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arxiv: 2605.26757 · v1 · pith:2ITS7QZ5 · submitted 2026-05-26 · quant-ph

Practical Entanglement Distillation Protocols with Quadratic Error Suppression

Elisa B\"aumer Marty This is my paper

Reviewed by Pith T0 review T1 audit T2 compute T3 formal T4 kernel 2026-06-29 17:34 UTCgrok-4.3pith:2ITS7QZ5record.jsonopen to challenge →

classification quant-ph
keywords entanglement distillationmodular quantum computingquadratic error suppressioninter-module operationssuperconducting processors
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The pith

A two-qubit-per-module protocol suppresses inter-module errors quadratically by reusing the noisy link with clean local gates.

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

The paper establishes practical entanglement distillation protocols for modular quantum hardware in which local operations inside a module are far more reliable than the entangling operations that connect modules. It replaces the standard LOCC model with one that permits repeated application of the same noisy inter-module gate during the protocol. The central protocol uses only two qubits per module and converts the dominant inter-module noise into quadratic suppression. Simulations and experiments on superconducting processors show this approach is more space- and time-efficient than prior small-scale distillation methods while achieving the same quadratic scaling.

Core claim

The authors design small-scale distillation protocols that minimize both qubit count and circuit depth in a modular setting. Their main protocol requires only two qubits per module yet achieves quadratic error suppression of inter-module errors when local operations have substantially lower error rates. The protocol is shown to outperform existing small-scale methods in space and time overhead and to deliver the best performance in both numerical simulations and hardware experiments on noisy links of current superconducting processors.

What carries the argument

The two-qubit-per-module distillation circuit that interleaves repeated uses of the noisy inter-module entangling gate with high-fidelity local operations and measurements to produce quadratic suppression of inter-module errors.

If this is right

  • Modular architectures can trade extra uses of the noisy link for quadratic improvement in link fidelity without large qubit overhead.
  • Space-optimal quadratic suppression becomes feasible at the scale of two qubits per module rather than requiring larger registers.
  • Distillation can serve as a practical primitive for overcoming noisy inter-module connections before full fault tolerance is reached.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same repeated-gate approach could be adapted to multi-module networks where each pair of modules shares a noisy link.
  • Protocols of this form might reduce the overhead of connecting dilution refrigerators or separate chips in near-term hardware.
  • The quadratic scaling suggests that further rounds of distillation could reach higher-order suppression with modest additional resources.

Load-bearing premise

Local operations inside each module have substantially lower error rates than the inter-module entangling operations.

What would settle it

An experiment that measures the distilled entanglement fidelity as a function of the raw inter-module gate error rate and finds that the suppression is no longer quadratic once local error rates become comparable to inter-module error rates.

Figures

Figures reproduced from arXiv: 2605.26757 by Elisa B\"aumer Marty.

Figure 1
Figure 1. Figure 1: FIG. 1: Existing protocols. Blue operations are local, red operations are noisy inter-module operations. [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Our new efficient protocols. Blue operations are local, red operations are noisy inter-module [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Simulations comparing the output error of the different protocols for varying inter-module error [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Experimental results comparing the different protocols. [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Implementation details of the experiments. [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
read the original abstract

Near-term and early fault-tolerant quantum computing architectures are expected to exhibit highly non-uniform error rates. In particular, local operations within a chip can be substantially more reliable than operations connecting different chips or dilution refrigerators. Such inter-module operations can therefore become a dominant bottleneck, even when quantum error correction is applied. Entanglement distillation provides a natural way to trade additional operations and qubits for higher-fidelity entanglement. Standard distillation protocols, however, are usually formulated in an LOCC resource model, in which several noisy Bell pairs are generated initially and all subsequent processing consists only of local operations and classical communication. Here, we consider a generalized model tailored to modular quantum computing hardware, in which the two modules have access to high-fidelity local operations and to repeated uses of the same noisy inter-module entangling operation during the protocol. We develop practical small-scale entanglement distillation protocols designed to minimize both space and time overhead. Remarkably, our main protocol requires only two qubits per module, yet achieves quadratic error suppression of inter-module errors, assuming local operations are much cleaner. Compared with existing small-scale protocols, our space-optimal protocol provides more space- and time-efficient quadratic error suppression and achieves the best performance in our simulations and experiments on noisy links of current superconducting quantum processors. These results suggest that inter-module-gate-assisted entanglement distillation can be a practical primitive for overcoming noisy links in modular quantum computing architectures.

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.

Referee Report

0 major / 2 minor

Summary. The manuscript develops entanglement distillation protocols for modular quantum computing architectures featuring non-uniform error rates, where local intra-module operations are high-fidelity but inter-module entangling gates are noisy. The central contribution is a space-optimal protocol using only two qubits per module that achieves quadratic suppression of inter-module errors by repeated use of the same noisy link, under the explicit assumption that local operations are substantially cleaner. The work claims this protocol is more space- and time-efficient than prior small-scale protocols and demonstrates superior performance in simulations and experiments on noisy links of current superconducting processors.

Significance. If the quadratic suppression result holds under the stated error model, the protocols could provide a practical primitive for mitigating noisy inter-module links in near-term modular systems. The explicit conditioning on cleaner local operations, the minimal two-qubit overhead, and the experimental validation on superconducting hardware are strengths that enhance applicability. The generalized resource model (beyond standard LOCC) and focus on both space and time overhead represent useful advances for hardware-aware protocol design.

minor comments (2)
  1. The abstract states that the main protocol 'achieves quadratic error suppression' but the main text should include an explicit statement of the error model (e.g., depolarizing or amplitude-damping on inter-module gates) and the precise definition of the quadratic scaling in the first results section.
  2. Table or figure comparing overheads with prior protocols (mentioned in the abstract) would benefit from an additional column listing the number of inter-module gate uses per distilled pair to make the time-efficiency claim immediately verifiable.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of the manuscript, recognition of the practical value of the two-qubit protocols under the stated error model, and recommendation for minor revision. No major comments were provided in the report.

Circularity Check

0 steps flagged

Derivation is self-contained with no circular reductions

full rationale

The paper presents a new entanglement distillation protocol for modular architectures that achieves quadratic suppression of inter-module errors under the explicitly stated assumption that local operations are substantially cleaner. This assumption is called out in the abstract as the operating regime and is not derived from or equivalent to the protocol's output performance. No self-definitional steps, fitted inputs renamed as predictions, or load-bearing self-citations appear in the claims; the central result is a constructive protocol whose properties follow from its design in the given error model rather than reducing to its own inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central performance claim rests on the domain assumption that local gate errors are negligible compared with inter-module errors; no free parameters or invented entities are visible in the abstract.

axioms (1)
  • domain assumption Local operations have substantially lower error rates than inter-module entangling operations.
    Explicitly invoked in the abstract to justify quadratic suppression.

pith-pipeline@v0.9.1-grok · 5767 in / 1036 out tokens · 31115 ms · 2026-06-29T17:34:35.903155+00:00 · methodology

discussion (0)

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Reference graph

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