3 Search Results for "Bavarian, Mohammad"

Document
DOI: 10.4230/LIPIcs.ESA.2024.101
Time-Efficient Quantum Entropy Estimator via Samplizer

Authors: Qisheng Wang and Zhicheng Zhang

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)

Abstract
Entropy is a measure of the randomness of a system. Estimating the entropy of a quantum state is a basic problem in quantum information. In this paper, we introduce a time-efficient quantum approach to estimating the von Neumann entropy S(ρ) and Rényi entropy S_α(ρ) of an N-dimensional quantum state ρ, given access to independent samples of ρ. Specifically, we provide the following quantum estimators. - A quantum estimator for S(ρ) with time complexity Õ(N²), improving the prior best time complexity Õ(N⁶) by Acharya, Issa, Shende, and Wagner (2020) and Bavarian, Mehraba, and Wright (2016). - A quantum estimator for S_α(ρ) with time complexity Õ(N^{4/α-2}) for 0 < α < 1 and Õ(N^{4-2/α}) for α > 1, improving the prior best time complexity Õ(N^{6/α}) for 0 < α < 1 and Õ(N⁶) for α > 1 by Acharya, Issa, Shende, and Wagner (2020), though at a cost of a slightly larger sample complexity. Moreover, these estimators are naturally extensible to the low-rank case. We also provide a sample lower bound Ω(max{N/ε, N^{1/α-1}/ε^{1/α}}) for estimating S_α(ρ). Technically, our method is quite different from the previous ones that are based on weak Schur sampling and Young diagrams. At the heart of our construction, is a novel tool called samplizer, which can "samplize" a quantum query algorithm to a quantum algorithm with similar behavior using only samples of quantum states; this suggests a unified framework for estimating quantum entropies. Specifically, when a quantum oracle U block-encodes a mixed quantum state ρ, any quantum query algorithm using Q queries to U can be samplized to a δ-close (in the diamond norm) quantum algorithm using Θ~(Q²/δ) samples of ρ. Moreover, this samplization is proven to be optimal, up to a polylogarithmic factor.
Cite as

Qisheng Wang and Zhicheng Zhang. Time-Efficient Quantum Entropy Estimator via Samplizer. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 101:1-101:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{wang_et_al:LIPIcs.ESA.2024.101,
  author =	{Wang, Qisheng and Zhang, Zhicheng},
  title =	{{Time-Efficient Quantum Entropy Estimator via Samplizer}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{101:1--101:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2024.101},
  URN =		{urn:nbn:de:0030-drops-211722},
  doi =		{10.4230/LIPIcs.ESA.2024.101},
  annote =	{Keywords: Quantum computing, entropy estimation, von Neumann entropy, R\'{e}nyi entropy, sample complexity}
}
Document
DOI: 10.4230/LIPIcs.CP.2024.20
Constraint Modelling with LLMs Using In-Context Learning

Authors: Kostis Michailidis, Dimos Tsouros, and Tias Guns

Published in: LIPIcs, Volume 307, 30th International Conference on Principles and Practice of Constraint Programming (CP 2024)

Abstract
Constraint Programming (CP) allows for the modelling and solving of a wide range of combinatorial problems. However, modelling such problems using constraints over decision variables still requires significant expertise, both in conceptual thinking and syntactic use of modelling languages. In this work, we explore the potential of using pre-trained Large Language Models (LLMs) as coding assistants, to transform textual problem descriptions into concrete and executable CP specifications. We present different transformation pipelines with explicit intermediate representations, and we investigate the potential benefit of various retrieval-augmented example selection strategies for in-context learning. We evaluate our approach on 2 datasets from the literature, namely NL4Opt (optimisation) and Logic Grid Puzzles (satisfaction), and a heterogeneous set of exercises from a CP course. The results show that pre-trained LLMs have promising potential for initialising the modelling process, with retrieval-augmented in-context learning significantly enhancing their modelling capabilities.
Cite as

Kostis Michailidis, Dimos Tsouros, and Tias Guns. Constraint Modelling with LLMs Using In-Context Learning. In 30th International Conference on Principles and Practice of Constraint Programming (CP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 307, pp. 20:1-20:27, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{michailidis_et_al:LIPIcs.CP.2024.20,
  author =	{Michailidis, Kostis and Tsouros, Dimos and Guns, Tias},
  title =	{{Constraint Modelling with LLMs Using In-Context Learning}},
  booktitle =	{30th International Conference on Principles and Practice of Constraint Programming (CP 2024)},
  pages =	{20:1--20:27},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-336-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{307},
  editor =	{Shaw, Paul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2024.20},
  URN =		{urn:nbn:de:0030-drops-207053},
  doi =		{10.4230/LIPIcs.CP.2024.20},
  annote =	{Keywords: Constraint Modelling, Constraint Acquisition, Constraint Programming, Large Language Models, In-Context Learning, Natural Language Processing, Named Entity Recognition, Retrieval-Augmented Generation, Optimisation}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2017.22
Parallel Repetition via Fortification: Analytic View and the Quantum Case

Authors: Mohammad Bavarian, Thomas Vidick, and Henry Yuen

Published in: LIPIcs, Volume 67, 8th Innovations in Theoretical Computer Science Conference (ITCS 2017)

Abstract
In a recent work, Moshkovitz [FOCS'14] presented a transformation n two-player games called "fortification", and gave an elementary proof of an (exponential decay) parallel repetition theorem for fortified two-player projection games. In this paper, we give an analytic reformulation of Moshkovitz's fortification framework, which was originally cast in combinatorial terms. This reformulation allows us to expand the scope of the fortification method to new settings. First, we show any game (not just projection games) can be fortified, and give a simple proof of parallel repetition for general fortified games. Then, we prove parallel repetition and fortification theorems for games with players sharing quantum entanglement, as well as games with more than two players. This gives a new gap amplification method for general games in the quantum and multiplayer settings, which has recently received much interest. An important component of our work is a variant of the fortification transformation, called "ordered fortification", that preserves the entangled value of a game. The original fortification of Moshkovitz does not in general preserve the entangled value of a game, and this was a barrier to extending the fortification framework to the quantum setting.
Cite as

Mohammad Bavarian, Thomas Vidick, and Henry Yuen. Parallel Repetition via Fortification: Analytic View and the Quantum Case. In 8th Innovations in Theoretical Computer Science Conference (ITCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 67, pp. 22:1-22:33, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{bavarian_et_al:LIPIcs.ITCS.2017.22,
  author =	{Bavarian, Mohammad and Vidick, Thomas and Yuen, Henry},
  title =	{{Parallel Repetition via Fortification: Analytic View and the Quantum Case}},
  booktitle =	{8th Innovations in Theoretical Computer Science Conference (ITCS 2017)},
  pages =	{22:1--22:33},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-029-3},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{67},
  editor =	{Papadimitriou, Christos H.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2017.22},
  URN =		{urn:nbn:de:0030-drops-81670},
  doi =		{10.4230/LIPIcs.ITCS.2017.22},
  annote =	{Keywords: Parallel repetition, quantum entanglement, non-local games}
}
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