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Paper Citation Record · LEDGER

Resource quantification for programming low-depth quantum circuits

As of 7 August 2026, this Paper Citation Record lists 54 of 54 outbound references and 0 inbound Pith citation observations for arXiv:2509.09642.

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

pith.paper-citation-record.v1
2509.09642 v2

Coverage vector

measured 54 of 54 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-04T18:59:22.126154Z

measured 54 of 54 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-07T06:34:17.273281+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

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measured 0 of 1 external citation measurements

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Reference resolution

54 of 54 outbound references displayed

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Outbound references

Observation 3ddf95f6-5cc7-44ca-bfea-26ed6aa2d5da · outbound

This paper cites Quantum Computing in the NISQ era and beyond.

Resource quantification for programming low-depth quantum circuits Quantum Computing in the NISQ era and beyond

Reference 1

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Observation ff798ab5-d7f3-478c-b8ed-37b266422aa1 · outbound

This paper cites A fast quantum mechanical algorithm for database search.

Resource quantification for programming low-depth quantum circuits A fast quantum mechanical algorithm for database search

Reference 2

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Observation c4ee69d4-ce5b-4a7e-91be-7ccc929a0f7c · outbound

This paper cites Polynomial-time algorithms for prime factorization and discrete loga- rithms on a quantum computer.

Resource quantification for programming low-depth quantum circuits Polynomial-time algorithms for prime factorization and discrete loga- rithms on a quantum computer

Reference 3

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Observation 99822bde-0e2b-4067-93ef-74f99425672a · outbound

This paper cites Quantum algorithm for linear systems of equations.

Resource quantification for programming low-depth quantum circuits Quantum algorithm for linear systems of equations

Reference 4

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source=pdf_text observed=2026-08-04T18:59:14.690196Z digest=sha256:cfc70a6b4d7da3df63580218f539575ead64ed8d13e67b9489011a67eba88b21

Observation e0536db2-2e03-4da3-8892-342d5703f939 · outbound

This paper cites Noisy intermediate-scale quantum algorithms.

Resource quantification for programming low-depth quantum circuits Noisy intermediate-scale quantum algorithms

Reference 5

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Observation b2f2ca85-9834-4bc3-8166-acf97d0a3121 · outbound

This paper cites Shallowquantumcircuits: Algorithms, complexity, andfaulttolerance.

Resource quantification for programming low-depth quantum circuits Shallowquantumcircuits: Algorithms, complexity, andfaulttolerance

Reference 6

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Observation 76b0fc00-3f55-4e68-983c-9669abe42715 · outbound

This paper cites Quantum advantage with shallow circuits.

Resource quantification for programming low-depth quantum circuits Quantum advantage with shallow circuits

Reference 7

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Observation 1543aa53-a3db-41d7-bd16-ed554937d237 · outbound

This paper cites Exponential separation between shallow quantum circuits and unbounded fan-in shallow classical circuits.

Resource quantification for programming low-depth quantum circuits Exponential separation between shallow quantum circuits and unbounded fan-in shallow classical circuits

Reference 8

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source=pdf_text observed=2026-08-04T18:59:15.088817Z digest=sha256:33be438e2035692dc5f22238a73b44300b4594d0e40ac443f958ce89961f13ce

Observation cebd26d0-ba26-47b3-9e0a-05d4e226d8a2 · outbound

This paper cites Delegating private quantum computations.

Resource quantification for programming low-depth quantum circuits Delegating private quantum computations

Reference 9

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source=pdf_text observed=2026-08-04T18:59:15.186923Z digest=sha256:3d97e8e00ae7c01d4754270abe261be815875c5b6f3325b1d2629d4e3b27b6b6

Observation f14d15d8-49d0-4f05-8317-2e4579ccceae · outbound

This paper cites A one-query lower bound for unitary synthesis and breaking quantum cryptography.

Resource quantification for programming low-depth quantum circuits A one-query lower bound for unitary synthesis and breaking quantum cryptography

Reference 10

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Observation 63f97500-bc5a-4cd6-94bd-075280cb8266 · outbound

This paper cites Programmable quantum gate arrays.

Resource quantification for programming low-depth quantum circuits Programmable quantum gate arrays

Reference 11

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source=pdf_text observed=2026-08-04T18:59:15.395922Z digest=sha256:a958a76235444ed68e691b4fd2b546c035832a79b6b7b0a053eb0a610bcb6c31

Observation f32c556b-e915-4032-8952-4a9b35c8cd69 · outbound

This paper cites Probabilistic implementation of universal quantum processors.

