12 Search Results for "Lin, Yu"

Document
DOI: 10.4230/LIPIcs.ESA.2023.81
Tight Bounds for Quantum Phase Estimation and Related Problems

Authors: Nikhil S. Mande and Ronald de Wolf

Published in: LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023)

Abstract
Phase estimation, due to Kitaev [arXiv'95], is one of the most fundamental subroutines in quantum computing, used in Shor’s factoring algorithm, optimization algorithms, quantum chemistry algorithms, and many others. In the basic scenario, one is given black-box access to a unitary U, and an eigenstate |ψ⟩ of U with unknown eigenvalue e^{iθ}, and the task is to estimate the eigenphase θ within ±δ, with high probability. The repeated application of U and U^{-1} is typically the most expensive part of phase estimation, so for us the cost of an algorithm will be that number of applications. Motivated by the "guided Hamiltonian problem" in quantum chemistry, we tightly characterize the cost of several variants of phase estimation where we are no longer given an arbitrary eigenstate, but are required to estimate the maximum eigenphase of U, aided by advice in the form of states (or a unitary preparing those states) which are promised to have at least a certain overlap γ with the top eigenspace. We give algorithms and matching lower bounds (up to logarithmic factors) for all ranges of parameters. We show a crossover point below which advice is not helpful: o(1/γ²) copies of the advice state (or o(1/γ) applications of an advice-preparing unitary) are not significantly better than having no advice at all. We also show that having knowledge of the eigenbasis of U does not significantly reduce cost. Our upper bounds use the subroutine of generalized maximum-finding of van Apeldoorn, Gilyén, Gribling, and de Wolf [Quantum'20], the state-based Hamiltonian simulation of Lloyd, Mohseni, and Rebentrost [Nature Physics'13], and several other techniques. Our lower bounds follow by reductions from a fractional version of the Boolean OR function with advice, which we lower bound by a simple modification of the adversary method of Ambainis [JCSS'02]. As an immediate consequence we also obtain a lower bound on the complexity of the Unitary recurrence time problem, matching an upper bound of She and Yuen [ITCS'23] and resolving an open question posed by them. Lastly, we study how efficiently one can reduce the error probability in the basic phase-estimation scenario. We show that an algorithm solving phase estimation to precision δ with error probability at most ε must have cost Ω(1/δ log(1/ε)), matching the obvious way to error-reduce the basic constant-error-probability phase estimation algorithm. This contrasts with some other scenarios in quantum computing (e.g. search) where error-reduction costs only a factor O(√{log(1/ε)}). Our lower bound technique uses a variant of the polynomial method with trigonometric polynomials.
Cite as

Nikhil S. Mande and Ronald de Wolf. Tight Bounds for Quantum Phase Estimation and Related Problems. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 81:1-81:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{mande_et_al:LIPIcs.ESA.2023.81,
  author =	{Mande, Nikhil S. and de Wolf, Ronald},
  title =	{{Tight Bounds for Quantum Phase Estimation and Related Problems}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{81:1--81:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2023.81},
  URN =		{urn:nbn:de:0030-drops-187346},
  doi =		{10.4230/LIPIcs.ESA.2023.81},
  annote =	{Keywords: Phase estimation, quantum computing}
}
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.ESA.2021.31
Feature Cross Search via Submodular Optimization

Authors: Lin Chen, Hossein Esfandiari, Gang Fu, Vahab S. Mirrokni, and Qian Yu

Published in: LIPIcs, Volume 204, 29th Annual European Symposium on Algorithms (ESA 2021)

Abstract
In this paper, we study feature cross search as a fundamental primitive in feature engineering. The importance of feature cross search especially for the linear model has been known for a while, with well-known textbook examples. In this problem, the goal is to select a small subset of features, combine them to form a new feature (called the crossed feature) by considering their Cartesian product, and find feature crosses to learn an accurate model. In particular, we study the problem of maximizing a normalized Area Under the Curve (AUC) of the linear model trained on the crossed feature column. First, we show that it is not possible to provide an n^{1/log log n}-approximation algorithm for this problem unless the exponential time hypothesis fails. This result also rules out the possibility of solving this problem in polynomial time unless 𝖯 = NP. On the positive side, by assuming the naïve Bayes assumption, we show that there exists a simple greedy (1-1/e)-approximation algorithm for this problem. This result is established by relating the AUC to the total variation of the commutator of two probability measures and showing that the total variation of the commutator is monotone and submodular. To show this, we relate the submodularity of this function to the positive semi-definiteness of a corresponding kernel matrix. Then, we use Bochner’s theorem to prove the positive semi-definiteness by showing that its inverse Fourier transform is non-negative everywhere. Our techniques and structural results might be of independent interest.
Cite as

