Paper Citation Record · LEDGER

Learning Enables Exponential-to-Polynomial Sampling Overhead Scaling in Quantum Divide-and-Conquer for Tree-Structured Circuits

As of 10 August 2026, this Paper Citation Record lists 24 of 24 outbound references and 2 inbound Pith citation observations for arXiv:2512.19623.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2512.19623 v2

Coverage vector

measured 24 of 24 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-03T14:50:33.167332Z

measured 26 of 26 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-09T06:31:02.800959+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-01T14:05:00.410672Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: pith, observed 2026-07-04T00:49:18.709410Z

Reference resolution

24 of 24 outbound references displayed

verified exact0
verified fuzzy0
unresolved24
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 2fe03c38-d7ea-4c9b-bfd8-3affe0df9ab6 · outbound

This paper cites an unresolved cited work.

Learning Enables Exponential-to-Polynomial Sampling Overhead Scaling in Quantum Divide-and-Conquer for Tree-Structured Circuits Unresolved cited work

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-03T14:50:33.076442Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6750d48d-b28c-46d0-a4ff-ced3e018faa1 · outbound

This paper cites Denote byO Φ := Φ†(O)the corresponding effective observable, and let ˜OΦ be its Hermitian approximation satisfying∥ ˜OΦ −O Φ∥∞ ≤ϵ.

Learning Enables Exponential-to-Polynomial Sampling Overhead Scaling in Quantum Divide-and-Conquer for Tree-Structured Circuits Denote byO Φ := Φ†(O)the corresponding effective observable, and let ˜OΦ be its Hermitian approximation satisfying∥ ˜OΦ −O Φ∥∞ ≤ϵ

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-03T14:50:33.081551Z

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Unavailable: canonical work link unavailable.

Observation 13d0563d-643f-4b44-8c6b-5253c7180b5c · outbound

This paper cites Denote byO Φ := Φ†(O)the corresponding effective observable, and let ˜OΦ be its Hermitian approximation satisfying∥ ˜OΦ − OΦ∥∞ ≤ϵ.

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-03T14:50:33.086508Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cc0bbe96-ed0a-4c5a-8e34-17e3e1411914 · outbound

This paper cites an unresolved cited work.

Learning Enables Exponential-to-Polynomial Sampling Overhead Scaling in Quantum Divide-and-Conquer for Tree-Structured Circuits Unresolved cited work

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-03T14:50:33.090563Z

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Unavailable: canonical work link unavailable.

Observation eb41212e-f7b4-45a8-86ca-21550e59e823 · outbound

This paper cites an unresolved cited work.

Learning Enables Exponential-to-Polynomial Sampling Overhead Scaling in Quantum Divide-and-Conquer for Tree-Structured Circuits Unresolved cited work

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-03T14:50:33.094770Z

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Unavailable: canonical work link unavailable.

Observation 18020288-57e0-4f09-b938-0a85cfe6cb4c · outbound

This paper cites Theorem 4 (Performance guarantee for ˆOΦ,x).LetΦ :L(C din )→L(C dout )be an unknown CPTP map, and letO∈H(C dout )be a known Hermitian operator.

Learning Enables Exponential-to-Polynomial Sampling Overhead Scaling in Quantum Divide-and-Conquer for Tree-Structured Circuits Theorem 4 (Performance guarantee for ˆOΦ,x).LetΦ :L(C din )→L(C dout )be an unknown CPTP map, and letO∈H(C dout )be a known Hermitian operator

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-03T14:50:33.099208Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ddaa5df7-cf60-4a80-9f0b-57bdc2e89d10 · outbound

This paper cites L[ i=1 Ei # ≤ LX i=1 Pr(Ei).(S47) In our analysis, we often use the following equivalent inequality obtained by applying De Morgan’s law: 1− LX i=1 Pr [Ec i ]≤Pr.

Learning Enables Exponential-to-Polynomial Sampling Overhead Scaling in Quantum Divide-and-Conquer for Tree-Structured Circuits L[ i=1 Ei # ≤ LX i=1 Pr(Ei).(S47) In our analysis, we often use the following equivalent inequality obtained by applying De Morgan’s law: 1− LX i=1 Pr [Ec i ]≤Pr

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-03T14:50:33.103603Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6d414332-3cea-4e67-a42a-80a6511e0e0d · outbound

This paper cites RO k=1 M(k) apr(Mk) ! ρ # −tr.

