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Documents authored by Witter, R. Teal

Document
DOI: 10.4230/LIPIcs.ESA.2023.36
Robust and Space-Efficient Dual Adversary Quantum Query Algorithms

Authors: Michael Czekanski, Shelby Kimmel, and R. Teal Witter

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

Abstract
The general adversary dual is a powerful tool in quantum computing because it gives a query-optimal bounded-error quantum algorithm for deciding any Boolean function. Unfortunately, the algorithm uses linear qubits in the worst case, and only works if the constraints of the general adversary dual are exactly satisfied. The challenge of improving the algorithm is that it is brittle to arbitrarily small errors since it relies on a reflection over a span of vectors. We overcome this challenge and build a robust dual adversary algorithm that can handle approximately satisfied constraints. As one application of our robust algorithm, we prove that for any Boolean function with polynomially many 1-valued inputs (or in fact a slightly weaker condition) there is a query-optimal algorithm that uses logarithmic qubits. As another application, we prove that numerically derived, approximate solutions to the general adversary dual give a bounded-error quantum algorithm under certain conditions. Further, we show that these conditions empirically hold with reasonable iterations for Boolean functions with small domains. We also develop several tools that may be of independent interest, including a robust approximate spectral gap lemma, a method to compress a general adversary dual solution using the Johnson-Lindenstrauss lemma, and open-source code to find solutions to the general adversary dual.
Cite as

Michael Czekanski, Shelby Kimmel, and R. Teal Witter. Robust and Space-Efficient Dual Adversary Quantum Query Algorithms. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 36:1-36:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{czekanski_et_al:LIPIcs.ESA.2023.36,
  author =	{Czekanski, Michael and Kimmel, Shelby and Witter, R. Teal},
  title =	{{Robust and Space-Efficient Dual Adversary Quantum Query Algorithms}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{36:1--36:19},
  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.2023.36},
  URN =		{urn:nbn:de:0030-drops-186890},
  doi =		{10.4230/LIPIcs.ESA.2023.36},
  annote =	{Keywords: Quantum Computing, Robust Quantum Algorithms, Johnson-Lindenstrauss Lemma, Span Programs, Query Complexity, Space Complexity}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2022.3
A Local Search Algorithm for the Min-Sum Submodular Cover Problem

Authors: Lisa Hellerstein, Thomas Lidbetter, and R. Teal Witter

Published in: LIPIcs, Volume 248, 33rd International Symposium on Algorithms and Computation (ISAAC 2022)

Abstract
We consider the problem of solving the Min-Sum Submodular Cover problem using local search. The Min-Sum Submodular Cover problem generalizes the NP-complete Min-Sum Set Cover problem, replacing the input set cover instance with a monotone submodular set function. A simple greedy algorithm achieves an approximation factor of 4, which is tight unless P=NP [Streeter and Golovin, NeurIPS, 2008]. We complement the greedy algorithm with analysis of a local search algorithm. Building on work of Munagala et al. [ICDT, 2005], we show that, using simple initialization, a straightforward local search algorithm achieves a (4+ε)-approximate solution in time O(n³log(n/ε)), provided that the monotone submodular set function is also second-order supermodular. Second-order supermodularity has been shown to hold for a number of submodular functions of practical interest, including functions associated with set cover, matching, and facility location. We present experiments on two special cases of Min-Sum Submodular Cover and find that the local search algorithm can outperform the greedy algorithm on small data sets.
Cite as

Lisa Hellerstein, Thomas Lidbetter, and R. Teal Witter. A Local Search Algorithm for the Min-Sum Submodular Cover Problem. In 33rd International Symposium on Algorithms and Computation (ISAAC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 248, pp. 3:1-3:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{hellerstein_et_al:LIPIcs.ISAAC.2022.3,
  author =	{Hellerstein, Lisa and Lidbetter, Thomas and Witter, R. Teal},
  title =	{{A Local Search Algorithm for the Min-Sum Submodular Cover Problem}},
  booktitle =	{33rd International Symposium on Algorithms and Computation (ISAAC 2022)},
  pages =	{3:1--3:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-258-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{248},
  editor =	{Bae, Sang Won and Park, Heejin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2022.3},
  URN =		{urn:nbn:de:0030-drops-172880},
  doi =		{10.4230/LIPIcs.ISAAC.2022.3},
  annote =	{Keywords: Local search, submodularity, second-order supermodularity, min-sum set cover}
}
Document
DOI: 10.4230/LIPIcs.TQC.2019.6
Applications of the Quantum Algorithm for st-Connectivity

Authors: Kai DeLorenzo, Shelby Kimmel, and R. Teal Witter

Published in: LIPIcs, Volume 135, 14th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2019)

Abstract
We present quantum algorithms for various problems related to graph connectivity. We give simple and query-optimal algorithms for cycle detection and odd-length cycle detection (bipartiteness) using a reduction to st-connectivity. Furthermore, we show that our algorithm for cycle detection has improved performance under the promise of large circuit rank or a small number of edges. We also provide algorithms for detecting even-length cycles and for estimating the circuit rank of a graph. All of our algorithms have logarithmic space complexity.
Cite as

Kai DeLorenzo, Shelby Kimmel, and R. Teal Witter. Applications of the Quantum Algorithm for st-Connectivity. In 14th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 135, pp. 6:1-6:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{delorenzo_et_al:LIPIcs.TQC.2019.6,
  author =	{DeLorenzo, Kai and Kimmel, Shelby and Witter, R. Teal},
  title =	{{Applications of the Quantum Algorithm for st-Connectivity}},
  booktitle =	{14th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2019)},
  pages =	{6:1--6:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-112-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{135},
  editor =	{van Dam, Wim and Man\v{c}inska, Laura},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2019.6},
  URN =		{urn:nbn:de:0030-drops-103984},
  doi =		{10.4230/LIPIcs.TQC.2019.6},
  annote =	{Keywords: graphs, algorithms, query complexity, quantum algorithms, span programs}
}
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