4 Search Results for "Hsieh, Shu-Kai"

Document
DOI: 10.4230/LIPIcs.CCC.2023.33
On the Impossibility of General Parallel Fast-Forwarding of Hamiltonian Simulation

Authors: Nai-Hui Chia, Kai-Min Chung, Yao-Ching Hsieh, Han-Hsuan Lin, Yao-Ting Lin, and Yu-Ching Shen

Published in: LIPIcs, Volume 264, 38th Computational Complexity Conference (CCC 2023)

Abstract
Hamiltonian simulation is one of the most important problems in the field of quantum computing. There have been extended efforts on designing algorithms for faster simulation, and the evolution time T for the simulation greatly affect algorithm runtime as expected. While there are some specific types of Hamiltonians that can be fast-forwarded, i.e., simulated within time o(T), for some large classes of Hamiltonians (e.g., all local/sparse Hamiltonians), existing simulation algorithms require running time at least linear in the evolution time T. On the other hand, while there exist lower bounds of Ω(T) circuit size for some large classes of Hamiltonian, these lower bounds do not rule out the possibilities of Hamiltonian simulation with large but "low-depth" circuits by running things in parallel. As a result, physical systems with system size scaling with T can potentially do a fast-forwarding simulation. Therefore, it is intriguing whether we can achieve fast Hamiltonian simulation with the power of parallelism. In this work, we give a negative result for the above open problem in various settings. In the oracle model, we prove that there are time-independent sparse Hamiltonians that cannot be simulated via an oracle circuit of depth o(T). In the plain model, relying on the random oracle heuristic, we show that there exist time-independent local Hamiltonians and time-dependent geometrically local Hamiltonians on n qubits that cannot be simulated via an oracle circuit of depth o(T/n^c), where the Hamiltonians act on n qubits, and c is a constant. Lastly, we generalize the above results and show that any simulators that are geometrically local Hamiltonians cannot do the simulation much faster than parallel quantum algorithms.
Cite as

Nai-Hui Chia, Kai-Min Chung, Yao-Ching Hsieh, Han-Hsuan Lin, Yao-Ting Lin, and Yu-Ching Shen. On the Impossibility of General Parallel Fast-Forwarding of Hamiltonian Simulation. In 38th Computational Complexity Conference (CCC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 264, pp. 33:1-33:45, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{chia_et_al:LIPIcs.CCC.2023.33,
  author =	{Chia, Nai-Hui and Chung, Kai-Min and Hsieh, Yao-Ching and Lin, Han-Hsuan and Lin, Yao-Ting and Shen, Yu-Ching},
  title =	{{On the Impossibility of General Parallel Fast-Forwarding of Hamiltonian Simulation}},
  booktitle =	{38th Computational Complexity Conference (CCC 2023)},
  pages =	{33:1--33:45},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-282-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{264},
  editor =	{Ta-Shma, Amnon},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2023.33},
  URN =		{urn:nbn:de:0030-drops-183038},
  doi =		{10.4230/LIPIcs.CCC.2023.33},
  annote =	{Keywords: Hamiltonian simulation, Depth lower bound, Parallel query lower bound}
}
Document
DOI: 10.4230/LIPIcs.TQC.2021.2
Quantum Pseudorandomness and Classical Complexity

Authors: William Kretschmer

Published in: LIPIcs, Volume 197, 16th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2021)

Abstract
We construct a quantum oracle relative to which BQP = QMA but cryptographic pseudorandom quantum states and pseudorandom unitary transformations exist, a counterintuitive result in light of the fact that pseudorandom states can be "broken" by quantum Merlin-Arthur adversaries. We explain how this nuance arises as the result of a distinction between algorithms that operate on quantum and classical inputs. On the other hand, we show that some computational complexity assumption is needed to construct pseudorandom states, by proving that pseudorandom states do not exist if BQP = PP. We discuss implications of these results for cryptography, complexity theory, and quantum tomography.
Cite as

William Kretschmer. Quantum Pseudorandomness and Classical Complexity. In 16th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 197, pp. 2:1-2:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{kretschmer:LIPIcs.TQC.2021.2,
  author =	{Kretschmer, William},
  title =	{{Quantum Pseudorandomness and Classical Complexity}},
  booktitle =	{16th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2021)},
  pages =	{2:1--2:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-198-6},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{197},
  editor =	{Hsieh, Min-Hsiu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2021.2},
  URN =		{urn:nbn:de:0030-drops-139975},
  doi =		{10.4230/LIPIcs.TQC.2021.2},
  annote =	{Keywords: pseudorandom quantum states, quantum Merlin-Arthur}
}
Document
DOI: 10.4230/LIPIcs.TQC.2021.3
Sample Efficient Algorithms for Learning Quantum Channels in PAC Model and the Approximate State Discrimination Problem

Authors: Kai-Min Chung and Han-Hsuan Lin

Published in: LIPIcs, Volume 197, 16th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2021)

