Paper Citation Record · LEDGER

Permutation-Invariant N-body gates via Tavis-Cummings Hamiltonian

As of 9 August 2026, this Paper Citation Record lists 28 of 28 outbound references and 1 inbound Pith citation observation for arXiv:2506.03453.

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

pith.paper-citation-record.v1
2506.03453 v3

Coverage vector

measured 28 of 28 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T11:17:05.312420Z

measured 29 of 29 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 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-06T22:39:22.355867Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-06T22:39:22.467978Z

Reference resolution

28 of 28 outbound references displayed

verified exact0
verified fuzzy18
unresolved9
parse uncertain0
malformed identifier1
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation d497c7d2-0ed9-4a7c-820d-4e6109b6a356 · outbound

This paper cites an unresolved cited work.

Permutation-Invariant N-body gates via Tavis-Cummings Hamiltonian Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-07T11:17:07.220867Z

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 4d8462ff-df41-463b-b652-f8e5b9c02ff6 · outbound

This paper cites In the|q, k⟩basis, ⟨q, k|HTC |q, k+ 1⟩=⟨q, k+ 1|H TC |q, k⟩= p (q−k)(k+ 1)(n−q+k+ 1),(C22) where0≤q≤ ∞andmax(0, q−n)≤k≤q−1.

Permutation-Invariant N-body gates via Tavis-Cummings Hamiltonian In the|q, k⟩basis, ⟨q, k|HTC |q, k+ 1⟩=⟨q, k+ 1|H TC |q, k⟩= p (q−k)(k+ 1)(n−q+k+ 1),(C22) where0≤q≤ ∞andmax(0, q−n)≤k≤q−1

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:17:07.127851Z

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 f33c83b4-1f75-4969-ae2e-bfff9e56430e · outbound

This paper cites an unresolved cited work.

Permutation-Invariant N-body gates via Tavis-Cummings Hamiltonian Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-07T11:17:07.062114Z

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 c660432f-631b-4520-85d8-0d2af4d6f87a · outbound

This paper cites In the following, we determine the projection of the Lie algebra generated byH TC,J z, anda †aonto this center.

Permutation-Invariant N-body gates via Tavis-Cummings Hamiltonian In the following, we determine the projection of the Lie algebra generated byH TC,J z, anda †aonto this center

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:17:06.987749Z

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 4a237453-b241-4e9f-9da3-014de4f4cbdb · outbound

This paper cites The first condition follows immediately from Theorem 13, and in the previous subsection, we proved that eachV∈ Vz satisfies the phase constraints in the second condition, Eq.(90).

Permutation-Invariant N-body gates via Tavis-Cummings Hamiltonian The first condition follows immediately from Theorem 13, and in the previous subsection, we proved that eachV∈ Vz satisfies the phase constraints in the second condition, Eq.(90)

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:17:06.208078Z

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 f5f8f2c8-0ad1-4154-a1c8-fec21a6494fd · outbound

This paper cites anharmonic.

Permutation-Invariant N-body gates via Tavis-Cummings Hamiltonian anharmonic

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:17:06.135061Z

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 d95662c6-6f83-45ce-bc86-b90a62b48285 · outbound

This paper cites Consider the two-level subspace spanned by|0⟩ eff :=|00⟩ ⊗ |0⟩osc and|1⟩ eff :=|11⟩ ⊗ |2⟩osc, and let these states denote the±1eigenstates, respectively, of Pauli matrixσ z.

Permutation-Invariant N-body gates via Tavis-Cummings Hamiltonian Consider the two-level subspace spanned by|0⟩ eff :=|00⟩ ⊗ |0⟩osc and|1⟩ eff :=|11⟩ ⊗ |2⟩osc, and let these states denote the±1eigenstates, respectively, of Pauli matrixσ z

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:17:05.473308Z

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 2ba92148-f6aa-4dc9-a841-99e9acfc91ee · outbound

This paper cites anharmonic.

Permutation-Invariant N-body gates via Tavis-Cummings Hamiltonian anharmonic

Reference 9

Resolution: malformed identifier; raw_fallback, observed 2026-08-07T11:17:06.913102Z

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 53a9a1fd-3af3-43b8-a56d-103c1ee30ca9 · outbound

This paper cites Therefore, the unitaries that can be realized using the Hamiltonians HTC and HTC can also be realized usingH TC together with the identical single-qubit gatesS ⊗n.

