{"id":"462f3596-6fc1-43ea-a374-079fabcb57a3","arxiv_id":"2505.17718","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Bias-preserving CZ gates plus small residual CNOT bias enable a 90% threshold improvement and up to 75% footprint reduction for the XZZX code in two-level qubits.","lead":"Two-level qubit platforms cannot use bias-preserving CNOT gates, but this paper shows bias-preserving CZ gates alone let the XZZX surface code exploit dephasing noise, raising the circuit-level threshold from 0.66% to 1.27% and cutting qubit counts by up to 75%. The authors introduce a hybrid biased-depolarizing noise model and back the claims with Stim and PyMatching simulations.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The 1.27% threshold rests on an unspecified residual-CNOT Pauli channel; the full 15-term error distribution is never given in the manuscript.","rationale":"The reader's weakest assumption is the availability and fidelity of native bias-preserving CZ gates. That is a real practical concern, but the paper is explicitly conditional on such gates existing, and the qualitative claim that CZs must be bias-preserving is supported by the Figure 2a versus 2b comparison. The more internal, quantitative soft spot is the residual-CNOT channel used to obtain the 1.27% threshold. Section IIIB advertises a 'more tailored' model, but the manuscript does not give the full Pauli error probabilities for the noisy CNOT; it only reports the ratio eta_CNOT. Since the matching decoder weights depend on the complete distribution, a channel with the same reported residual bias can produce materially different thresholds. This is exactly the kind of under-specified parameter that determines whether the central numerical claim holds. The paper does provide code on GitHub and uses a standard Stim plus PyMatching pipeline, which is real supporting evidence and makes the proposed check feasible. If the code contains a reasonable, well-documented CNOT channel and the threshold is insensitive to the alternative channels, the concern lands weakly and the conditional acceptance stands; if the threshold moves substantially, the headline quantitative claim needs revision.","tokens_in":29316,"tokens_out":15402,"duration_ms":134221,"concrete_test":"Obtain the exact CNOT error probabilities from the GitHub repository, or ask the authors for the 15-entry Pauli table used to generate the eta_CNOT curves. Then rerun the threshold simulation at eta_sys = 1000 with two alternative CNOT channels matched to the same total error rate p and the same eta_CNOT = 5: (i) Z weight placed only on ZI and IZ with no ZZ enhancement, and (ii) the channel obtained directly from the Pauli transfer matrix of Appendix B. If the threshold drops by more than roughly 0.1 percentage points, or falls below about 1.1%, the headline claim is sensitive to an unspecified modeling choice; if it stays near 1.2-1.27%, the concern is resolved.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The numerical headline (threshold ~1.27%, 90% improvement, footprint reductions) is produced by Section IIIB's 'more tailored' HBD model, in which CNOT gates carry the residual bias computed in Section II. But the manuscript never specifies the actual two-qubit Pauli channel used for those CNOTs: Appendix E defines only the generic HBD model with depolarizing CNOTs, and Section IIIB merely says that the tuple (eta_sys, eta_CNOT) uses 'the values obtained in Section II.' A residual bias eta_CNOT ~ 5 is not a complete channel: two channels can both have the same p_Z/(p_X+p_Y) ratio yet differ in how Z weight is split among ZI, IZ, and ZZ, and in the rates of X, Y, and mixed terms. The XZZX matching decoder is sensitive to exactly those details, because edge weights in the decoding graph depend on the full probability distribution over Pauli errors. The claimed jump from 0.93% (depolarizing CNOT) to 1.27% is attributed almost entirely to this residual channel, so an unspecified, or accidentally favorable, choice of the 15 error probabilities is the load-bearing element. The absence of threshold error bars makes it harder to tell whether the residual-CNOT gain is statistically robust.