Learning Enables Exponential-to-Polynomial Sampling Overhead Scaling in Quantum Divide-and-Conquer for Tree-Structured Circuits RO k=1 M(k) apr(Mk) ! ρ # −tr

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-03T14:50:33.107396Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6108e9bc-195e-4dd4-8790-088586ef3bea · outbound

This paper cites Assume that we have access only to devices whose size is bounded by the maximal number of qubits required to representρandΦ (i1,...,il) for each l= 1, ..., L.

Learning Enables Exponential-to-Polynomial Sampling Overhead Scaling in Quantum Divide-and-Conquer for Tree-Structured Circuits Assume that we have access only to devices whose size is bounded by the maximal number of qubits required to representρandΦ (i1,...,il) for each l= 1, ..., L

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-03T14:50:33.111204Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8efb8815-fb1d-4312-97bd-9b210fb1ce65 · outbound

This paper cites RO i1=1 ˜Mi1 ρ # ≤ϵ 0.(S474) Similarly, it is sufficient to take ϵ0 = ϵ 2 ,(S475) by the triangle inequality, ˆµ−tr.

Learning Enables Exponential-to-Polynomial Sampling Overhead Scaling in Quantum Divide-and-Conquer for Tree-Structured Circuits RO i1=1 ˜Mi1 ρ # ≤ϵ 0.(S474) Similarly, it is sufficient to take ϵ0 = ϵ 2 ,(S475) by the triangle inequality, ˆµ−tr

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-03T14:50:33.114916Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 46a3a0f2-a698-48e0-b0e4-fb03a13f9fbb · outbound

This paper cites First, we summarize the good-tomography event for the learning procedure at each depth.

Learning Enables Exponential-to-Polynomial Sampling Overhead Scaling in Quantum Divide-and-Conquer for Tree-Structured Circuits First, we summarize the good-tomography event for the learning procedure at each depth

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-03T14:50:33.118726Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0f115a98-a197-4593-bb5d-09fabe769d12 · outbound

This paper cites 7 at the wires betweenΦ i andΦ i+1 for i= 0, ..., L−1.

Learning Enables Exponential-to-Polynomial Sampling Overhead Scaling in Quantum Divide-and-Conquer for Tree-Structured Circuits 7 at the wires betweenΦ i andΦ i+1 for i= 0, ..., L−1

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-03T14:50:33.122431Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation df9319df-27fd-4454-b57c-29d9a3dd6f62 · outbound

This paper cites an unresolved cited work.

Learning Enables Exponential-to-Polynomial Sampling Overhead Scaling in Quantum Divide-and-Conquer for Tree-Structured Circuits Unresolved cited work

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-03T14:50:33.126090Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bfb6248f-dc77-422c-98d2-e5401cbff49c · outbound

This paper cites Ex[τ ⊗2 x ] RO r=1 EUr U † r |vr ηi,s⟩ ⟨vr ηi,s|U r ⊗2 # (S521) =p 2 ηi ω2 ηi,sd2Rtr.

Learning Enables Exponential-to-Polynomial Sampling Overhead Scaling in Quantum Divide-and-Conquer for Tree-Structured Circuits Ex[τ ⊗2 x ] RO r=1 EUr U † r |vr ηi,s⟩ ⟨vr ηi,s|U r ⊗2 # (S521) =p 2 ηi ω2 ηi,sd2Rtr

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-03T14:50:33.130255Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8041a3e7-31c3-4b4d-ae71-4f1b394a2d59 · outbound

This paper cites an unresolved cited work.

Learning Enables Exponential-to-Polynomial Sampling Overhead Scaling in Quantum Divide-and-Conquer for Tree-Structured Circuits Unresolved cited work

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-03T14:50:33.134417Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c66aec8a-389a-40b3-a40a-f99b6fa1b7b6 · outbound

This paper cites In the following, we briefly review these two approaches and explain how our results relate to the existing methods.