Permutation-Invariant N-body gates via Tavis-Cummings Hamiltonian Therefore, the unitaries that can be realized using the Hamiltonians HTC and HTC can also be realized usingH TC together with the identical single-qubit gatesS ⊗n

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:17:06.834039Z

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 c1035099-f9f8-4412-ac4c-c6e467ced988 · outbound

This paper cites an unresolved cited work.

Permutation-Invariant N-body gates via Tavis-Cummings Hamiltonian Unresolved cited work

Reference 11

Resolution: unresolved; raw_fallback, observed 2026-08-07T11:17:06.769508Z

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 dd90ce81-9b0b-49fd-ba7c-f1a42b06bbac · outbound

This paper cites an unresolved cited work.

Permutation-Invariant N-body gates via Tavis-Cummings Hamiltonian Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-07T11:17:06.688412Z

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 da214154-5ed6-46b0-87d8-8e0f4c58ae28 · outbound

This paper cites anharmonicity.

Permutation-Invariant N-body gates via Tavis-Cummings Hamiltonian anharmonicity

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:17:06.600278Z

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 86a3efac-5752-4a43-bc56-3bdaaf7e49e0 · outbound

This paper cites an unresolved cited work.

Permutation-Invariant N-body gates via Tavis-Cummings Hamiltonian Unresolved cited work

Reference 14

Resolution: unresolved; raw_fallback, observed 2026-08-07T11:17:06.528586Z

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 0eabba58-8940-40b1-9412-0d77d791b74d · outbound

This paper cites That is, SV U(1)×Sn Πqmax sym = [V U(1)×Sn ,V U(1)×Sn ]Πqmax sym = qmaxM q=0 SU Hq, j=n/2 ⊂ VzΠqmax sym .(G5) whereΠ qmax sym is the projector to Lqmax q=0 Hq, j=n/2.

Permutation-Invariant N-body gates via Tavis-Cummings Hamiltonian That is, SV U(1)×Sn Πqmax sym = [V U(1)×Sn ,V U(1)×Sn ]Πqmax sym = qmaxM q=0 SU Hq, j=n/2 ⊂ VzΠqmax sym .(G5) whereΠ qmax sym is the projector to Lqmax q=0 Hq, j=n/2

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:17:06.470887Z

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 086d015d-9f45-41c9-bb96-9d0e3b09d8c0 · outbound

This paper cites Nevertheless, in this section, we show that aside from relative phases, pairwise correlations due to accidental symmetry are theonlysuch restrictions.

Permutation-Invariant N-body gates via Tavis-Cummings Hamiltonian Nevertheless, in this section, we show that aside from relative phases, pairwise correlations due to accidental symmetry are theonlysuch restrictions

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:17:06.388403Z

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 ff6d33ba-bf80-45f5-8c4a-a82dafd23d0b · outbound

This paper cites First, recall that any unitaryV∈ Vz realized by HamiltoniansH TC andJ z can be decomposed into a product, V= LY ℓ=1 e−iHTCrl e−iJzsℓ :r ℓ, sℓ ∈[−T, T](G14) for finiteLand timeT.

Permutation-Invariant N-body gates via Tavis-Cummings Hamiltonian First, recall that any unitaryV∈ Vz realized by HamiltoniansH TC andJ z can be decomposed into a product, V= LY ℓ=1 e−iHTCrl e−iJzsℓ :r ℓ, sℓ ∈[−T, T](G14) for finiteLand timeT

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:17:06.282090Z

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 3385c156-55ab-4c9b-8bfb-e350562573da · outbound

This paper cites That is, we consider general initial states|ψ⟩ ⊗ |0⟩osc, where|ψ⟩ ∈C2 ⊗C 2 is an arbitrary state ofn= 2qubits.

Permutation-Invariant N-body gates via Tavis-Cummings Hamiltonian That is, we consider general initial states|ψ⟩ ⊗ |0⟩osc, where|ψ⟩ ∈C2 ⊗C 2 is an arbitrary state ofn= 2qubits

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:17:06.047992Z

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 0322166b-7ade-4dbe-840c-1c6cf76de86b · outbound

This paper cites an unresolved cited work.

Permutation-Invariant N-body gates via Tavis-Cummings Hamiltonian Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-07T11:17:05.972774Z

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 0d8cfb90-6583-4ba7-8498-3f3429348827 · outbound

This paper cites 2-step”, “4-step.