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper addresses whether biased noise can be leveraged for quantum error correction with two-level qubits despite the no-go theorem against bias-preserving CNOT gates. The authors use Lindblad simulations to show that CNOT gates retain a residual bias of about 5 for high system bias, and they argue that CZ gates can be implemented natively in a bias-preserving manner in several platforms. They introduce a hybrid biased-depolarizing (HBD) circuit-level noise model and numerically study the rotated XZZX surface code. The central results are that bias-preserving CZ gates are critical (threshold improves from 0.66% to 0.93% at high bias) and that including the residual CNOT bias raises the threshold to about 1.27% (a ~90% improvement over the standard depolarizing model), with qubit footprint reductions up to 75% at p=0.003. The paper also discusses implications for specific platforms and provides a public code repository.","tokens_in":29554,"tokens_out":8022,"duration_ms":61095,"significance":"If the quantitative claims hold, the paper resolves an important open question: it shows that the no-go theorem on bias-preserving CNOT gates does not preclude leveraging noise bias for two-level qubit QEC at the circuit level, provided native bias-preserving CZ gates are available. The introduction of the HBD noise model is a useful contribution, and the numerical study is extensive, with large Monte Carlo shot counts and a public code repository. The qualitative insight that residual CNOT bias helps is likely robust. However, the quantitative headline results depend on the exact residual-CNOT Pauli channel, which is not specified in the manuscript, limiting the ability to verify or reproduce the reported thresholds and footprint reductions.","major_comments":[{"comment":"The manuscript never specifies the two-qubit Pauli channel used for the residually biased CNOT gates in the circuit-level simulations. Section III B states that the tuple (η_sys, η_CNOT) uses the values obtained in Section II, but a bias ratio η_CNOT ≈ 5 does not uniquely determine the 15 non-identity two-qubit error probabilities; two channels with the same ratio can differ in the split among ZI, IZ, ZZ and in the non-Z rates. Since the minimum-weight perfect-matching decoder edge weights depend on the full error distribution, the threshold improvement from 0.93% (Figure 2a) to 1.27% (Table III) and the footprint reductions in Tables IV and V are directly dependent on this unspecified channel. Please provide the exact error probabilities (or a formula derived from the Lindblad simulation) for all Pauli terms in the CNOT channel, including the per-η_sys values, so that the simulations are reproducible.","section":"§III B, Appendix E"},{"comment":"The definition of the residual bias η_CNOT for a two-qubit channel is not given. It is unclear whether η_CNOT is the ratio of the total probability of errors with a Z on either qubit to the total of all other non-identity errors, or some other aggregation. Since the values of η_CNOT obtained from Figure 1 are used as input to the circuit-level simulations (Section III B), an unambiguous definition is required to interpret the mapping from η_sys to the CNOT noise channel.","section":"§II, Figure 1"}],"minor_comments":[{"comment":"The abstract quotes a 90% threshold improvement and the text of §III B 1 gives 91%, while the caption of Figure 3 says 93%. These numbers should be reconciled to a single consistent value derived from Table III.","section":"Abstract, §III B 1, Figure 3"},{"comment":"The statement that silicon spin qubits 'could operate well below threshold right now' overstates the present situation: Table I shows that for silicon spin qubits only the weak-exchange limit yields a bias-preserving CZ gate, and the required fidelity has not been experimentally demonstrated. The claim should be qualified accordingly.","section":"§IV"},{"comment":"The values of η_CNOT corresponding to each η_sys are only shown in a plot (Figure 1); a table of these values (or an equation for the fitting curve) would make the simulation inputs explicit and facilitate reproduction.","section":"§II, Figure 1"},{"comment":"There are typographical errors in the appendix titles and bibliography, e.g., 'Liebfried' for 'Leibfried' in Appendix C and 'tehcnologies' in the title of Appendix C.","section":"Appendix C and bibliography"},{"comment":"The paper would benefit from error bars or confidence intervals on the threshold estimates, or at least a plot of the raw logical error rates for the relevant distances, to support the statistical significance of the claimed threshold differences.","section":"§III B"}],"recommendation":"major_revision","confidential_remarks":"The main issue is the unspecified residual-CNOT Pauli channel, which is load-bearing for the headline threshold and footprint numbers. The authors appear to have the simulation code available, so providing the channel (or an explicit construction from the Lindblad simulation) should be straightforward. Once that is added, the paper may be suitable for publication after a careful check of the reported percentage improvements."