Improved Quantum Algorithms for Reinforcement Learning Under a Generative Model | Paper Citation Record

Observation 76fdd918-7bd3-4e42-913b-042422c4c0d2 · outbound

This paper cites Abanin, Laleh Aghababaie-Beni, Igor Aleiner, Trond I.

Improved Quantum Algorithms for Reinforcement Learning Under a Generative Model Abanin, Laleh Aghababaie-Beni, Igor Aleiner, Trond I

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:07:18.646160Z

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Observation 85d247fb-41c2-425b-9c94-72b505e32164 · outbound

This paper cites An introduction to quantum machine learning: from quantum logic to quantum deep learning.Quantum Machine Intelligence, 3(2):28, Nov 2021.

Improved Quantum Algorithms for Reinforcement Learning Under a Generative Model An introduction to quantum machine learning: from quantum logic to quantum deep learning.Quantum Machine Intelligence, 3(2):28, Nov 2021

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:07:18.632320Z

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Observation 37408673-af90-494d-a973-0ef87c4374eb · outbound

This paper cites Doriguello, Alessandro Luongo, and Miklos Santha.

Improved Quantum Algorithms for Reinforcement Learning Under a Generative Model Doriguello, Alessandro Luongo, and Miklos Santha

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:07:18.620663Z

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Observation 73a7406c-769d-4718-a6bd-433367a55a14 · outbound

This paper cites A Bit of Freedom Goes a Long Way: Classical and Quantum Algorithms for Reinforcement Learning under a Generative Model.

Improved Quantum Algorithms for Reinforcement Learning Under a Generative Model A Bit of Freedom Goes a Long Way: Classical and Quantum Algorithms for Reinforcement Learning under a Generative Model

Reference 4

Resolution: verified exact; local_arxiv, observed 2026-08-15T15:07:18.047918Z

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Observation e4e43875-34a1-4d4f-b359-f08200ae3e38 · outbound

This paper cites Bardin, Rami Barends, Rupak Biswas, Sergio Boixo, Fernando G.

Improved Quantum Algorithms for Reinforcement Learning Under a Generative Model Bardin, Rami Barends, Rupak Biswas, Sergio Boixo, Fernando G

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:07:18.609973Z

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Observation 864ff43d-0202-4ab3-b0a1-db2c8fc5b5a5 · outbound

This paper cites Optimal control of Markov processes with incomplete state information I.Journal of mathematical analysis and applications, 10:174–205, 1965.

Improved Quantum Algorithms for Reinforcement Learning Under a Generative Model Optimal control of Markov processes with incomplete state information I.Journal of mathematical analysis and applications, 10:174–205, 1965

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:07:18.598404Z

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Observation 4f90531e-a76b-43c4-8fb0-34c1324b86ad · outbound

This paper cites Springer Science & Business Media, 2011.

Improved Quantum Algorithms for Reinforcement Learning Under a Generative Model Springer Science & Business Media, 2011

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:07:18.587406Z

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Observation 74f13b6c-50b0-4a0a-9421-e36ce1843644 · outbound

This paper cites Artificial intelligence framework for simulating clinical decision-making: A Markov decision process approach.Artificial intelligence in medicine, 57(1):9–19, 2013.

Improved Quantum Algorithms for Reinforcement Learning Under a Generative Model Artificial intelligence framework for simulating clinical decision-making: A Markov decision process approach.Artificial intelligence in medicine, 57(1):9–19, 2013

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:07:18.576857Z

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Observation 30989889-863a-4340-91ee-44918bc453a2 · outbound

This paper cites Athena scientific, 2012.

Improved Quantum Algorithms for Reinforcement Learning Under a Generative Model Athena scientific, 2012

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:07:18.565374Z

Source-reported events for the cited work

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Observation d44b796c-d79f-412a-9d46-d009bc1ba4f9 · outbound

This paper cites Athena Scientific, 2022.

Improved Quantum Algorithms for Reinforcement Learning Under a Generative Model Athena Scientific, 2022

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:07:18.555073Z

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Observation 3f6e532e-5997-42cc-bff4-734a7f1509d0 · outbound

This paper cites Quantum machine learning.Nature, 549(7671):195–202, Sep 2017.

