3 Search Results for "Mittal, Tushant"

Document
DOI: 10.4230/LIPIcs.TQC.2023.11
On the Power of Nonstandard Quantum Oracles

Authors: Roozbeh Bassirian, Bill Fefferman, and Kunal Marwaha

Published in: LIPIcs, Volume 266, 18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023)

Abstract
We study how the choices made when designing an oracle affect the complexity of quantum property testing problems defined relative to this oracle. We encode a regular graph of even degree as an invertible function f, and present f in different oracle models. We first give a one-query QMA protocol to test if a graph encoded in f has a small disconnected subset. We then use representation theory to show that no classical witness can help a quantum verifier efficiently decide this problem relative to an in-place oracle. Perhaps surprisingly, a simple modification to the standard oracle prevents a quantum verifier from efficiently deciding this problem, even with access to an unbounded witness.
Cite as

Roozbeh Bassirian, Bill Fefferman, and Kunal Marwaha. On the Power of Nonstandard Quantum Oracles. In 18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 266, pp. 11:1-11:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{bassirian_et_al:LIPIcs.TQC.2023.11,
  author =	{Bassirian, Roozbeh and Fefferman, Bill and Marwaha, Kunal},
  title =	{{On the Power of Nonstandard Quantum Oracles}},
  booktitle =	{18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023)},
  pages =	{11:1--11:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-283-9},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{266},
  editor =	{Fawzi, Omar and Walter, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2023.11},
  URN =		{urn:nbn:de:0030-drops-183215},
  doi =		{10.4230/LIPIcs.TQC.2023.11},
  annote =	{Keywords: quantum complexity, QCMA, expander graphs, representation theory}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2022.87
Symbolic Determinant Identity Testing and Non-Commutative Ranks of Matrix Lie Algebras

Authors: Gábor Ivanyos, Tushant Mittal, and Youming Qiao

Published in: LIPIcs, Volume 215, 13th Innovations in Theoretical Computer Science Conference (ITCS 2022)

Abstract
One approach to make progress on the symbolic determinant identity testing (SDIT) problem is to study the structure of singular matrix spaces. After settling the non-commutative rank problem (Garg-Gurvits-Oliveira-Wigderson, Found. Comput. Math. 2020; Ivanyos-Qiao-Subrahmanyam, Comput. Complex. 2018), a natural next step is to understand singular matrix spaces whose non-commutative rank is full. At present, examples of such matrix spaces are mostly sporadic, so it is desirable to discover them in a more systematic way. In this paper, we make a step towards this direction, by studying the family of matrix spaces that are closed under the commutator operation, that is, matrix Lie algebras. On the one hand, we demonstrate that matrix Lie algebras over the complex number field give rise to singular matrix spaces with full non-commutative ranks. On the other hand, we show that SDIT of such spaces can be decided in deterministic polynomial time. Moreover, we give a characterization for the matrix Lie algebras to yield a matrix space possessing singularity certificates as studied by Lovász (B. Braz. Math. Soc., 1989) and Raz and Wigderson (Building Bridges II, 2019).
Cite as

Gábor Ivanyos, Tushant Mittal, and Youming Qiao. Symbolic Determinant Identity Testing and Non-Commutative Ranks of Matrix Lie Algebras. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 87:1-87:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

Copy BibTex To Clipboard

@InProceedings{ivanyos_et_al:LIPIcs.ITCS.2022.87,
  author =	{Ivanyos, G\'{a}bor and Mittal, Tushant and Qiao, Youming},
  title =	{{Symbolic Determinant Identity Testing and Non-Commutative Ranks of Matrix Lie Algebras}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{87:1--87:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-217-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{215},
  editor =	{Braverman, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2022.87},
  URN =		{urn:nbn:de:0030-drops-156837},
  doi =		{10.4230/LIPIcs.ITCS.2022.87},
  annote =	{Keywords: derandomization, polynomial identity testing, symbolic determinant, non-commutative rank, Lie algebras}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2022.88
Explicit Abelian Lifts and Quantum LDPC Codes