Resource quantification for programming low-depth quantum circuits Probabilistic implementation of universal quantum processors

Reference 12

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source=pdf_text observed=2026-08-04T18:59:15.493996Z digest=sha256:2d5be54fd68acdc03b953a9d22cf5c10c859a3e0cf4dae7ae0bde60e7b14a123

Observation 55f809d2-1988-46f9-8bd7-683d7b4355ad · outbound

This paper cites Measurement-based quantum computation beyond the one-way model.

Resource quantification for programming low-depth quantum circuits Measurement-based quantum computation beyond the one-way model

Reference 13

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source=pdf_text observed=2026-08-04T18:59:15.596984Z digest=sha256:f8a3521b8396650d620045ac2beb1dfc42e600ec261bb0057a7641714a3a899a

Observation 0693fdd8-2b4d-4fac-b292-cede79564ee7 · outbound

This paper cites Asymptotic teleportation scheme as a uni- versal programmable quantum processor.

Resource quantification for programming low-depth quantum circuits Asymptotic teleportation scheme as a uni- versal programmable quantum processor

Reference 14

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Observation 2316c581-c1d3-43da-8f6f-6f4cb9d4964e · outbound

This paper cites Resource quan- tification for the no-programing theorem.

Resource quantification for programming low-depth quantum circuits Resource quan- tification for the no-programing theorem

Reference 15

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Observation a7eeb86e-b05e-4a63-a8be-5b294bf78db4 · outbound

This paper cites Optimal universal program- ming of unitary gates.

Resource quantification for programming low-depth quantum circuits Optimal universal program- ming of unitary gates

Reference 16

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Observation efa334dd-e1c3-474c-9dd0-9b23aadb9a0f · outbound

This paper cites Programmability of covariant quantum channels.

Resource quantification for programming low-depth quantum circuits Programmability of covariant quantum channels

Reference 17

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Observation 66b9f84d-82dd-46e3-9e48-e4b6f85b4c15 · outbound

This paper cites Port-Based State Preparation and Appli- cations.

Resource quantification for programming low-depth quantum circuits Port-Based State Preparation and Appli- cations

Reference 18

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Observation ab25b236-d728-4fb4-9284-7ecf10e2c278 · outbound

This paper cites Quantum Advantage in Storage and Retrieval of Isometry Channels.

Resource quantification for programming low-depth quantum circuits Quantum Advantage in Storage and Retrieval of Isometry Channels

Reference 19

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Observation c301107f-14bc-4da4-83d4-0387c33aeb6b · outbound

This paper cites Computational complexity: A modern approach.

Resource quantification for programming low-depth quantum circuits Computational complexity: A modern approach

Reference 20

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Observation 9186b78e-d999-4e94-847f-b157c37f960d · outbound

This paper cites Linear growth of quantum circuit complexity.

Resource quantification for programming low-depth quantum circuits Linear growth of quantum circuit complexity

Reference 21

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Observation e3166fa6-6190-49ff-b980-837a994d6840 · outbound

This paper cites Approximatet-designs in generic circuit architectures.

Resource quantification for programming low-depth quantum circuits Approximatet-designs in generic circuit architectures

Reference 22

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source=pdf_text observed=2026-08-04T18:59:16.681767Z digest=sha256:b4ffec7205cf49cc45e4e2785cdb11d1cf5a1f53c3df98221402d25e0a0c5ebd

Observation a522ef84-d1e7-4715-b1a5-040879f73f88 · outbound

This paper cites Learning quantum states and unitaries of bounded gate complex- ity.

Resource quantification for programming low-depth quantum circuits Learning quantum states and unitaries of bounded gate complex- ity

Reference 23

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Observation 056b952a-b2e9-42b9-a758-64d9233ed0b8 · outbound

This paper cites Learning shallow quantum circuits.

Resource quantification for programming low-depth quantum circuits Learning shallow quantum circuits

Reference 24

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source=pdf_text observed=2026-08-04T18:59:17.022362Z digest=sha256:faf17de4b8b02646f1d713f7ebdaecfdd82311d607d149495ea1ee394135a68e

Observation 50821610-4a75-4ac6-969d-7707238e377d · outbound

This paper cites Compression of quantum shallow-circuit states.

