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Paper Citation Record · LEDGER

Resource quantification for programming low-depth quantum circuits

As of 14 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

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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 2026-08-13T06:32:02.005865+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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source=pdf_text observed=2026-08-04T18:59:14.496670Z digest=sha256:637cf7b18c660f037ceef4b000cb31dd10ffdba8e61167e965edddb1c4cf6dec

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:d629fc0c4901bdcf2aa11745c8e5478925dd4acd08bf1612b2d976280edb624b

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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source=pdf_text observed=2026-08-04T18:59:14.787904Z digest=sha256:f7cdfeb87e2e98559066d6508f4665b06d8fc4c3a895d6839880dcb14f968575

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:a6a9aab15c91af6b686e199bab4237e3b886aee611433ec2d1ee5c16a1eb38bc

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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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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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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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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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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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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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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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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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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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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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:b8ecf804f14c58170f795a3227653b55018e8efdb620e0664d96ad6be08e1419

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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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=sha256:8d281998eb28d98dc6631c5f73bf947b5ca8a26faabe0954adfc212a7eb11746

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=sha256:4739798ad9ca2f28c14674d30f394536090d4f1266b9a2e7d0beebb2dcc2a866

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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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=sha256:936d156fe05669d2a7f096b99a9709b2dc720da63b5a7808a3b28df7df07b801

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:ab306bd179c0ab2598e905c8f3f1c8d07b5b4a6908d4b6da5dad8de3da1ef0d1

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=sha256:35f4e2e576fe8e3f4993026304f256c475e00dad7d15f36096bda22fabf1253b

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:a3da96933335b7d0c007d990d8716ce9201e332494efa0c040eeb137d9e14e44

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=sha256:08064b632b401572a38f081248776b52a26a9cc0fbef24f6850deeb0f09eadb7

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=sha256:3125368be2247a09c694f7e83cb81865a7d3c81f682de45b1d225117b4e3ca6c

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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source=pdf_text observed=2026-08-04T18:59:20.541021Z digest=sha256:2c443a9d0cfdce694f148ce73c7a281fc8d82508b36d6378bbc970847d51419d

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:bfba53a118e7387972067b2f0cbebb8e348b96f4312ed041c3000e54c933e040

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:e8deca6719609c85e1402c37f17547d74e4e2abcc3d67b1ab86fcb2834febf50

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=sha256:3e64daa0261458528fa361a15dcf9a6904570a957c9d155e64faa2945963d47a

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=sha256:2285a6e44bfed820f2a958456f01a709f15fecc14cec5b8eb92d35205af6ea37

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=sha256:5218675b1c2d4137e0aad6cd50751c8df776d149f5612641c6ac508030d11c26

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=sha256:50816a87d885e43a5bb27d74e417c94c3a4dbf13402e0897a2a6640cd4339480

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=sha256:216c38d34dec1fb6c96e892c363bdbd36da258e31f31111e468f0bae78e31dbf

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=sha256:2ba13b654933627681f0e437222fd05c4584e43cef03896e34dba7f43a026b87

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=sha256:8d17c0d1a42c6099888050641a6e32e3e1047a849ba1bf1ef68559efc30e1efb

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=sha256:8ccfb8a22e498deceafaaf04ee4909fd1a518abbd34c29a5dcc1d3f767f6e519

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