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear [X],\n\nQuick take: this paper is worth engaging with, but the headline numbers are less solid than the prose suggests. The central claim—that native bias-preserving CZ gates, together with the modest residual bias that remains in CNOTs, let the XZZX surface code exploit dephasing bias even in two-level qubits where bias-preserving CNOTs are impossible—is well motivated and, on the qualitative level, supported by the numerics. That is a genuinely useful message for the community, and the HBD noise model is a reasonable step toward circuit-level analysis for these platforms.\n\nWhat's actually new: the residual CNOT bias computation (eta_CNOT ~5 for large system bias), the first circuit-level XZZX thresholds with non-bias-preserving CNOTs, and the clean comparison showing bias-preserving CZ gates are the critical ingredient (Fig 2a vs 2b). The footprint tables are a nice practical addition. Code is promised on GitHub, which helps reproducibility.\n\nThe soft spots are real, and they cluster on the quantitative claims. The 1.27% threshold in Section IIIB is generated by a CNOT Pauli channel that is never described. The paper tells you the residual bias ratio eta_CNOT, but a ratio does not fix the channel: two channels with the same p_Z/(p_X+p_Y) can differ in how Z weight is split among ZI, IZ, ZZ, and in the X, Y, and mixed terms. The MWPM decoder edge weights depend on the full distribution, and since the jump from 0.93% (depolarizing CNOT) to 1.27% is attributed to this residual channel, an unspecified—possibly accidentally favorable—choice of the 15 probabilities is load-bearing. No threshold error bars are given either, so it's hard to tell whether the residual-bias gain is statistically solid. This is not a fatal flaw; it's a reproducibility gap that a revision can close by publishing the actual Pauli error probabilities (or a precise pointer to the simulation code). The native-CZ assumption is also platform-dependent: for silicon spins only the weak-exchange limit qualifies, and that hasn't been demonstrated at the required fidelity.\n\nBottom line: this is a serious paper with a plausible central idea and a clear path to a strong version. It deserves peer review, but the referees should push hard for the missing channel specification and error bars.\n\nBest,\n[Your name]","headline":"A plausible and useful central idea, but the 1.27% threshold number depends on a residual CNOT error channel the paper never actually specifies.","tokens_in":30135,"tokens_out":3067,"would_cite":true,"duration_ms":25304,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["81P73","81P68"],"pacs":[],"model":"deepseek-v4-flash","headline":"Native bias-preserving CZ gates let the XZZX code exploit biased noise, raising its threshold from 0.66% to 1.27% and cutting qubit footprints by up to 75%.","keywords":["biased noise","XZZX surface code","circuit-level noise","bias-preserving CZ gate","two-level qubits","dephasing errors","quantum error correction","qubit footprint"],"falsifier":"Measure the full two-qubit Pauli error channel of a natively implemented CZ gate and of a CNOT gate in a dephasing-biased platform, such as weak-exchange silicon spin qubits or Rydberg atoms; if the CZ channel's ratio of Z errors to X/Y errors is near 1, or if the CNOT channel's residual bias falls well below $\\eta\\approx 5$, then the predicted 0.66% to 1.27% threshold jump and the 75% footprint reduction should fail to appear in a distance-scaling memory experiment.","tokens_in":29070,"feed_emoji":"🛡️","tokens_out":12190,"duration_ms":83123,"temperature":0.7,"pith_summary":"Quantum error correction tailored to biased noise works well in idealized code-capacity models, but a no-go theorem says that two-level qubits cannot have bias-preserving