Resource quantification for programming low-depth quantum circuits Compression of quantum shallow-circuit states

Reference 25

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Observation 6ae1b8bb-e77b-4c35-9a03-93862edd5333 · outbound

This paper cites Quantum computation and quantum infor- mation: 10th anniversary edition.

Resource quantification for programming low-depth quantum circuits Quantum computation and quantum infor- mation: 10th anniversary edition

Reference 26

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Observation 84ae3a4a-0377-4fe3-af18-cb20c91d81d8 · outbound

This paper cites On the pauli spectrum ofQAC0.

Resource quantification for programming low-depth quantum circuits On the pauli spectrum ofQAC0

Reference 27

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source=pdf_text observed=2026-08-04T18:59:17.320003Z digest=sha256:3505d439ba037565dc3daba47fb81432a89f80dee135ce0714f57542b53c79bd

Observation ca570eef-bfac-4b9f-8ac4-85d34a4796a8 · outbound

This paper cites Symmetry, representations, and invariants.

Resource quantification for programming low-depth quantum circuits Symmetry, representations, and invariants

Reference 28

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source=pdf_text observed=2026-08-04T18:59:17.449122Z digest=sha256:72558d5ec1ec7641df5e3e701e3f16ddf86c7ec4e9fe1ed728ba43ffcb634e22

Observation 3be07542-525c-4931-8b70-067464bb01e9 · outbound

This paper cites Applications of coherent classical communication and the schur transform to quantum information theory.

Resource quantification for programming low-depth quantum circuits Applications of coherent classical communication and the schur transform to quantum information theory

Reference 29

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Observation c3ce7935-3145-4999-81ed-e49cf41360d4 · outbound

This paper cites Simple Con- structions of Linear-Depth t-Designs and Pseudorandom Unitaries.

Resource quantification for programming low-depth quantum circuits Simple Con- structions of Linear-Depth t-Designs and Pseudorandom Unitaries

Reference 30

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Observation 50524999-5ca6-41a2-a5d8-cc03fd2d8de7 · outbound

This paper cites Exact and approximate unitary 2-designs and their application to fidelity estimation.

Resource quantification for programming low-depth quantum circuits Exact and approximate unitary 2-designs and their application to fidelity estimation

Reference 31

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source=pdf_text observed=2026-08-04T18:59:18.167668Z digest=sha256:55a51647907ee16f568d90f245caf99f875ba2d82aad259f0dee1ff16ad6ef01

Observation 0430f2cb-08bb-4acf-88d0-8e8ff366f3cf · outbound

This paper cites Optimal quantum learning of a unitary transformation.

Resource quantification for programming low-depth quantum circuits Optimal quantum learning of a unitary transformation

Reference 32

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source=pdf_text observed=2026-08-04T18:59:18.416198Z digest=sha256:90729841201b0d08e9475eb6e9eeb005a0555676038a7662ab0426b437a35958

Observation dc080732-36e3-491f-b464-92cf3f1c0c13 · outbound

This paper cites Scalable noise estimation with random unitary operators.

Resource quantification for programming low-depth quantum circuits Scalable noise estimation with random unitary operators

Reference 33

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source=pdf_text observed=2026-08-04T18:59:18.627573Z digest=sha256:1e5df61971a3ad6384e4d68cf67b2f7f28fdf40df69a5f287a9a292fde075244

Observation a26557fa-c5a1-4ed5-8978-7561708bc024 · outbound

This paper cites Creating superpositions that correspond to efficiently integrable probability distributions.

Resource quantification for programming low-depth quantum circuits Creating superpositions that correspond to efficiently integrable probability distributions

Reference 34

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source=pdf_text observed=2026-08-04T18:59:18.781520Z digest=sha256:3aade2a05880292f127343126662d929e4fd2d38c8bb76d180e2ccb9d47e5833

Observation 6dbc155e-f147-4625-8ae6-f8295b5b2f0f · outbound

This paper cites An efficient high dimensional quantum Schur transform.

Resource quantification for programming low-depth quantum circuits An efficient high dimensional quantum Schur transform

Reference 35

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source=pdf_text observed=2026-08-04T18:59:18.912781Z digest=sha256:97a3bf52c08b121211d36218afac3ca08fd460fb3e66f7d8c49bfeca6c403910

Observation a631a203-0c46-4f7c-a682-1247faad0be2 · outbound

This paper cites Quantum state preparation with optimal circuit depth: Implementations and applications.

