Paper Citation Record · LEDGER

Number-Theoretic Characterizations of Some Restricted Clifford+T Circuits

As of 15 August 2026, this Paper Citation Record lists 43 of 43 outbound references and 1 inbound Pith citation observation for arXiv:1908.06076.

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

pith.paper-citation-record.v1
1908.06076 v3

Coverage vector

measured 43 of 43 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-14T13:12:30.098146Z

measured 44 of 44 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-14T06:32:32.682623+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-06-27T09:36:28.925871Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-03T11:18:03.778919Z

Reference resolution

43 of 43 outbound references displayed

verified exact15
verified fuzzy3
unresolved23
parse uncertain0
malformed identifier1
metadata mismatch1

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 892061ff-4f72-4498-bca0-0e6e5dcafc18 · outbound

This paper cites The Classification of Reversible Bit Operations.

Number-Theoretic Characterizations of Some Restricted Clifford+T Circuits The Classification of Reversible Bit Operations

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-14T13:12:29.823552Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1665461e-04dd-4313-ab83-e4b6ad93b467 · outbound

This paper cites A Simple Proof that Toffoli and Hadamard are Quantum Universal.

Number-Theoretic Characterizations of Some Restricted Clifford+T Circuits A Simple Proof that Toffoli and Hadamard are Quantum Universal

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-14T13:12:29.830767Z

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Unavailable: canonical work link unavailable.

Observation 7163ea45-0e94-4769-bec6-a9c30ad4efc9 · outbound

This paper cites Amy and M.

Number-Theoretic Characterizations of Some Restricted Clifford+T Circuits Amy and M

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-14T13:12:29.839645Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 84ae0804-a46a-4a7c-a416-f366f1a9a857 · outbound

This paper cites an unresolved cited work.

Number-Theoretic Characterizations of Some Restricted Clifford+T Circuits Unresolved cited work

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-14T13:12:29.846792Z

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Observation 41bb1767-10de-4ad1-bbf4-32e287cae6c3 · outbound

This paper cites an unresolved cited work.

Number-Theoretic Characterizations of Some Restricted Clifford+T Circuits Unresolved cited work

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-14T13:12:29.853287Z

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Unavailable: canonical work link unavailable.

Observation 86ee14c2-48b3-457b-8c38-1d96769e3fec · outbound

This paper cites an unresolved cited work.

Number-Theoretic Characterizations of Some Restricted Clifford+T Circuits Unresolved cited work

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-14T13:12:29.862631Z

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Observation 400b9f86-5ebb-4dd0-aee3-e1977e00c70f · outbound

This paper cites an unresolved cited work.

Number-Theoretic Characterizations of Some Restricted Clifford+T Circuits Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-14T13:12:31.490071Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 492c0b42-8d08-4328-a4f8-7a06970fae3f · outbound

This paper cites Backens and A.

Number-Theoretic Characterizations of Some Restricted Clifford+T Circuits Backens and A

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-14T13:12:29.877929Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3c358e72-5bcf-4f1e-93de-df2f7be4cf9f · outbound

This paper cites Elementary gates for quantum computation.

Number-Theoretic Characterizations of Some Restricted Clifford+T Circuits Elementary gates for quantum computation

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-14T13:12:29.884202Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 237dd48e-4d79-46df-8084-253eb3678fce · outbound

This paper cites an unresolved cited work.

Number-Theoretic Characterizations of Some Restricted Clifford+T Circuits Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-14T13:12:31.471092Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation fc4111bf-6a26-4078-9fb7-6a4a472241d8 · outbound

This paper cites Bian and P.

Number-Theoretic Characterizations of Some Restricted Clifford+T Circuits Bian and P

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:12:31.452769Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 3b97cd13-014f-4158-a4c0-1aae230c3ae3 · outbound

This paper cites Efficient Decomposition of Single-Qubit Gates into $V$ Basis Circuits.

Number-Theoretic Characterizations of Some Restricted Clifford+T Circuits Efficient Decomposition of Single-Qubit Gates into $V$ Basis Circuits

Reference 12

Resolution: verified exact; local_arxiv, observed 2026-08-14T13:12:31.100456Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 84805c83-683e-4556-ba34-030f225b2eec · outbound

This paper cites Efficient synthesis of probabilistic quantum circuits with fallback.

Number-Theoretic Characterizations of Some Restricted Clifford+T Circuits Efficient synthesis of probabilistic quantum circuits with fallback

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-14T13:12:29.904168Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ab95b90e-7382-4279-a972-e194344382ce · outbound

This paper cites Bouland and S.

Number-Theoretic Characterizations of Some Restricted Clifford+T Circuits Bouland and S

Reference 14

Resolution: verified exact; doi, observed 2026-08-14T13:12:30.283410Z

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 018728d1-ffee-4131-9628-7ab39f22c041 · outbound

This paper cites De Vos, R.

Number-Theoretic Characterizations of Some Restricted Clifford+T Circuits De Vos, R

Reference 15

Resolution: verified exact; doi, observed 2026-08-14T13:12:30.260693Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 1e77d030-dba5-4e8f-9ccc-fe6539ac03b9 · outbound

This paper cites Exact synthesis of single-qubit unitaries over Clifford-cyclotomic gate sets.

