_{\mathrm{th}}\simeq0.212σth​≃0.212 for the selected BB sequence and 0.1420.1420.142 for the tricycle sequence, corresponding to squeezing requirements of approximately 10.46 dB10.46\,\mathrm{dB}10.46dB and 13.94 dB13.94\,\mathrm{dB}13.94dB, respectively. These results show that analog GKP information continues to improve decoding under circuit-level noise. Under the common simulation assumptions used here, the selected BB sequence also yields a higher finite-size crossing estimate than the selected tricycle sequence.