Resource quantification for programming low-depth quantum circuits Quantum state preparation with optimal circuit depth: Implementations and applications

Reference 36

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source=pdf_text observed=2026-08-04T18:59:19.108909Z digest=sha256:5bf541904111b24b23539e723a55ff77bd305876dd43a3024d945590ce31daff

Observation e7659a31-dec4-45b0-9efe-77ed09b41623 · outbound

This paper cites Approximate unitary t-designs by short ran- dom quantum circuits using nearest-neighbor and long-range gates.

Resource quantification for programming low-depth quantum circuits Approximate unitary t-designs by short ran- dom quantum circuits using nearest-neighbor and long-range gates

Reference 37

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source=pdf_text observed=2026-08-04T18:59:19.282665Z digest=sha256:0a787b95b58a46399241c472fd91de5b3ec5726c9002e3755c52d0b6c9d20643

Observation 8a6dd2c3-4786-47d6-9769-7fcf41696556 · outbound

This paper cites Efficient approximate unitary designs from random pauli rotations.

Resource quantification for programming low-depth quantum circuits Efficient approximate unitary designs from random pauli rotations

Reference 38

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source=pdf_text observed=2026-08-04T18:59:19.451070Z digest=sha256:e2f8bf9bdc68453964486b8b5456c78e58052db4ac058e25e7735b35570676b8

Observation 4aa6bc20-4e26-439d-b820-8f1d897003d5 · outbound

This paper cites Incompressibility and spectral gaps of random circuits.

Resource quantification for programming low-depth quantum circuits Incompressibility and spectral gaps of random circuits

Reference 39

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source=pdf_text observed=2026-08-04T18:59:19.661409Z digest=sha256:c15cce8dce41de0332506f431f8c07bd8e22d938e7493e6f9cb4306ca9dd7fca

Observation 389dccd9-2502-4376-8f8e-113397fa846d · outbound

This paper cites Random unitaries in extremely low depth.

Resource quantification for programming low-depth quantum circuits Random unitaries in extremely low depth

Reference 40

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source=pdf_text observed=2026-08-04T18:59:19.829234Z digest=sha256:b6d6f153ff176dd19863fe398569f3985ca8dd2ea7f49edb788eee4eedd21edb

Observation 377a17be-f160-458a-a948-ffb5ef27ee3e · outbound

This paper cites Optimal estimation of group transformations using entanglement.

Resource quantification for programming low-depth quantum circuits Optimal estimation of group transformations using entanglement

Reference 41

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source=pdf_text observed=2026-08-04T18:59:19.994606Z digest=sha256:8f598c4cbf0823284cfa79bd03d6541dd1379cd0d8c248f6810bf1f08596a25a

Observation ce062aba-ae4d-486e-b236-afb47e2dd2a3 · outbound

This paper cites Query-optimal estimation of unitary channels in diamond distance.

Resource quantification for programming low-depth quantum circuits Query-optimal estimation of unitary channels in diamond distance

Reference 42

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source=pdf_text observed=2026-08-04T18:59:20.131146Z digest=sha256:f1ebeefaa86386c6956a7d19adadb5978a2fe4911a8e5359004be2e1db9f475f

Observation b97cc8f0-56fd-4a3a-8f37-ae6dba7ef9e4 · outbound

This paper cites Synthesis of quantum logic circuits.

Resource quantification for programming low-depth quantum circuits Synthesis of quantum logic circuits

Reference 43

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source=pdf_text observed=2026-08-04T18:59:20.325573Z digest=sha256:54f1cd6c274027c19b6208f702cc96151c1e10a95d4632795dfbe171900179dd

Observation 4574e658-59d8-4aae-acc8-9a6f0fab508b · outbound

This paper cites Classical and quantum computation.

Resource quantification for programming low-depth quantum circuits Classical and quantum computation

Reference 44

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Observation 2dcbe4de-7f00-4f2d-976f-ca6e5059b0e9 · outbound

This paper cites Bounds for the quantity of information transmitted by a quantum communication channel.

Resource quantification for programming low-depth quantum circuits Bounds for the quantity of information transmitted by a quantum communication channel

Reference 45

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source=pdf_text observed=2026-08-04T18:59:20.725544Z digest=sha256:9e88c9b24aa8ede5ee59a5ec83e70ebdda6bfcbed917e069a58e4c86f830ed02

Observation 1676e25f-7254-4758-89d0-669a9008e857 · outbound

This paper cites Tight uniform continuity bounds for quantum entropies: Condi- tional entropy, relative entropy distance and energy constraints.