Number-Theoretic Characterizations of Some Restricted Clifford+T Circuits Exact synthesis of single-qubit unitaries over Clifford-cyclotomic gate sets

Reference 16

Resolution: verified exact; local_arxiv, observed 2026-08-14T13:12:31.056017Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation d597d032-4553-46a0-b4a4-cfc9dfc6d2df · outbound

This paper cites Exact synthesis of multiqubit Clifford+T circuits.

Number-Theoretic Characterizations of Some Restricted Clifford+T Circuits Exact synthesis of multiqubit Clifford+T circuits

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-14T13:12:29.926359Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ece8c4bc-441b-4780-9b65-50f29be55b6c · outbound

This paper cites Remarks on Matsumoto and Amano's normal form for single-qubit Clifford+T operators.

Number-Theoretic Characterizations of Some Restricted Clifford+T Circuits Remarks on Matsumoto and Amano's normal form for single-qubit Clifford+T operators

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-14T13:12:29.932866Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 279da940-a4bd-47bf-a974-687abfa1cecd · outbound

This paper cites An algorithm for the T-count.

Number-Theoretic Characterizations of Some Restricted Clifford+T Circuits An algorithm for the T-count

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-14T13:12:29.938945Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 19f9b582-7ce9-49df-a56c-a7c8b03fac34 · outbound

This paper cites Generators and relations for the group $U_4(\mathbb{Z}[1/\sqrt{2},i])$.

Number-Theoretic Characterizations of Some Restricted Clifford+T Circuits Generators and relations for the group $U_4(\mathbb{Z}[1/\sqrt{2},i])$

Reference 20

Resolution: verified exact; local_arxiv, observed 2026-08-14T13:12:30.977706Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation e01274a0-1a7d-426b-9227-c31fda6f5bcf · outbound

This paper cites The Classification of Clifford Gates over Qubits.

Number-Theoretic Characterizations of Some Restricted Clifford+T Circuits The Classification of Clifford Gates over Qubits

Reference 21

Resolution: verified exact; local_arxiv, observed 2026-08-14T13:12:30.950391Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation b459f2be-ef82-496a-a3eb-cd543a8360d4 · outbound

This paper cites Real Randomized Benchmarking.

Number-Theoretic Characterizations of Some Restricted Clifford+T Circuits Real Randomized Benchmarking

Reference 22

Resolution: verified exact; local_arxiv, observed 2026-08-14T13:12:30.918335Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 9e37c0c2-a27b-4a36-bd39-441e89fa435d · outbound

This paper cites An Efficient Quantum Compiler that reduces $T$ count.

Number-Theoretic Characterizations of Some Restricted Clifford+T Circuits An Efficient Quantum Compiler that reduces $T$ count

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-14T13:12:29.962385Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f3f6e3ce-03c1-4379-b243-4d90700cb866 · outbound

This paper cites Jeandel, S.

Number-Theoretic Characterizations of Some Restricted Clifford+T Circuits Jeandel, S

Reference 24

Resolution: verified exact; doi, observed 2026-08-14T13:12:30.240518Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation a770d4c6-1cab-4c39-94dc-4e8ff632f6f9 · outbound

This paper cites A framework for exact synthesis.

Number-Theoretic Characterizations of Some Restricted Clifford+T Circuits A framework for exact synthesis

Reference 25

Resolution: verified exact; local_arxiv, observed 2026-08-14T13:12:30.872520Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 26bcc804-2462-4d61-9c71-4ebecdb41f6a · outbound

This paper cites Fast and efficient exact synthesis of single qubit unitaries generated by Clifford and T gates.

Number-Theoretic Characterizations of Some Restricted Clifford+T Circuits Fast and efficient exact synthesis of single qubit unitaries generated by Clifford and T gates

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-14T13:12:29.980896Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 458563a0-eda1-47bc-a59c-c675d993505a · outbound

This paper cites Asymptotically Optimal Topological Quantum Compiling.

Number-Theoretic Characterizations of Some Restricted Clifford+T Circuits Asymptotically Optimal Topological Quantum Compiling

Reference 27

Resolution: verified exact; local_arxiv, observed 2026-08-14T13:12:30.813009Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 76de1b29-0c9f-451b-bc64-c208ed1c5ffd · outbound

This paper cites Kliuchnikov, D.

Number-Theoretic Characterizations of Some Restricted Clifford+T Circuits Kliuchnikov, D

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:12:31.431995Z

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation d96293c4-f115-4d3d-9d0f-128aa7424f60 · outbound

This paper cites Representation of Quantum Circuits with Clifford and $\pi/8$ Gates.

Number-Theoretic Characterizations of Some Restricted Clifford+T Circuits Representation of Quantum Circuits with Clifford and $\pi/8$ Gates

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-14T13:12:30.009511Z

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Unavailable: canonical work link unavailable.

Observation 2fb006a9-a319-473e-8c1f-9dee6ba17c04 · outbound

This paper cites Meuli, M.