Improved Quantum Algorithms for Reinforcement Learning Under a Generative Model Quantum machine learning.Nature, 549(7671):195–202, Sep 2017

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:07:18.544609Z

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Observation 98f0a11c-1f32-4c28-b6bc-a8cd0d2e499a · outbound

This paper cites Distributed autonomous virtual resource management in datacenters using finite-Markov decision process.

Improved Quantum Algorithms for Reinforcement Learning Under a Generative Model Distributed autonomous virtual resource management in datacenters using finite-Markov decision process

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:07:18.533933Z

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Observation 2809a7d0-3c42-405e-9da5-f27f7fd01c74 · outbound

This paper cites Quantum Algorithms and Lower Bounds for Linear Regression with Norm Constraints.

Improved Quantum Algorithms for Reinforcement Learning Under a Generative Model Quantum Algorithms and Lower Bounds for Linear Regression with Norm Constraints

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-15T15:07:17.778989Z

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Observation 6b5ab5a9-bb43-48f1-b977-097dd4d671e2 · outbound

This paper cites Oberoi, and Pooya Ron- agh.

Improved Quantum Algorithms for Reinforcement Learning Under a Generative Model Oberoi, and Pooya Ron- agh

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:07:18.522967Z

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Observation 3a979d2c-0726-4b84-a521-a4df185ec708 · outbound

This paper cites Quantum reinforcement learning.IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 38(5):1207–1220, 2008.

Improved Quantum Algorithms for Reinforcement Learning Under a Generative Model Quantum reinforcement learning.IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 38(5):1207–1220, 2008

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:07:18.510832Z

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Observation c3ad0f1d-bd4a-4b5d-b30c-6ddc0e1ee8c1 · outbound

This paper cites Do you know what q-means?.

Improved Quantum Algorithms for Reinforcement Learning Under a Generative Model Do you know what q-means?

Reference 16

Resolution: verified exact; local_arxiv, observed 2026-08-15T15:07:18.017727Z

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Observation f5cf0bcd-db74-484a-9c30-d2cca021790e · outbound

This paper cites A Quantum Algorithm for Finding the Minimum.

Improved Quantum Algorithms for Reinforcement Learning Under a Generative Model A Quantum Algorithm for Finding the Minimum

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-15T15:07:17.796253Z

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Observation 17852fab-f591-4266-b696-76175f05ec1a · outbound

This paper cites Springer Science & Business Media, 2012.

Improved Quantum Algorithms for Reinforcement Learning Under a Generative Model Springer Science & Business Media, 2012

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:07:18.499851Z

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Observation b78a6104-f4bf-483d-a43d-da2474b6e3fd · outbound

This paper cites an unresolved cited work.

Improved Quantum Algorithms for Reinforcement Learning Under a Generative Model Unresolved cited work

Reference 19

Resolution: unresolved; raw_fallback, observed 2026-08-15T15:07:18.489165Z

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Observation cb725a40-5257-4948-8d49-2b04415cf7a3 · outbound

This paper cites Architectures for a quantum random access memory.Phys.

Improved Quantum Algorithms for Reinforcement Learning Under a Generative Model Architectures for a quantum random access memory.Phys

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:07:18.477208Z

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Observation 2a3c6c84-5a44-4691-a93c-07e7b44bdfd3 · outbound

This paper cites Quantum random access memory.

Improved Quantum Algorithms for Reinforcement Learning Under a Generative Model Quantum random access memory

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:07:18.465944Z

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Observation fa4686bb-2bfe-4091-afdc-5aa80df6f518 · outbound

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

Improved Quantum Algorithms for Reinforcement Learning Under a Generative Model A fast quantum mechanical algorithm for database search

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:07:18.455360Z

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Observation cf12dd33-18e0-4e1b-8426-952f7d123e7a · outbound

This paper cites Theses, Universit´ e Paris Cit´ e, July 2021.

Improved Quantum Algorithms for Reinforcement Learning Under a Generative Model Theses, Universit´ e Paris Cit´ e, July 2021

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:07:18.444985Z

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Observation 229cef5e-4b19-4a10-ac0a-937ae61ae0cb · outbound

This paper cites Quantum Sub-Gaussian Mean Estimator.