Lin Chen, Hossein Esfandiari, Gang Fu, Vahab S. Mirrokni, and Qian Yu. Feature Cross Search via Submodular Optimization. In 29th Annual European Symposium on Algorithms (ESA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 204, pp. 31:1-31:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{chen_et_al:LIPIcs.ESA.2021.31,
  author =	{Chen, Lin and Esfandiari, Hossein and Fu, Gang and Mirrokni, Vahab S. and Yu, Qian},
  title =	{{Feature Cross Search via Submodular Optimization}},
  booktitle =	{29th Annual European Symposium on Algorithms (ESA 2021)},
  pages =	{31:1--31:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-204-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{204},
  editor =	{Mutzel, Petra and Pagh, Rasmus and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2021.31},
  URN =		{urn:nbn:de:0030-drops-146124},
  doi =		{10.4230/LIPIcs.ESA.2021.31},
  annote =	{Keywords: Feature engineering, feature cross, submodularity}
}
Document
DOI: 10.4230/LIPIcs.WABI.2021.11
LRBinner: Binning Long Reads in Metagenomics Datasets

Authors: Anuradha Wickramarachchi and Yu Lin

Published in: LIPIcs, Volume 201, 21st International Workshop on Algorithms in Bioinformatics (WABI 2021)

Abstract
Advancements in metagenomics sequencing allow the study of microbial communities directly from their environments. Metagenomics binning is a key step in the species characterisation of microbial communities. Next-generation sequencing reads are usually assembled into contigs for metagenomics binning mainly due to the limited information within short reads. Third-generation sequencing provides much longer reads that have lengths similar to the contigs assembled from short reads. However, existing contig-binning tools cannot be directly applied on long reads due to the absence of coverage information and the presence of high error rates. The few existing long-read binning tools either use only composition or use composition and coverage information separately. This may ignore bins that correspond to low-abundance species or erroneously split bins that correspond to species with non-uniform coverages. Here we present a reference-free binning approach, LRBinner, that combines composition and coverage information of complete long-read datasets. LRBinner also uses a distance-histogram-based clustering algorithm to extract clusters with varying sizes. The experimental results on both simulated and real datasets show that LRBinner achieves the best binning accuracy against the baselines. Moreover, we show that binning reads using LRBinner prior to assembly reduces computational resources for assembly while attaining satisfactory assembly qualities.
Cite as

Anuradha Wickramarachchi and Yu Lin. LRBinner: Binning Long Reads in Metagenomics Datasets. In 21st International Workshop on Algorithms in Bioinformatics (WABI 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 201, pp. 11:1-11:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{wickramarachchi_et_al:LIPIcs.WABI.2021.11,
  author =	{Wickramarachchi, Anuradha and Lin, Yu},
  title =	{{LRBinner: Binning Long Reads in Metagenomics Datasets}},
  booktitle =	{21st International Workshop on Algorithms in Bioinformatics (WABI 2021)},
  pages =	{11:1--11:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-200-6},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{201},
  editor =	{Carbone, Alessandra and El-Kebir, Mohammed},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2021.11},
  URN =		{urn:nbn:de:0030-drops-143644},
  doi =		{10.4230/LIPIcs.WABI.2021.11},
  annote =	{Keywords: Metagenomics binning, long reads, machine learning, clustering}
}
Document
DOI: 10.4230/LIPIcs.WABI.2020.8
GraphBin2: Refined and Overlapped Binning of Metagenomic Contigs Using Assembly Graphs

Authors: Vijini G. Mallawaarachchi, Anuradha S. Wickramarachchi, and Yu Lin

Published in: LIPIcs, Volume 172, 20th International Workshop on Algorithms in Bioinformatics (WABI 2020)

