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CHSH Violations using Dynamic Circuits

T0 review · 4 major / 5 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read On chains beyond ten qubits, dynamic circuits preserve more non-classical correlation than SWAP-based CNOTs.

desk verdict Useful distance-dependent CHSH dataset for dynamic vs unitary CNOTs, but the post-selection filter inflates the post-processed claim and the boundary results lack statistical support. read the letter →

arxiv 2504.18429 v2 pith:2PSXXDD2 submitted 2025-04-25 quant-ph

Jean-Baptiste Waring , Christophe Pere , Sébastien Le Beux This is my paper · ORCID
classification quant-ph
keywords CHSHinequalityBellstatedynamiccircuitsLAQCCentanglementpreservationmid-circuitmeasurementNISQsuperconductingqubits
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper reports an experimental comparison of three ways to generate a Bell state between two distant qubits on a 127-qubit superconducting processor: a unitary CNOT implemented by moving one qubit through SWAP gates, a dynamic circuit that uses mid-circuit measurements and classical feedforward to implement the CNOT remotely, and a post-processed version of the dynamic circuit that keeps only shots where the intervening ancillas would not have needed corrections. Using the CHSH parameter $S$ as a distance-dependent measure of entanglement quality, the authors find that the unitary approach starts near $|S|\approx 2.64$ but falls below the classical bound $|S|=2$ beyond about six qubits, while the dynamic approach decays more slowly and yields higher $|S|$ than the unitary one for distances beyond roughly ten qubits. The post-processed approach gives the highest values throughout, staying above $|S|=2$ up to 13 qubits. A sympathetic reader would take this as evidence that dynamic-circuit-style routing can preserve long-range non-classical correlations better than SWAP chains, and that on current hardware the remaining bottleneck is the cost of mid-circuit measurement and feedforward rather than the dynamic-circuit construction itself.

What carries the argument

The load-bearing mechanism is the LAQCC-style dynamic CNOT: a chain of Bell pairs prepared among ancilla qubits, mid-circuit measurements on two ancilla registers $(z,x)$, and classical feedforward of the measured bits to decide whether $X$ or $Z$ corrections are applied. The post-processed variant deletes the feedforward and instead filters the final measurements, keeping shots where the XOR of the $z$ register and the XOR of the $x$ register are both zero. The CHSH parameter, computed from measured expectation values of $ZZ$, $ZX$, $XZ$, and $XX$ across a sweep of the rotation angle $\phi$, serves as the metric that quantifies how much non-classical correlation survives at each qubit separation.

What would settle it

Compute $S$ separately for each ancilla-XOR outcome bin and check whether it varies across bins; if the zero-XOR subspace is not representative, the per-bin values will differ beyond statistical error, while an unbiased filter would show bin-independent $S$.

Watch

Extended reading notes

Core claim

The central discovery is that dynamic circuits mitigate the distance-dependent degradation of entanglement more effectively than unitary SWAP-based routing on this hardware, even though they underperform at short distances. At a 12-qubit separation the maximum CHSH value of the dynamic implementation is about 0.12 higher than the unitary implementation ($\approx 1.39$ versus $\approx 1.27$), while the post-processed value sits near the classical bound at $\approx 2.01$. The post-processed implementation, which removes the feedforward and mid-circuit measurement overhead by filtering on the ancillary registers, achieves the highest max($|S|$) values at every measured distance and maintains violations ($|S|>2$) up to 13 qubits. The authors interpret the gap between the dynamic and post-processed curves as a quantitative measure of the feedforward and measurement overhead that currently prevents dynamic circuits from reaching their theoretical potential.

Load-bearing premise

The load-bearing premise is that keeping only shots where the XOR of the ancilla $z$-register and the XOR of the ancilla $x$-register are both zero gives an unbiased estimate of what an ideal dynamic circuit with perfect feedforward would produce; if those discarded shots are systematically different, the post-processed CHSH values are inflated and the reported feedforward overhead is overstated.

Editorial extensions

If this is right

  • Algorithm designers on connectivity-limited hardware can expect dynamic routing to become the better choice for long-distance entangling gates, with a crossover on this processor around 10–11 qubits.
  • Faster mid-circuit measurement and classical feedforward should move that crossover to shorter distances and lift the dynamic curve toward the post-processed curve.
  • The post-processed curve is a practical upper bound for what a noiseless dynamic circuit on this hardware could achieve, so the gap between the two curves quantifies the feedforward overhead.
  • CHSH violations can serve as a complementary benchmark to fidelity for evaluating entanglement-preserving routing strategies on near-term devices.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the zero-XOR filter is unbiased, the dynamic-versus-post-processed gap isolates the combined cost of mid-circuit measurement errors, feedforward latency, and conditional-gate errors; repeating the measurement on a processor with faster feedforward and checking whether the gap shrinks would test this decomposition.
  • The same experimental protocol could be applied to other connectivity-limited architectures, using only calibration data to predict the distance at which dynamic routing overtakes SWAP-based routing.
  • Because post-processing discards shots exponentially with the number of ancillas, the post-processed advantage likely degrades at larger separations than the 15-qubit range tested, so extrapolating beyond 13 qubits is unsafe.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper reports an experimental comparison of three ways to implement a long-range CNOT for Bell-state preparation on the 127-qubit IBM Quantum Eagle processor ibm_quebec: a unitary SWAP-based implementation, a dynamic circuit with mid-circuit measurements and classical feedforward, and a post-processed version that omits the feedforward corrections. Entanglement quality is quantified by the maximum CHSH parameter max(|S|) obtained from a phase sweep. The central claims are that dynamic circuits preserve distance-dependent entanglement better than unitary circuits beyond roughly 10 qubits, that the post-processed implementation gives |S| > 2 up to 13 qubits, and that the gap between dynamic and post-processed results quantifies the overhead of mid-circuit measurement and feedforward on current hardware. The authors acknowledge the locality loophole and state that the post-processing approach is not scalable.