Number-Theoretic Characterizations of Some Restricted Clifford+T Circuits Meuli, M

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:12:31.409611Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 4df4107e-d847-486e-950d-0fc8da6dd378 · outbound

This paper cites an unresolved cited work.

Number-Theoretic Characterizations of Some Restricted Clifford+T Circuits Unresolved cited work

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-14T13:12:30.029800Z

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Observation 986df269-8b5b-4557-a4cd-79fb60a44ede · outbound

This paper cites Super-Golden-Gates for PU(2).

Number-Theoretic Characterizations of Some Restricted Clifford+T Circuits Super-Golden-Gates for PU(2)

Reference 32

Resolution: verified exact; local_arxiv, observed 2026-08-14T13:12:30.579619Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 52ff186c-f060-4732-a8fa-94318097163a · outbound

This paper cites Optimal ancilla-free Clifford+V approximation of z-rotations.

Number-Theoretic Characterizations of Some Restricted Clifford+T Circuits Optimal ancilla-free Clifford+V approximation of z-rotations

Reference 33

Resolution: verified exact; local_arxiv, observed 2026-08-14T13:12:30.537348Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation b5f61490-3cb1-4e89-8f6e-b6c560b85f9f · outbound

This paper cites Optimal ancilla-free Clifford+T approximation of z-rotations.

Number-Theoretic Characterizations of Some Restricted Clifford+T Circuits Optimal ancilla-free Clifford+T approximation of z-rotations

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-14T13:12:30.052591Z

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Observation 2e422ebf-583f-4195-a7e8-3c367d00b9c5 · outbound

This paper cites A 2 rebit gate universal for quantum computing.

Number-Theoretic Characterizations of Some Restricted Clifford+T Circuits A 2 rebit gate universal for quantum computing

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-14T13:12:30.059431Z

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Observation d977bcd0-8355-4d1d-9658-b26a3a4e9bf7 · outbound

This paper cites Selinger.

Number-Theoretic Characterizations of Some Restricted Clifford+T Circuits Selinger

Reference 36

Resolution: verified exact; doi, observed 2026-08-14T13:12:30.199383Z

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation cd979e54-b19e-494c-bbb6-2ec8b926724a · outbound

This paper cites Both Toffoli and Controlled-NOT need little help to do universal quantum computation.

Number-Theoretic Characterizations of Some Restricted Clifford+T Circuits Both Toffoli and Controlled-NOT need little help to do universal quantum computation

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-14T13:12:30.072260Z

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Unavailable: canonical work link unavailable.

Observation 81b8a1f1-b17b-47a7-a7b7-813354146127 · outbound

This paper cites an unresolved cited work.

Number-Theoretic Characterizations of Some Restricted Clifford+T Circuits Unresolved cited work

Reference 38

Resolution: unresolved; raw_fallback, observed 2026-08-14T13:12:31.391338Z

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 66bcec66-8714-4a21-9eee-ad2c2eab6bd2 · outbound

This paper cites Welch, A.

Number-Theoretic Characterizations of Some Restricted Clifford+T Circuits Welch, A

Reference 39

Resolution: malformed identifier; doi_truncated, observed 2026-08-14T13:12:30.158830Z

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Observation 699cd9f2-76b8-4ff3-a0db-0653920cf209 · outbound

This paper cites an unresolved cited work.

Number-Theoretic Characterizations of Some Restricted Clifford+T Circuits Unresolved cited work

Reference 41

Resolution: verified exact; doi, observed 2026-08-14T13:12:30.181429Z

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation e1849f92-1666-4408-a21e-07b3ffd708e5 · outbound

This paper cites Efficient Approximation of Diagonal Unitaries over the Clifford+T Basis.

Number-Theoretic Characterizations of Some Restricted Clifford+T Circuits Efficient Approximation of Diagonal Unitaries over the Clifford+T Basis

Reference 43

Resolution: verified exact; local_arxiv, observed 2026-08-14T13:12:30.454063Z

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 5da25d4c-9464-419b-898a-8ea4f0eedb19 · outbound

This paper cites Also available from arXiv:1212.6964.

Number-Theoretic Characterizations of Some Restricted Clifford+T Circuits Also available from arXiv:1212.6964

Reference 2016

Resolution: metadata mismatch; raw_fallback, observed 2026-08-14T13:12:30.785573Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 224f1c37-fcfd-4f94-98cb-d68ed300993a · outbound

This paper cites an unresolved cited work.

Number-Theoretic Characterizations of Some Restricted Clifford+T Circuits Unresolved cited work

Reference 2018

Resolution: unresolved; no resolver link, observed 2026-08-14T13:12:30.023300Z

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Unavailable: canonical work link unavailable.

Pith citing papers

Observation 48b52e8e-ccef-4cb3-9a71-484b31dfb598 · inbound

Geometric Algebra Quantum Gate Decomposition cites this paper.

Geometric Algebra Quantum Gate Decomposition Number-Theoretic Characterizations of Some Restricted Clifford+T Circuits

Reference 17

Resolution: verified exact; arxiv_id, observed 2026-07-03T11:18:03.780195Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.