CNOT gates, which seemed to rule out circuit-level bias tailoring for most hardware. This paper argues that the bias can still be exploited if the syndrome extraction circuit's CZ gates are implemented natively in a bias-preserving way and if the unavoidable CNOT gates retain even a modest residual bias. Under the proposed hybrid biased-depolarizing circuit-level noise model, the rotated XZZX surface code's threshold rises from about 0.66% to 1.27% (a roughly 90% improvement), and the qubit footprint needed to reach Mega-, Giga-, and Teraquop error rates falls by up to about 75%. If the CZ gates are not bias-preserving, the threshold barely moves, so the native CZ implementation is the decisive ingredient.","feed_headline":"Native CZ gates push XZZX threshold to 1.27%","feed_subtitle":"Two-level qubits can use their natural dephasing bias after all, cutting qubit counts by up to 75 percent.","key_machinery":"The load-bearing object is the hybrid biased-depolarizing (HBD) circuit-level noise model, which classifies each syndrome-extraction element as either bias-preserving or depolarizing: native CZ gates are followed by two-qubit Pauli noise with bias $\\eta$ (pure dephasing errors $\\eta$ times more likely than the others), while CNOT, Hadamard, preparation, and measurement are followed by depolarizing or symmetric noise, with every element failing at the same rate $p$. The second pillar is a Lindblad master-equation computation of the CNOT noise channel for the interaction $H_{\\mathrm{CNOT}} = V[(\\mathbb{I}+Z)/2\\otimes \\mathbb{I} + (\\mathbb{I}-Z)/2\\otimes X]$, which shows that the phase-flip bias is reduced but not removed, saturating near $\\eta_{\\mathrm{CNOT}}\\approx 5$ for system bias above $\\eta\\sim 1000$. The XZZX syndrome extraction pattern (XZZX rather than ZXXZ) is then chosen so that the bias-preserving CZ gates carry most of the syndrome extraction and the residually biased CNOT gates boost the overall biased noise, which is what moves the threshold.","core_discovery":"The paper establishes that the no-go theorem for bias-preserving CNOT gates does not, by itself, prevent two-level qubits from leveraging biased noise in quantum error correction. The key discovery is that bias-preserving CZ gates are sufficient, provided they are performed natively in a way that commutes with the dominant dephasing channel, and that CNOT gates still carry a residual bias that saturates near $\\eta_{\\mathrm{CNOT}}\\approx 5$. With these ingredients, the rotated XZZX surface code under the proposed hybrid biased-depolarizing circuit-level noise model reaches a threshold of about 1.27% for system bias $\\eta\\geq 1000$, compared with 0.66% for standard depolarizing circuit-level noise; when the CZ gates are depolarizing, the threshold saturates near 0.7%. Footprint estimates at physical error rate $p=0.003$ show reductions of 57% up to 76% for system biases of $\\eta\\geq 10$, and at $p=0.001$ the reductions are between 33% and 54%.","pith_inferences":["If a platform's CNOT pulses preserve more than the $\\eta_{\\mathrm{CNOT}}\\approx 5$ seen for the paper's specific interaction Hamiltonian, the threshold gains would be larger than the 1.27% reported here, making the residual CNOT bias a design target rather than a fixed limitation.","At realistic non-identically distributed error rates, where single-qubit Hadamard gates fail much less often than two-qubit gates, the CZ-only compilation's extra Hadamard layers would cost less than in the equal-rate HBD model, so the 0.53% to 0.8% result is likely a conservative estimate for real devices.","The same design rule, use native ZZ-type interactions for syndrome extraction and avoid compiling CZ through CNOT plus Hadamard, should transfer to bias-tailored qLDPC codes, whose circuit-level syndrome extraction is also entangling-gate-dominated, potentially giving even larger overhead reductions than the surface-code numbers.","A direct test on a single device would be to run the same XZZX memory experiment twice, once with a native bias-preserving CZ gate and once with a compiled depolarizing CZ gate; the paper predicts the depolarizing version's threshold should stay near 0.7% while the native version approaches 1.27%."],"forward_implications":["With bias-preserving CZ gates and residually biased CNOT gates, the rotated XZZX code's threshold rises from 0.66% for depolarizing circuit-level