Abstract
Metagenomic sequencing allows us to study structure, diversity and ecology in microbial communities without the necessity of obtaining pure cultures. In many metagenomics studies, the reads obtained from metagenomics sequencing are first assembled into longer contigs and these contigs are then binned into clusters of contigs where contigs in a cluster are expected to come from the same species. As different species may share common sequences in their genomes, one assembled contig may belong to multiple species. However, existing tools for contig binning only support non-overlapped binning, i.e., each contig is assigned to at most one bin (species). In this paper, we introduce GraphBin2 which refines the binning results obtained from existing tools and, more importantly, is able to assign contigs to multiple bins. GraphBin2 uses the connectivity and coverage information from assembly graphs to adjust existing binning results on contigs and to infer contigs shared by multiple species. Experimental results on both simulated and real datasets demonstrate that GraphBin2 not only improves binning results of existing tools but also supports to assign contigs to multiple bins.
Cite as

Vijini G. Mallawaarachchi, Anuradha S. Wickramarachchi, and Yu Lin. GraphBin2: Refined and Overlapped Binning of Metagenomic Contigs Using Assembly Graphs. In 20th International Workshop on Algorithms in Bioinformatics (WABI 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 172, pp. 8:1-8:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{mallawaarachchi_et_al:LIPIcs.WABI.2020.8,
  author =	{Mallawaarachchi, Vijini G. and Wickramarachchi, Anuradha S. and Lin, Yu},
  title =	{{GraphBin2: Refined and Overlapped Binning of Metagenomic Contigs Using Assembly Graphs}},
  booktitle =	{20th International Workshop on Algorithms in Bioinformatics (WABI 2020)},
  pages =	{8:1--8:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-161-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{172},
  editor =	{Kingsford, Carl and Pisanti, Nadia},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2020.8},
  URN =		{urn:nbn:de:0030-drops-127974},
  doi =		{10.4230/LIPIcs.WABI.2020.8},
  annote =	{Keywords: Metagenomics binning, contigs, assembly graphs, overlapped binning}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2020.27
Symbolic Execution Game Semantics

Authors: Yu-Yang Lin and Nikos Tzevelekos

Published in: LIPIcs, Volume 167, 5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020)

Abstract
We present a framework for symbolically executing and model checking higher-order programs with external (open) methods. We focus on the client-library paradigm and in particular we aim to check libraries with respect to any definable client. We combine traditional symbolic execution techniques with operational game semantics to build a symbolic execution semantics that captures arbitrary external behaviour. We prove the symbolic semantics to be sound and complete. This yields a bounded technique by imposing bounds on the depth of recursion and callbacks. We provide an implementation of our technique in the 𝕂 framework and showcase its performance on a custom benchmark based on higher-order coding errors such as reentrancy bugs.
Cite as

Yu-Yang Lin and Nikos Tzevelekos. Symbolic Execution Game Semantics. In 5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 167, pp. 27:1-27:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{lin_et_al:LIPIcs.FSCD.2020.27,
  author =	{Lin, Yu-Yang and Tzevelekos, Nikos},
  title =	{{Symbolic Execution Game Semantics}},
  booktitle =	{5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020)},
  pages =	{27:1--27:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-155-9},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{167},
  editor =	{Ariola, Zena M.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2020.27},
  URN =		{urn:nbn:de:0030-drops-123493},
  doi =		{10.4230/LIPIcs.FSCD.2020.27},
  annote =	{Keywords: game semantics, symbolic execution, higher-order open programs}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2019.27
Quantum SDP Solvers: Large Speed-Ups, Optimality, and Applications to Quantum Learning

Authors: Fernando G. S. L. Brandão, Amir Kalev, Tongyang Li, Cedric Yen-Yu Lin, Krysta M. Svore, and Xiaodi Wu

Published in: LIPIcs, Volume 132, 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)