Improved Quantum Algorithms for Reinforcement Learning Under a Generative Model Quantum Sub-Gaussian Mean Estimator

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:07:18.434736Z

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Observation 48e8c4f8-efbc-4abe-9edc-0a84498d2d39 · outbound

This paper cites Quantum Chebyshev’s Inequality and Applica- tions.

Improved Quantum Algorithms for Reinforcement Learning Under a Generative Model Quantum Chebyshev’s Inequality and Applica- tions

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:07:18.422829Z

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Observation 5adfd34a-b7e5-46b1-945c-4576bd52103b · outbound

This paper cites Harrow, Avinatan Hassidim, and Seth Lloyd.

Improved Quantum Algorithms for Reinforcement Learning Under a Generative Model Harrow, Avinatan Hassidim, and Seth Lloyd

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:07:18.411363Z

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Observation 91a210ff-3ebd-47e9-84a8-70e67bfe553f · outbound

This paper cites Springer Science & Business Media, 2007.

Improved Quantum Algorithms for Reinforcement Learning Under a Generative Model Springer Science & Business Media, 2007

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:07:18.398925Z

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Observation 1b2c57c7-c34c-4c59-8a1b-efc817b8d854 · outbound

This paper cites an unresolved cited work.

Improved Quantum Algorithms for Reinforcement Learning Under a Generative Model Unresolved cited work

Reference 28

Resolution: unresolved; raw_fallback, observed 2026-08-15T15:07:18.387764Z

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Observation c1367d74-a346-4546-b394-8a8db37d8a2f · outbound

This paper cites Quantum Policy Gra- dient Algorithms.

Improved Quantum Algorithms for Reinforcement Learning Under a Generative Model Quantum Policy Gra- dient Algorithms

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:07:18.377523Z

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Observation 94c45e17-edd7-4756-951a-69fcd08d4e7b · outbound

This paper cites Uni- versity of London, University College London (United Kingdom), 2003.

Improved Quantum Algorithms for Reinforcement Learning Under a Generative Model Uni- versity of London, University College London (United Kingdom), 2003

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:07:18.366844Z

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Observation f0b51de7-2ee8-411f-8847-25b948fa0184 · outbound

This paper cites an unresolved cited work.

Improved Quantum Algorithms for Reinforcement Learning Under a Generative Model Unresolved cited work

Reference 31

Resolution: unresolved; raw_fallback, observed 2026-08-15T15:07:18.356005Z

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Observation 60e83481-2558-4740-993f-f286326e8be2 · outbound

This paper cites Finite-sample convergence rates for Q-learning and indirect algorithms.Advances in neural information processing systems, 11, 1998.

Improved Quantum Algorithms for Reinforcement Learning Under a Generative Model Finite-sample convergence rates for Q-learning and indirect algorithms.Advances in neural information processing systems, 11, 1998

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Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:07:18.344788Z

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Observation 039d77a4-2c71-4c95-8226-9dbf7049fea3 · outbound

This paper cites Finite-sample convergence rates for Q-learning and indirect algorithms.

Improved Quantum Algorithms for Reinforcement Learning Under a Generative Model Finite-sample convergence rates for Q-learning and indirect algorithms

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:07:18.333506Z

Source-reported events for the cited work

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Observation d0831de8-d230-4a96-b0d0-d35ed27b3296 · outbound

This paper cites q-means: A quantum algorithm for unsupervised machine learning.

Improved Quantum Algorithms for Reinforcement Learning Under a Generative Model q-means: A quantum algorithm for unsupervised machine learning

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Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:07:18.322662Z

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Observation 16568c67-4190-4663-b979-ea1f049b906a · outbound

This paper cites Quantum Recommendation Systems.

Improved Quantum Algorithms for Reinforcement Learning Under a Generative Model Quantum Recommendation Systems

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Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:07:18.310644Z

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Observation 9b5e63d1-1c1d-4db8-a459-11156ea50159 · outbound

This paper cites Mean estimation when you have the source code; or, quantum Monte Carlo methods.