noise to about 1.27% at system bias $\\eta\\geq 1000$; in the HBD model without CNOT residual bias the improvement is smaller, from 0.66% to about 0.93%.","If CZ gates are implemented in a non-bias-preserving way, the threshold saturates near 0.7%, so the native bias-preserving CZ implementation is the decisive ingredient rather than the XZZX code alone.","At physical error rate $p=0.003$, the qubit footprint for Mega-, Giga-, and Teraquop operation falls by up to roughly 75% (for the Teraquop target, from 8977 qubits to as few as 2177) once the system bias exceeds $\\eta\\approx 100$.","At $p=0.001$, footprint reductions are smaller, between 33% and 54%, and the leading-order space-time cost, which scales as $d^3$ in the code distance, drops by 45% to 88% depending on bias and target regime.","When the CNOT gates are compiled as CZ plus Hadamard layers (the only-entangling-gate-is-CZ compilation), the threshold still improves, from about 0.53% to 0.8%, showing that the effect survives with CZ-only syndrome extraction circuits."],"supporting_citations":[{"why":"Defines the XZZX surface code and supplies the code-capacity biased-noise threshold baseline that motivates extending bias tailoring to circuit-level noise.","marker":"[4]"},{"why":"States the no-go theorem that bias-preserving CNOT gates cannot be built for finite-dimensional two-level qubits, the obstacle this paper works around.","marker":"[25]"},{"why":"Supplies the CNOT interaction Hamiltonian and the Pauli-transfer-matrix method used to compute the residual CNOT bias, as well as the bias-preserving gate framework.","marker":"[27]"},{"why":"Provides the practical XZZX code context with non-bias-preserving CNOT gates and the hook-error discussion used to choose the XZZX syndrome extraction pattern.","marker":"[26]"},{"why":"Supplies the p=0.003 state-of-the-art CZ gate error rate used as one of the two experimental operating points for the qubit-footprint projections.","marker":"[42]"},{"why":"Shows how Rydberg-blockade CZ gates can be made bias-preserving, one of the native implementations supporting the broad platform claim.","marker":"[28]"}],"fun_headline_variants":["Bias-preserving CZ gates lift XZZX threshold to 1.27%","Native CZ gates enable biased-noise QEC on two-level qubits","XZZX code hits 1.27% threshold with bias-preserving CZ","Two-level qubits leverage bias via native CZ gates","Threshold up to 1.27% with bias-preserving CZ on XZZX"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The gains rest on the availability of a native CZ gate whose noise channel remains strongly biased toward Z errors; if the CZ gate in a real device is depolarizing, for example because it is compiled from CNOT plus Hadamard or implemented with strong-exchange interactions, the threshold improvement essentially disappears.","fun_headline_variants_meta":{"raw":{"variants":["Bias-preserving CZ gates lift XZZX threshold to 1.27%","Native CZ gates enable biased-noise QEC on two-level qubits","XZZX code hits 1.27% threshold with bias-preserving CZ","Two-level qubits leverage bias via native CZ gates","Threshold up to 1.27% with bias-preserving CZ on XZZX"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00088,"raw_usage":{"total_tokens":3838,"prompt_tokens":1017,"completion_tokens":2821,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":633,"completion_tokens_details":{"reasoning_tokens":2717}},"tokens_in":633,"tokens_out":2821,"duration_ms":23740,"temperature":1.0,"reasoning_tokens":2717,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T14:42:09.293308+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the full two-qubit Pauli error channel of a natively implemented CZ gate and of a CNOT gate in a dephasing-biased platform, such as weak-exchange silicon spin qubits or Rydberg atoms; if the CZ channel's ratio of Z errors to X/Y errors is near 1, or if the CNOT channel's residual bias falls well below $\\eta\\approx 5$, then the predicted 0.66% to 1.27% threshold jump and the 75% footprint reduction should fail to appear in a distance-scaling memory experiment.","supporting_citations":[{"cited_title":"Coherent and non-unitary errors in ZZ-generated gates","cited_arxiv_id":"2304.14212","evidence_quote":"Supplies the p=0.003 state-of-the-art CZ gate error rate used as one of the two experimental operating points for the qubit-footprint projections."}],"review_version":1}