Abstract
We give two new quantum algorithms for solving semidefinite programs (SDPs) providing quantum speed-ups. We consider SDP instances with m constraint matrices, each of dimension n, rank at most r, and sparsity s. The first algorithm assumes an input model where one is given access to an oracle to the entries of the matrices at unit cost. We show that it has run time O~(s^2 (sqrt{m} epsilon^{-10} + sqrt{n} epsilon^{-12})), with epsilon the error of the solution. This gives an optimal dependence in terms of m, n and quadratic improvement over previous quantum algorithms (when m ~~ n). The second algorithm assumes a fully quantum input model in which the input matrices are given as quantum states. We show that its run time is O~(sqrt{m}+poly(r))*poly(log m,log n,B,epsilon^{-1}), with B an upper bound on the trace-norm of all input matrices. In particular the complexity depends only polylogarithmically in n and polynomially in r. We apply the second SDP solver to learn a good description of a quantum state with respect to a set of measurements: Given m measurements and a supply of copies of an unknown state rho with rank at most r, we show we can find in time sqrt{m}*poly(log m,log n,r,epsilon^{-1}) a description of the state as a quantum circuit preparing a density matrix which has the same expectation values as rho on the m measurements, up to error epsilon. The density matrix obtained is an approximation to the maximum entropy state consistent with the measurement data considered in Jaynes' principle from statistical mechanics. As in previous work, we obtain our algorithm by "quantizing" classical SDP solvers based on the matrix multiplicative weight update method. One of our main technical contributions is a quantum Gibbs state sampler for low-rank Hamiltonians, given quantum states encoding these Hamiltonians, with a poly-logarithmic dependence on its dimension, which is based on ideas developed in quantum principal component analysis. We also develop a "fast" quantum OR lemma with a quadratic improvement in gate complexity over the construction of Harrow et al. [Harrow et al., 2017]. We believe both techniques might be of independent interest.
Cite as

Fernando G. S. L. Brandão, Amir Kalev, Tongyang Li, Cedric Yen-Yu Lin, Krysta M. Svore, and Xiaodi Wu. Quantum SDP Solvers: Large Speed-Ups, Optimality, and Applications to Quantum Learning. In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 27:1-27:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{brandao_et_al:LIPIcs.ICALP.2019.27,
  author =	{Brand\~{a}o, Fernando G. S. L. and Kalev, Amir and Li, Tongyang and Lin, Cedric Yen-Yu and Svore, Krysta M. and Wu, Xiaodi},
  title =	{{Quantum SDP Solvers: Large Speed-Ups, Optimality, and Applications to Quantum Learning}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{27:1--27:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-109-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{132},
  editor =	{Baier, Christel and Chatzigiannakis, Ioannis and Flocchini, Paola and Leonardi, Stefano},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.27},
  URN =		{urn:nbn:de:0030-drops-106036},
  doi =		{10.4230/LIPIcs.ICALP.2019.27},
  annote =	{Keywords: quantum algorithms, semidefinite program, convex optimization}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2018.4
A Complete Characterization of Unitary Quantum Space

Authors: Bill Fefferman and Cedric Yen-Yu Lin

Published in: LIPIcs, Volume 94, 9th Innovations in Theoretical Computer Science Conference (ITCS 2018)

Abstract
Motivated by understanding the power of quantum computation with restricted number of qubits, we give two complete characterizations of unitary quantum space bounded computation. First we show that approximating an element of the inverse of a well-conditioned efficiently encoded 2^k(n) x 2^k(n) matrix is complete for the class of problems solvable by quantum circuits acting on O(k(n)) qubits with all measurements at the end of the computation. Similarly, estimating the minimum eigenvalue of an efficiently encoded Hermitian 2^k(n) x 2^k(n) matrix is also complete for this class. In the logspace case, our results improve on previous results of Ta-Shma by giving new space-efficient quantum algorithms that avoid intermediate measurements, as well as showing matching hardness results. Additionally, as a consequence we show that preciseQMA, the version of QMA with exponentially small completeness-soundess gap, is equal to PSPACE. Thus, the problem of estimating the minimum eigenvalue of a local Hamiltonian to inverse exponential precision is PSPACE-complete, which we show holds even in the frustration-free case. Finally, we can use this characterization to give a provable setting in which the ability to prepare the ground state of a local Hamiltonian is more powerful than the ability to prepare PEPS states. Interestingly, by suitably changing the parameterization of either of these problems we can completely characterize the power of quantum computation with simultaneously bounded time and space.
Cite as

Bill Fefferman and Cedric Yen-Yu Lin. A Complete Characterization of Unitary Quantum Space. In 9th Innovations in Theoretical Computer Science Conference (ITCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 94, pp. 4:1-4:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{fefferman_et_al:LIPIcs.ITCS.2018.4,
  author =	{Fefferman, Bill and Lin, Cedric Yen-Yu},
  title =	{{A Complete Characterization of Unitary Quantum Space}},
  booktitle =	{9th Innovations in Theoretical Computer Science Conference (ITCS 2018)},
  pages =	{4:1--4:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-060-6},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{94},
  editor =	{Karlin, Anna R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2018.4},
  URN =		{urn:nbn:de:0030-drops-83242},
  doi =		{10.4230/LIPIcs.ITCS.2018.4},
  annote =	{Keywords: Quantum complexity, space complexity, complete problems, QMA}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2016.64
The (1|1)-Centroid Problem on the Plane Concerning Distance Constraints