Improved Quantum Algorithms for Reinforcement Learning Under a Generative Model Mean estimation when you have the source code; or, quantum Monte Carlo methods

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Observation 6e4dd1bb-79b2-43c2-96c6-a314569af390 · outbound

This paper cites Breaking the sample size barrier in model-based reinforcement learning with a generative model.

Improved Quantum Algorithms for Reinforcement Learning Under a Generative Model Breaking the sample size barrier in model-based reinforcement learning with a generative model

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Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:07:18.286831Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation c8adb182-bc25-448f-806c-d74ec21f4db1 · outbound

This paper cites Quantum algorithms for supervised and unsupervised machine learning.

Improved Quantum Algorithms for Reinforcement Learning Under a Generative Model Quantum algorithms for supervised and unsupervised machine learning

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Unavailable: canonical work link unavailable.

Observation a055fbe5-0ecb-43d5-8ba7-87097e58dd05 · outbound

This paper cites an unresolved cited work.

Improved Quantum Algorithms for Reinforcement Learning Under a Generative Model Unresolved cited work

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Resolution: unresolved; raw_fallback, observed 2026-08-15T15:07:18.275513Z

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Observation 4822e019-28ef-4d58-836f-49a44bc3df0f · outbound

This paper cites Quantum speedup of Monte Carlo methods.Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 471(2181):20150301, 2015.

Improved Quantum Algorithms for Reinforcement Learning Under a Generative Model Quantum speedup of Monte Carlo methods.Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 471(2181):20150301, 2015

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Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:07:18.265223Z

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Observation 1408c7db-2adc-4fbf-bb52-9abb25f8c598 · outbound

This paper cites Springer Nature, 2022.

Improved Quantum Algorithms for Reinforcement Learning Under a Generative Model Springer Nature, 2022

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Source-reported events for the cited work

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Observation b72b90ba-6da9-49fb-a805-36dfd2a1a2b1 · outbound

This paper cites Cambridge university press, 2010.

Improved Quantum Algorithms for Reinforcement Learning Under a Generative Model Cambridge university press, 2010

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Source-reported events for the cited work

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Observation 88199678-b974-48fd-b53c-dc94d2a24bd7 · outbound

This paper cites John Wiley & Sons, 2007.

Improved Quantum Algorithms for Reinforcement Learning Under a Generative Model John Wiley & Sons, 2007

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Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:07:18.230589Z

Source-reported events for the cited work

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Observation 19c0f45a-e4eb-4366-9907-f87f25abf150 · outbound

This paper cites John Wiley & Sons, 2014.

Improved Quantum Algorithms for Reinforcement Learning Under a Generative Model John Wiley & Sons, 2014

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Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:07:18.218676Z

Source-reported events for the cited work

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Observation 3b1659b3-e573-4acb-81b3-1f8dc6177a24 · outbound

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Improved Quantum Algorithms for Reinforcement Learning Under a Generative Model Quantum support vector machine for big data classification.Phys

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Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:07:18.207261Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation f96e0cb4-f3a1-4117-b8c4-89e42c2e3bf2 · outbound

This paper cites Saggio, B.

Improved Quantum Algorithms for Reinforcement Learning Under a Generative Model Saggio, B

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Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:07:18.196370Z

Source-reported events for the cited work

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Observation 74f98c6a-cc08-4628-9bcd-87ef7c9f532d · outbound

This paper cites Markov models in health care.Einstein (S˜ ao Paulo), 8:376–379, 2010.

Improved Quantum Algorithms for Reinforcement Learning Under a Generative Model Markov models in health care.Einstein (S˜ ao Paulo), 8:376–379, 2010

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Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:07:18.185291Z

Source-reported events for the cited work

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Observation 49d2b317-1941-43a4-8601-26098e18a2e0 · outbound

This paper cites An introduction to quantum machine learning.Contemporary Physics, 56(2):172–185, 2015.

Improved Quantum Algorithms for Reinforcement Learning Under a Generative Model An introduction to quantum machine learning.Contemporary Physics, 56(2):172–185, 2015

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Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:07:18.174534Z

Source-reported events for the cited work

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Observation 4898ae91-7999-4517-bba4-0b2c3d3d8a5c · outbound

This paper cites an unresolved cited work.