Significance. If the central comparison were sound, this would be a useful experimental benchmark: it uses a direct, parameter-free CHSH metric on a programmable general-purpose processor, spans a wide range of qubit separations, and complements prior fidelity-based studies of dynamic circuits. The paper is transparent about the locality loophole and the non-scalability of the post-processing route, and it reports raw-shot statistics with no fitted free parameters. However, the main quantitative claims currently rest on a post-selection procedure that is not an unbiased proxy for ideal feedforward, and the boundary claims (|S| > 2 at 13 qubits, dynamic-over-unitary advantage beyond 10 qubits) are not supported with statistical significance. These issues are load-bearing, so the manuscript needs major revision before the stated conclusions can be accepted.

major comments (4)
  1. [Section III.B.3 and Fig. 2(d)] The post-processing filter is not an unbiased emulation of ideal feedforward. The ancilla parities are syndrome bits of the LAQCC protocol; retaining only shots with zero XOR in both ancilla registers discards shots in which a data-qubit error would have triggered a feedforward correction. The retained subensemble is therefore a heralded conditional state, not the unconditional output of a dynamic circuit with ideal feedforward. This is analogous to a detection-loophole selection in a Bell test: the CHSH value of the retained subensemble can exceed 2 even when the unconditional correlations are classical. Consequently, the statement that the post-processed approach 'yields the highest CHSH values' and the interpretation in Section V.A that the dynamic-versus-post-processed gap measures feedforward overhead are not justified. The authors should reanalyze all shots by classically propagating the measured parities as Pauli-frame corrections to the final data-qubit outcomes, or explicitly present the post-selected results as conditional/error-detected and refrain from using them as a proxy for ideal dynamic circuits.
  2. [Section IV.B and Fig. 3(a)] The boundary claims are not supported statistically. At 13 qubits the reported mean max(|S|) is approximately 2.01, which is within the noise of the classical bound 2, and the 12-qubit dynamic-versus-unitary difference is approximately 0.12 (1.39 versus 1.27). No confidence intervals, standard errors, or hypothesis tests are reported for the n = 20 repetitions, so statements such as 'demonstrating improved distance-dependent entanglement preservation' and '|S| > 2 up to 13 qubits' are not quantitatively established. The authors should report per-distance means with confidence intervals and perform a significance test for (i) max(|S|) > 2 at each distance and (ii) dynamic max(|S|) > unitary max(|S|) beyond 10 qubits.
  3. [Section IV.A] The claim that the retained fraction 'decreases exponentially with the number of ancillary qubits' is inconsistent with the parity-based filter defined in Section III.B.3 and Fig. 2(d). If the filter is the overall XOR of the z-register and the overall XOR of the x-register, then in the ideal case each parity is 0 with probability 1/2, so the retention probability is about 1/4 independent of distance. If the actual filter instead requires a particular per-ancilla pattern, that stronger post-selection must be stated explicitly, and its effect on the reported shot statistics and on the CHSH estimate must be quantified. As written, the text cannot support the claimed exponential decay or the assertion that 10,000 shots per observable remain sufficient at the largest distances.
  4. [Section IV.B and Abstract] The cross-over claim that dynamic circuits outperform unitary circuits 'beyond 10 qubits' is weakened by the observation that at those distances both implementations are far below the classical bound (for example, dynamic max(|S|) is about 1.43 at 11 qubits and about 1.39 at 12 qubits). Reporting this as 'improved distance-dependent entanglement preservation' requires showing that the small differences are not due to calibration drift, crosstalk, or other distance-correlated hardware effects. A per-distance calibration and drift characterization, or at least a discussion of how the 20 repetitions were distributed in time, is needed to make this claim credible.
minor comments (5)
  1. [Section I] The introduction states that the unitary approach maintains |S| > 2 up to 7 qubits, while Section IV.B says 'below the classical bound for distances beyond approximately 6 qubits'; these threshold statements should be made consistent.
  2. [Section I] There is a typo, 'Circtuits', in the introduction; it should read 'Circuits'.
  3. [Fig. 3(a)] The horizontal axis of Fig. 3(a) appears to be a path length along selected hardware qubits rather than physical distance; the text should define 'qubit distance' explicitly and explain the non-uniform gaps in the axis labels.
  4. [Section III.C.2] The use of M3 readout mitigation is described only for final measurement outcomes; it would be helpful to state explicitly whether mid-circuit measurement errors on ancillary qubits are also corrected or characterized, since these dominate the dynamic-circuit comparison.
  5. [Section IV.A] The sentence 'To ensure statistical robustness, the entire experiment is repeated multiple times' and the later statement 'calculated from statistics over n = 20 sampled repetitions' are vague: the authors should report whether the 20 repetitions are independent runs on different calibration dates or repeated submissions within a single calibration window.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: direct hardware benchmark with external CHSH/LAQCC references and no fitted parameters.