Authors: Hung-I Yu, Tien-Ching Lin, and Der-Tsai Lee

Published in: LIPIcs, Volume 64, 27th International Symposium on Algorithms and Computation (ISAAC 2016)

Abstract
In 1982, Drezner proposed the (1|1)-centroid problem on the plane, in which two players, called the leader and the follower, open facilities to provide service to customers in a competitive manner. The leader opens the first facility, and then the follower opens the second. Each customer will patronize the facility closest to him (ties broken in favor of the leader's one), thereby decides the market share of the two players. The goal is to find the best position for the leader’s facility so that his market share is maximized. The best algorithm for this problem is an O(n^2 log n)-time parametric search approach, which searches over the space of possible market share values. In the same paper, Drezner also proposed a general version of (1|1)-centroid problem by introducing a minimal distance constraint R, such that the follower's facility is not allowed to be located within a distance R from the leader's. He proposed an O(n^5 log n)-time algorithm for this general version by identifying O(n^4) points as the candidates of the optimal solution and checking the market share for each of them. In this paper, we develop a new parametric search approach searching over the O(n^4) candidate points, and present an O(n^2 log n)-time algorithm for the general version, thereby closing the O(n^3) gap between the two bounds.
Cite as

Hung-I Yu, Tien-Ching Lin, and Der-Tsai Lee. The (1|1)-Centroid Problem on the Plane Concerning Distance Constraints. In 27th International Symposium on Algorithms and Computation (ISAAC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 64, pp. 64:1-64:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{yu_et_al:LIPIcs.ISAAC.2016.64,
  author =	{Yu, Hung-I and Lin, Tien-Ching and Lee, Der-Tsai},
  title =	{{The (1|1)-Centroid Problem on the Plane Concerning Distance Constraints}},
  booktitle =	{27th International Symposium on Algorithms and Computation (ISAAC 2016)},
  pages =	{64:1--64:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-026-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{64},
  editor =	{Hong, Seok-Hee},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2016.64},
  URN =		{urn:nbn:de:0030-drops-68337},
  doi =		{10.4230/LIPIcs.ISAAC.2016.64},
  annote =	{Keywords: competitive facility, Euclidean plane, parametric search}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2016.14
Space-Efficient Error Reduction for Unitary Quantum Computations

Authors: Bill Fefferman, Hirotada Kobayashi, Cedric Yen-Yu Lin, Tomoyuki Morimae, and Harumichi Nishimura

Published in: LIPIcs, Volume 55, 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)

Abstract
This paper presents a general space-efficient method for error reduction for unitary quantum computation. Consider a polynomial-time quantum computation with completeness c and soundness s, either with or without a witness (corresponding to QMA and BQP, respectively). To convert this computation into a new computation with error at most 2^{-p}, the most space-efficient method known requires extra workspace of O(p*log(1/(c-s))) qubits. This space requirement is too large for scenarios like logarithmic-space quantum computations. This paper shows an errorreduction method for unitary quantum computations (i.e., computations without intermediate measurements) that requires extra workspace of just O(log(p/(c-s))) qubits. This in particular gives the first method of strong amplification for logarithmic-space unitary quantum computations with two-sided bounded error. This also leads to a number of consequences in complexity theory, such as the uselessness of quantum witnesses in bounded-error logarithmic-space unitary quantum computations, the PSPACE upper bound for QMA with exponentially-small completeness-soundness gap, and strong amplification for matchgate computations.
Cite as

Bill Fefferman, Hirotada Kobayashi, Cedric Yen-Yu Lin, Tomoyuki Morimae, and Harumichi Nishimura. Space-Efficient Error Reduction for Unitary Quantum Computations. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 14:1-14:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