Resource quantification for programming low-depth quantum circuits Tight uniform continuity bounds for quantum entropies: Condi- tional entropy, relative entropy distance and energy constraints

Reference 46

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source=pdf_text observed=2026-08-04T18:59:20.860834Z digest=sha256:a0ba42fc65ba53a4f16988bad590f98e95c54e326ecf2ea1a0d5d2770a3e5743

Observation 222375b2-2b3c-4cb7-903c-2efe07c640de · outbound

This paper cites Asymptotic values for degrees associated with strips of young dia- grams.

Resource quantification for programming low-depth quantum circuits Asymptotic values for degrees associated with strips of young dia- grams

Reference 47

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source=pdf_text observed=2026-08-04T18:59:21.052153Z digest=sha256:55625dedfdaa4e8ce697bfcd739bfa899d1d08c287cf7f397a4dcf1d5d5466d1

Observation 90c3223a-af6f-4bee-906a-e8d76a008f7c · outbound

This paper cites Optimal compression for identically prepared qubit states.

Resource quantification for programming low-depth quantum circuits Optimal compression for identically prepared qubit states

Reference 48

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source=pdf_text observed=2026-08-04T18:59:21.197499Z digest=sha256:627cf5a67861b67843035e37f439aafa9ee9ef8d4c8ad5b960a0488cf546e095

Observation 04f38cd8-7d93-4561-bf16-74321f02eeff · outbound

This paper cites On the computa- tional power ofQAC 0 with barely superlinear ancillae.

Resource quantification for programming low-depth quantum circuits On the computa- tional power ofQAC 0 with barely superlinear ancillae

Reference 49

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source=pdf_text observed=2026-08-04T18:59:21.369173Z digest=sha256:060cff95d7dbf38f29a5cace7454d149af52828c9f66dfdcde817432396bff41

Observation 236dcad7-1101-41b7-869a-a6881ad50d4e · outbound

This paper cites Operator Lipschitz functions (English translation).

Resource quantification for programming low-depth quantum circuits Operator Lipschitz functions (English translation)

Reference 50

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source=pdf_text observed=2026-08-04T18:59:21.528752Z digest=sha256:4241c58ae8f432c3a42b8fcbe5db61c0bb2a062e92bba2c50aa6026536e90302

Observation cc122e69-3729-4764-946f-1b7e50261408 · outbound

This paper cites Quantum state and unitary learn- ing implies circuit lower bounds.

Resource quantification for programming low-depth quantum circuits Quantum state and unitary learn- ing implies circuit lower bounds

Reference 51

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source=pdf_text observed=2026-08-04T18:59:21.763409Z digest=sha256:d66d09b77fc6d7ed0c733190f4d8c8cfa89fa05548b178cb3356cf6ad94dc836

Observation 16187431-5ae5-4125-9a7f-aa5fd92badd8 · outbound

This paper cites On the geometry of stabi- lizer states.

Resource quantification for programming low-depth quantum circuits On the geometry of stabi- lizer states

Reference 52

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source=pdf_text observed=2026-08-04T18:59:21.963762Z digest=sha256:7d6528b0b1f8fb327ae0883eadb0517d70a5962b04a8cf0864b1f94651f294e5

Observation d7034119-22b2-436d-bc13-ff6035e29e50 · outbound

This paper cites Restrictions on realizable unitary operations imposed by symmetry and locality.

Resource quantification for programming low-depth quantum circuits Restrictions on realizable unitary operations imposed by symmetry and locality

Reference 53

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source=pdf_text observed=2026-08-04T18:59:22.126154Z digest=sha256:dbe06ca84df3b60fde33ae898799b51da2dcd0dc6570175c7b0cd178900f736e

Observation 8fb3f222-c0c6-4547-97ac-28d4411567dc · outbound

This paper cites IEEE Computer Society.

Resource quantification for programming low-depth quantum circuits IEEE Computer Society

Reference 492

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source=pdf_text observed=2026-08-04T18:59:17.992275Z digest=sha256:c954fbc3c98288759c2db319e5a36964bed5c99e0f83a7b1c051ccad2fdcb2de

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