Permutation-Invariant N-body gates via Tavis-Cummings Hamiltonian 2-step”, “4-step

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:17:05.886358Z

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 6be995c8-94f9-457d-a5a9-f0626be41c70 · outbound

This paper cites Additionally, in theq= 2, j= 1sector,Fis Hermitian and thus is its own inverse,π 2,1(F) =π 2,1(F †) =π 2,1(F −1).

Permutation-Invariant N-body gates via Tavis-Cummings Hamiltonian Additionally, in theq= 2, j= 1sector,Fis Hermitian and thus is its own inverse,π 2,1(F) =π 2,1(F †) =π 2,1(F −1)

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:17:05.827577Z

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 913de6c0-a273-4da7-952d-e6070006505b · outbound

This paper cites an unresolved cited work.

Permutation-Invariant N-body gates via Tavis-Cummings Hamiltonian Unresolved cited work

Reference 24

Resolution: unresolved; raw_fallback, observed 2026-08-07T11:17:05.731037Z

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 1b2bc230-92ef-457d-9a87-efa6fd67eb52 · outbound

This paper cites Implementing five two-qubit gates: interaction times, and decompositions in terms of Eq.(25).

Permutation-Invariant N-body gates via Tavis-Cummings Hamiltonian Implementing five two-qubit gates: interaction times, and decompositions in terms of Eq.(25)

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:17:05.674641Z

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 cbee3e0f-0f27-4ab3-88b4-34173e5edc5d · outbound

This paper cites Table VI lists the parameters of differentA-gates used to implement CZ, SW AP, iSW AP, √ iSW AP,Vqub.↔osc., andA(π 1,1(F †).

Permutation-Invariant N-body gates via Tavis-Cummings Hamiltonian Table VI lists the parameters of differentA-gates used to implement CZ, SW AP, iSW AP, √ iSW AP,Vqub.↔osc., andA(π 1,1(F †)

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:17:05.598012Z

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 1ada0e92-e5d2-4916-a7cd-b1ca5ee990f5 · outbound

This paper cites At the end of this section, we give an alternative proof using a geometric argument that explains why there should exist anglesϕ 0 andϕ 1 satisfying the above identity.

Permutation-Invariant N-body gates via Tavis-Cummings Hamiltonian At the end of this section, we give an alternative proof using a geometric argument that explains why there should exist anglesϕ 0 andϕ 1 satisfying the above identity

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:17:05.520897Z

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 6d880215-18ed-493a-b82a-8e80be013a19 · outbound

This paper cites an unresolved cited work.

Permutation-Invariant N-body gates via Tavis-Cummings Hamiltonian Unresolved cited work

Reference 64

Resolution: unresolved; raw_fallback, observed 2026-08-07T11:17:07.426346Z

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 03f7c009-cb44-4bf2-b166-d64d10199008 · outbound

This paper cites Hybrid Oscillator-Qubit Quantum Processors: Simulating Fermions, Bosons, and Gauge Fields.

Permutation-Invariant N-body gates via Tavis-Cummings Hamiltonian Hybrid Oscillator-Qubit Quantum Processors: Simulating Fermions, Bosons, and Gauge Fields

Reference 65

Resolution: unresolved; no resolver link, observed 2026-08-07T11:17:04.374509Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c86ffa10-b1ad-42ce-8081-dca6cab13810 · outbound

This paper cites D’Alessandro,Introduction to Quantum Control and Dy- namics, Chapman & Hall/CRC Applied Mathematics & Non- linear Science (CRC Press, 2007).

Permutation-Invariant N-body gates via Tavis-Cummings Hamiltonian D’Alessandro,Introduction to Quantum Control and Dy- namics, Chapman & Hall/CRC Applied Mathematics & Non- linear Science (CRC Press, 2007)

Reference 66

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:17:07.361593Z

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 c5c71626-77ca-47f1-9fb9-28e6a306d85a · outbound

This paper cites phase-shifted.

Permutation-Invariant N-body gates via Tavis-Cummings Hamiltonian phase-shifted

Reference 67

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:17:07.291771Z

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.

Pith citing papers

Observation 6de3f60b-07ab-4cab-9402-4fa08ffbcdcf · inbound

Implementation and representation of qudit multi-controlled unitaries and hypergraph states by N-body angular momentum couplings cites this paper.

Implementation and representation of qudit multi-controlled unitaries and hypergraph states by N-body angular momentum couplings Permutation-Invariant N-body gates via Tavis-Cummings Hamiltonian

Reference 70

Resolution: verified exact; local_arxiv, observed 2026-08-06T22:39:22.529501Z

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.