Improved Quantum Algorithms for Reinforcement Learning Under a Generative Model Unresolved cited work

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Resolution: unresolved; raw_fallback, observed 2026-08-15T15:07:18.163719Z

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Observation a44f9f50-51e2-48ed-a7a7-0c6ec0fe6fdd · outbound

This paper cites Near-optimal time and sample complexities for solving Markov decision processes with a generative model.

Improved Quantum Algorithms for Reinforcement Learning Under a Generative Model Near-optimal time and sample complexities for solving Markov decision processes with a generative model

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Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:07:18.152788Z

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Observation 586d3623-ae27-45b1-a367-31593668c139 · outbound

This paper cites Variance reduced value iteration and faster algorithms for solving Markov decision processes.

Improved Quantum Algorithms for Reinforcement Learning Under a Generative Model Variance reduced value iteration and faster algorithms for solving Markov decision processes

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Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:07:18.141776Z

Source-reported events for the cited work

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Observation eed16f05-0071-483f-87ce-90623dfd941b · outbound

This paper cites Markov decision processes for screening and treat- ment of chronic diseases.Markov Decision Processes in Practice, pages 189–222, 2017.

Improved Quantum Algorithms for Reinforcement Learning Under a Generative Model Markov decision processes for screening and treat- ment of chronic diseases.Markov Decision Processes in Practice, pages 189–222, 2017

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Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:07:18.130353Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation feee4c3a-406d-4be4-81d8-f20b63bdf1ad · outbound

This paper cites MIT press Cambridge, 1998.

Improved Quantum Algorithms for Reinforcement Learning Under a Generative Model MIT press Cambridge, 1998

Reference 53

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:07:18.118530Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation d2119d0f-b354-44de-a553-503de4b722a1 · outbound

This paper cites Synthesis Lectures on Artificial Intelligence and Machine Learning.

Improved Quantum Algorithms for Reinforcement Learning Under a Generative Model Synthesis Lectures on Artificial Intelligence and Machine Learning

Reference 54

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:07:18.106154Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation fd891404-1e21-4677-8f80-08305e5d52a3 · outbound

This paper cites Quantum algorithms for reinforcement learning with a generative model.

Improved Quantum Algorithms for Reinforcement Learning Under a Generative Model Quantum algorithms for reinforcement learning with a generative model

Reference 55

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:07:18.095025Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation bc8f3511-b7a3-4145-baf7-4c4b66f058fb · outbound

This paper cites Randomized Linear Programming Solves the Discounted Markov Decision Problem In Nearly-Linear (Sometimes Sublinear) Running Time.

Improved Quantum Algorithms for Reinforcement Learning Under a Generative Model Randomized Linear Programming Solves the Discounted Markov Decision Problem In Nearly-Linear (Sometimes Sublinear) Running Time

Reference 56

Resolution: unresolved; no resolver link, observed 2026-08-15T15:07:17.938278Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2246e1c5-14e1-4e24-87d3-3f0303500692 · outbound

This paper cites an unresolved cited work.

Improved Quantum Algorithms for Reinforcement Learning Under a Generative Model Unresolved cited work

Reference 57

Resolution: unresolved; raw_fallback, observed 2026-08-15T15:07:18.083819Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 493a2f05-cc7b-4ab0-9c12-c8528a3a8c17 · outbound

This paper cites an unresolved cited work.

Improved Quantum Algorithms for Reinforcement Learning Under a Generative Model Unresolved cited work

Reference 58

Resolution: unresolved; raw_fallback, observed 2026-08-15T15:07:18.072201Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 9ffe56c9-f9d5-427b-8553-d06e9a8fbea8 · outbound

This paper cites Provably efficient exploration in quantum reinforcement learning with logarithmic worst-case regret.

Improved Quantum Algorithms for Reinforcement Learning Under a Generative Model Provably efficient exploration in quantum reinforcement learning with logarithmic worst-case regret

Reference 59

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:07:18.060115Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Coverage vector

Reference resolution

Outbound references

Pith citing papers