Learning Enables Exponential-to-Polynomial Sampling Overhead Scaling in Quantum Divide-and-Conquer for Tree-Structured Circuits In the following, we briefly review these two approaches and explain how our results relate to the existing methods

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-03T14:50:33.138140Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 73d68d47-9b64-4dbf-849e-bbb364328720 · outbound

This paper cites an unresolved cited work.

Learning Enables Exponential-to-Polynomial Sampling Overhead Scaling in Quantum Divide-and-Conquer for Tree-Structured Circuits Unresolved cited work

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-03T14:50:33.141938Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 466447d1-abe4-45c0-9102-7308dcc65a30 · outbound

This paper cites an unresolved cited work.

Learning Enables Exponential-to-Polynomial Sampling Overhead Scaling in Quantum Divide-and-Conquer for Tree-Structured Circuits Unresolved cited work

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-03T14:50:33.145522Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 344520d4-486b-4499-8139-2ad921d8815f · outbound

This paper cites an unresolved cited work.

Learning Enables Exponential-to-Polynomial Sampling Overhead Scaling in Quantum Divide-and-Conquer for Tree-Structured Circuits Unresolved cited work

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-03T14:50:33.148997Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 03489dbe-3ffb-4dc8-a799-cb13c2dd490f · outbound

This paper cites an unresolved cited work.

Learning Enables Exponential-to-Polynomial Sampling Overhead Scaling in Quantum Divide-and-Conquer for Tree-Structured Circuits Unresolved cited work

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-03T14:50:33.152464Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cdd87fa6-7652-4c35-8166-935d5e4c842e · outbound

This paper cites an unresolved cited work.

Learning Enables Exponential-to-Polynomial Sampling Overhead Scaling in Quantum Divide-and-Conquer for Tree-Structured Circuits Unresolved cited work

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-03T14:50:33.155839Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b71f76d2-9cc0-487e-af88-0fa6b1cd22c5 · outbound

This paper cites LO” denotes local operations without classical communication, whereas “LOCC.

Learning Enables Exponential-to-Polynomial Sampling Overhead Scaling in Quantum Divide-and-Conquer for Tree-Structured Circuits LO” denotes local operations without classical communication, whereas “LOCC

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-03T14:50:33.159798Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 53f8c617-3402-444c-bf50-9c44e742f96c · outbound

This paper cites In this subsection, we focus on wire cuts, which are most relevant to our work, and discuss how existing constructions relate to our results.

Learning Enables Exponential-to-Polynomial Sampling Overhead Scaling in Quantum Divide-and-Conquer for Tree-Structured Circuits In this subsection, we focus on wire cuts, which are most relevant to our work, and discuss how existing constructions relate to our results

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-03T14:50:33.163694Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8582ff3e-93e9-46ff-b232-e3154c47b85a · outbound

This paper cites Below, we summarize the main prior works [113–115], and show that these works can be reformulated in the language of expectation-value-level QPDs.

Learning Enables Exponential-to-Polynomial Sampling Overhead Scaling in Quantum Divide-and-Conquer for Tree-Structured Circuits Below, we summarize the main prior works [113–115], and show that these works can be reformulated in the language of expectation-value-level QPDs

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-03T14:50:33.167332Z

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Unavailable: canonical work link unavailable.

Pith citing papers

Observation 0d417c14-d1a9-4693-ae52-5010a7dd5a14 · inbound

Scalable quantum circuit knitting using a weak-coupling approximation cites this paper.

Scalable quantum circuit knitting using a weak-coupling approximation Learning Enables Exponential-to-Polynomial Sampling Overhead Scaling in Quantum Divide-and-Conquer for Tree-Structured Circuits

Reference 17

Resolution: verified exact; local_arxiv, observed 2026-07-04T00:49:18.711601Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation fc63e5bd-7c37-4a9a-9d37-1fc88beede29 · inbound

MOSAIQC: Mixed-topology-aware Optimization for Scalable Approximate noise-Informed Quantum circuit Cutting cites this paper.

MOSAIQC: Mixed-topology-aware Optimization for Scalable Approximate noise-Informed Quantum circuit Cutting Learning Enables Exponential-to-Polynomial Sampling Overhead Scaling in Quantum Divide-and-Conquer for Tree-Structured Circuits

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-01T14:05:00.410672Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.