Abstract
The probably approximately correct (PAC) model [Leslie G. Valiant, 1984] is a well studied model in classical learning theory. Here, we generalize the PAC model from concepts of Boolean functions to quantum channels, introducing PAC model for learning quantum channels, and give two sample efficient algorithms that are analogous to the classical "Occam’s razor" result [Blumer et al., 1987]. The classical Occam’s razor algorithm is done trivially by excluding any concepts not compatible with the input-output pairs one gets, but such an approach is not immediately possible with a concept class of quantum channels, because the outputs are unknown quantum states from the quantum channel. To study the quantum state learning problem associated with PAC learning quantum channels, we focus on the special case where the channels all have constant output. In this special case, learning the channels reduce to a problem of learning quantum states that is similar to the well known quantum state discrimination problem [Joonwoo Bae and Leong-Chuan Kwek, 2017], but with the extra twist that we allow ε-trace-distance-error in the output. We call this problem Approximate State Discrimination, which we believe is a natural problem that is of independent interest. We give two algorithms for learning quantum channels in PAC model. The first algorithm has sample complexity O((log|C| + log(1/ δ))/(ε²)), but only works when the outputs are pure states, where C is the concept class, ε is the error of the output, and δ is the probability of failure of the algorithm. The second algorithm has sample complexity O((log³|C|(log|C|+log(1/ δ)))/(ε²)), and work for mixed state outputs. Some implications of our results are that we can PAC-learn a polynomial sized quantum circuit in polynomial samples, and approximate state discrimination can be solved in polynomial samples even when the size of the input set is exponential in the number of qubits, exponentially better than a naive state tomography.
Cite as

Kai-Min Chung and Han-Hsuan Lin. Sample Efficient Algorithms for Learning Quantum Channels in PAC Model and the Approximate State Discrimination Problem. In 16th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 197, pp. 3:1-3:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{chung_et_al:LIPIcs.TQC.2021.3,
  author =	{Chung, Kai-Min and Lin, Han-Hsuan},
  title =	{{Sample Efficient Algorithms for Learning Quantum Channels in PAC Model and the Approximate State Discrimination Problem}},
  booktitle =	{16th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2021)},
  pages =	{3:1--3:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-198-6},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{197},
  editor =	{Hsieh, Min-Hsiu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2021.3},
  URN =		{urn:nbn:de:0030-drops-139984},
  doi =		{10.4230/LIPIcs.TQC.2021.3},
  annote =	{Keywords: PAC learning, Quantum PAC learning, Sample Complexity, Approximate State Discrimination, Quantum information}
}
Document
Short Paper
DOI: 10.4230/OASIcs.LDK.2019.24
The Secret to Popular Chinese Web Novels: A Corpus-Driven Study

Authors: Yi-Ju Lin and Shu-Kai Hsieh

Published in: OASIcs, Volume 70, 2nd Conference on Language, Data and Knowledge (LDK 2019)

Abstract
What is the secret to writing popular novels? The issue is an intriguing one among researchers from various fields. The goal of this study is to identify the linguistic features of several popular web novels as well as how the textual features found within and the overall tone interact with the genre and themes of each novel. Apart from writing style, non-textual information may also reveal details behind the success of web novels. Since web fiction has become a major industry with top writers making millions of dollars and their stories adapted into published books, determining essential elements of "publishable" novels is of importance. The present study further examines how non-textual information, namely, the number of hits, shares, favorites, and comments, may contribute to several features of the most popular published and unpublished web novels. Findings reveal that keywords, function words, and lexical diversity of a novel are highly related to its genres and writing style while dialogue proportion shows the narration voice of the story. In addition, relatively shorter sentences are found in these novels. The data also reveal that the number of favorites and comments serve as significant predictors for the number of shares and hits of unpublished web novels, respectively; however, the number of hits and shares of published web novels is more unpredictable.
Cite as

Yi-Ju Lin and Shu-Kai Hsieh. The Secret to Popular Chinese Web Novels: A Corpus-Driven Study. In 2nd Conference on Language, Data and Knowledge (LDK 2019). Open Access Series in Informatics (OASIcs), Volume 70, pp. 24:1-24:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{lin_et_al:OASIcs.LDK.2019.24,
  author =	{Lin, Yi-Ju and Hsieh, Shu-Kai},
  title =	{{The Secret to Popular Chinese Web Novels: A Corpus-Driven Study}},
  booktitle =	{2nd Conference on Language, Data and Knowledge (LDK 2019)},
  pages =	{24:1--24:8},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-105-4},
  ISSN =	{2190-6807},
  year =	{2019},
  volume =	{70},
  editor =	{Eskevich, Maria and de Melo, Gerard and F\"{a}th, Christian and McCrae, John P. and Buitelaar, Paul and Chiarcos, Christian and Klimek, Bettina and Dojchinovski, Milan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.LDK.2019.24},
  URN =		{urn:nbn:de:0030-drops-103882},
  doi =		{10.4230/OASIcs.LDK.2019.24},
  annote =	{Keywords: Popular Chinese Web Novels, NLP techniques, Sentiment Analysis, Publication of Web novels}
}
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