Copy BibTex To Clipboard

@InProceedings{fefferman_et_al:LIPIcs.ICALP.2016.14,
  author =	{Fefferman, Bill and Kobayashi, Hirotada and Yen-Yu Lin, Cedric and Morimae, Tomoyuki and Nishimura, Harumichi},
  title =	{{Space-Efficient Error Reduction for Unitary Quantum Computations}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{14:1--14:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-013-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{55},
  editor =	{Chatzigiannakis, Ioannis and Mitzenmacher, Michael and Rabani, Yuval and Sangiorgi, Davide},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2016.14},
  URN =		{urn:nbn:de:0030-drops-62975},
  doi =		{10.4230/LIPIcs.ICALP.2016.14},
  annote =	{Keywords: space-bounded computation, quantum Merlin-Arthur proof systems, error reduction, quantum computing}
}
Document
DOI: 10.4230/LIPIcs.TQC.2015.1
Oracles with Costs

Authors: Shelby Kimmel, Cedric Yen-Yu Lin, and Han-Hsuan Lin

Published in: LIPIcs, Volume 44, 10th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2015)

Abstract
While powerful tools have been developed to analyze quantum query complexity, there are still many natural problems that do not fit neatly into the black box model of oracles. We create a new model that allows multiple oracles with differing costs. This model captures more of the difficulty of certain natural problems. We test this model on a simple problem, Search with Two Oracles, for which we create a quantum algorithm that we prove is asymptotically optimal. We further give some evidence, using a geometric picture of Grover's algorithm, that our algorithm is exactly optimal.
Cite as

Shelby Kimmel, Cedric Yen-Yu Lin, and Han-Hsuan Lin. Oracles with Costs. In 10th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 44, pp. 1-26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{kimmel_et_al:LIPIcs.TQC.2015.1,
  author =	{Kimmel, Shelby and Lin, Cedric Yen-Yu and Lin, Han-Hsuan},
  title =	{{Oracles with Costs}},
  booktitle =	{10th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2015)},
  pages =	{1--26},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-96-5},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{44},
  editor =	{Beigi, Salman and K\"{o}nig, Robert},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2015.1},
  URN =		{urn:nbn:de:0030-drops-55459},
  doi =		{10.4230/LIPIcs.TQC.2015.1},
  annote =	{Keywords: Quantum Algorithms, Query Complexity, Amplitude Amplification}
}
Document
DOI: 10.4230/LIPIcs.CCC.2015.537
Upper Bounds on Quantum Query Complexity Inspired by the Elitzur-Vaidman Bomb Tester

Authors: Cedric Yen-Yu Lin and Han-Hsuan Lin

Published in: LIPIcs, Volume 33, 30th Conference on Computational Complexity (CCC 2015)

Abstract
Inspired by the Elitzur-Vaidman bomb testing problem [Elitzur/Vaidman 1993], we introduce a new query complexity model, which we call bomb query complexity B(f). We investigate its relationship with the usual quantum query complexity Q(f), and show that B(f)=Theta(Q(f)^2). This result gives a new method to upper bound the quantum query complexity: we give a method of finding bomb query algorithms from classical algorithms, which then provide nonconstructive upper bounds on Q(f)=Theta(sqrt(B(f))). We subsequently were able to give explicit quantum algorithms matching our upper bound method. We apply this method on the single-source shortest paths problem on unweighted graphs, obtaining an algorithm with O(n^(1.5)) quantum query complexity, improving the best known algorithm of O(n^(1.5) * sqrt(log(n))) [Furrow, 2008]. Applying this method to the maximum bipartite matching problem gives an O(n^(1.75)) algorithm, improving the best known trivial O(n^2) upper bound.
Cite as

Cedric Yen-Yu Lin and Han-Hsuan Lin. Upper Bounds on Quantum Query Complexity Inspired by the Elitzur-Vaidman Bomb Tester. In 30th Conference on Computational Complexity (CCC 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 33, pp. 537-566, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{lin_et_al:LIPIcs.CCC.2015.537,
  author =	{Lin, Cedric Yen-Yu and Lin, Han-Hsuan},
  title =	{{Upper Bounds on Quantum Query Complexity Inspired by the Elitzur-Vaidman Bomb Tester}},
  booktitle =	{30th Conference on Computational Complexity (CCC 2015)},
  pages =	{537--566},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-81-1},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{33},
  editor =	{Zuckerman, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2015.537},
  URN =		{urn:nbn:de:0030-drops-50635},
  doi =		{10.4230/LIPIcs.CCC.2015.537},
  annote =	{Keywords: Quantum Algorithms, Query Complexity, Elitzur-Vaidman Bomb Tester, Adversary Method, Maximum Bipartite Matching}
}
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