full rationale

The paper makes no parametric fits and derives no theoretical quantities; its central result is a direct measurement of CHSH values for three circuit implementations on ibm_quebec. The LAQCC circuit identity is imported from external prior work ([5], [7], [13]) not authored by the present authors, and CHSH is an external standard benchmark. No equation is defined in terms of another equation's output, and no fitted input is renamed as prediction. The only step that could resemble circularity is the post-processing filter that retains zero-parity ancilla shots and labels it as the ideal no-correction branch (Section III.B.3); even if this filter were biased as a proxy for ideal feedforward, that is an empirical validity concern, not a logical reduction of the paper's claim to its inputs. The paper also discloses the locality loophole (Section V.C) and non-scalability of post-processing (Section IV.A), further indicating the claims are presented as measurements with caveats rather than as derived consequences. Therefore no circular step can be quoted, and the score is 0.

Assumptions & free parameters 0 free parameters · 7 assumptions · 0 invented entities

The paper introduces no new physical entities and fits no free parameters. It rests on standard quantum mechanics, the CHSH framework, prior LAQCC circuit identities, and hardware-specific assumptions about error mitigation and qubit selection. The most fragile of these is the post-selection unbiasedness assumption, which is explicitly stated in Section III.B.3.

assumptions (7)
  • standard math CHSH inequality: local realistic models satisfy |S| <= 2, while quantum mechanics allows up to 2*sqrt(2).
    Invoked in Section II.C to define the violation threshold and the quantum domain.
  • standard math The Bell state preparation with Hadamard and CNOT, followed by Ry(phi), produces the expected CHSH correlations.
    Section III.A; standard quantum mechanics for the measurement scheme.
  • domain assumption The LAQCC/dynamic circuit is logically equivalent to the unitary CNOT implementation.
    Taken from references [5] and [7]; Section II.A and III.B.2. The paper does not re-derive the equivalence.
  • domain assumption Retaining shots with zero XOR of the z-ancilla register and zero XOR of the x-ancilla register isolates the ideal no-correction case.
    Section III.B.3; load-bearing for the post-processed comparison, as discussed in the weakest assumption.
  • domain assumption M3 readout error mitigation correctly corrects assignment errors on this hardware.
    Section III.C.2; relies on the mthree package [23].
  • domain assumption Dynamical decoupling pulses do not introduce correlated errors that bias the comparison between the three implementations.
    Section III.C.2; the same settings are used for all three methods.
  • domain assumption The selected linear chain of qubits and the calibration data are representative for distance-dependent comparison.
    Section III.C.1; the chain is chosen based on calibration and the final layout is verified to match.

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Pith. "Pith review of CHSH Violations using Dynamic Circuits." pith.science (2026). https://pith.science/paper/2PSXXDD2

@misc{pith2026250418429,
  author       = {Pith},
  title        = {Pith review of: CHSH Violations using Dynamic Circuits},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2PSXXDD2}},
  note         = {Machine review of arXiv:2504.18429}
}
read the original abstract

Scalable quantum computing relies on high-quality, long-range entanglement, a challenge on noisy, near-term devices. The need for practical insights for near-term algorithm design calls for trade-offs exploration in implementing dynamic circuits on current hardware. In this work, we experimentally compare three CNOT implementations for generating Bell states across varying qubit separations on a 127-qubit IBM Quantum Eagle processor (ibm_quebec): a unitary (SWAP-based) approach, a dynamic approach with mid-circuit measurements and classical feedforward, and a post-processed approach. We use Clauser-Horne-Shimony-Holt (CHSH) inequality violations to quantify entanglement quality. We observe that, beyond 10 qubits, dynamic circuits lead to higher |S| values than the unitary approach, demonstrating improved distance-dependent entanglement preservation. The post-processed approach yields the highest CHSH values, reaching |S| > 2 up to 13 qubits. Our results underscore the critical need for faster classical feedforward and higher readout fidelity.

Figures

Figures reproduced from arXiv: 2504.18429 by the authors.

Figure 1
Figure 1. Conceptual space-time diagram of a CHSH test. Entanglement is [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Circuit diagrams, hardware, and qubit selection for the CHSH experiments. (a) Base CHSH circuit: Bell state preparation using Hadamard and CNOT gates, [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Experimental results of CNOT implementations for CHSH experiments across varying distances on the 127-qubit IBM Quantum Eagle processor [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

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