Authors: Fernando Granha Jeronimo, Tushant Mittal, Ryan O'Donnell, Pedro Paredes, and Madhur Tulsiani

Published in: LIPIcs, Volume 215, 13th Innovations in Theoretical Computer Science Conference (ITCS 2022)

Abstract
For an abelian group H acting on the set [𝓁], an (H,𝓁)-lift of a graph G₀ is a graph obtained by replacing each vertex by 𝓁 copies, and each edge by a matching corresponding to the action of an element of H. Expanding graphs obtained via abelian lifts, form a key ingredient in the recent breakthrough constructions of quantum LDPC codes, (implicitly) in the fiber bundle codes by Hastings, Haah and O'Donnell [STOC 2021] achieving distance Ω̃(N^{3/5}), and in those by Panteleev and Kalachev [IEEE Trans. Inf. Theory 2021] of distance Ω(N/log(N)). However, both these constructions are non-explicit. In particular, the latter relies on a randomized construction of expander graphs via abelian lifts by Agarwal et al. [SIAM J. Discrete Math 2019]. In this work, we show the following explicit constructions of expanders obtained via abelian lifts. For every (transitive) abelian group H ⩽ Sym(𝓁), constant degree d ≥ 3 and ε > 0, we construct explicit d-regular expander graphs G obtained from an (H,𝓁)-lift of a (suitable) base n-vertex expander G₀ with the following parameters: ii) λ(G) ≤ 2√{d-1} + ε, for any lift size 𝓁 ≤ 2^{n^{δ}} where δ = δ(d,ε), iii) λ(G) ≤ ε ⋅ d, for any lift size 𝓁 ≤ 2^{n^{δ₀}} for a fixed δ₀ > 0, when d ≥ d₀(ε), or iv) λ(G) ≤ Õ(√d), for lift size "exactly" 𝓁 = 2^{Θ(n)}. As corollaries, we obtain explicit quantum lifted product codes of Panteleev and Kalachev of almost linear distance (and also in a wide range of parameters) and explicit classical quasi-cyclic LDPC codes with wide range of circulant sizes. Items (i) and (ii) above are obtained by extending the techniques of Mohanty, O'Donnell and Paredes [STOC 2020] for 2-lifts to much larger abelian lift sizes (as a byproduct simplifying their construction). This is done by providing a new encoding of special walks arising in the trace power method, carefully "compressing" depth-first search traversals. Result (iii) is via a simpler proof of Agarwal et al. [SIAM J. Discrete Math 2019] at the expense of polylog factors in the expansion.
Cite as

Fernando Granha Jeronimo, Tushant Mittal, Ryan O'Donnell, Pedro Paredes, and Madhur Tulsiani. Explicit Abelian Lifts and Quantum LDPC Codes. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 88:1-88:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

Copy BibTex To Clipboard

@InProceedings{jeronimo_et_al:LIPIcs.ITCS.2022.88,
  author =	{Jeronimo, Fernando Granha and Mittal, Tushant and O'Donnell, Ryan and Paredes, Pedro and Tulsiani, Madhur},
  title =	{{Explicit Abelian Lifts and Quantum LDPC Codes}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{88:1--88:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-217-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{215},
  editor =	{Braverman, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2022.88},
  URN =		{urn:nbn:de:0030-drops-156846},
  doi =		{10.4230/LIPIcs.ITCS.2022.88},
  annote =	{Keywords: Graph lifts, expander graphs, quasi-cyclic LDPC codes, quantum LDPC codes}
}
  • Refine by Author
  • 2 Mittal, Tushant
  • 1 Bassirian, Roozbeh
  • 1 Fefferman, Bill
  • 1 Ivanyos, Gábor
  • 1 Jeronimo, Fernando Granha
  • Show More...

  • Refine by Classification
  • 2 Theory of computation → Pseudorandomness and derandomization
  • 1 Theory of computation → Algebraic complexity theory
  • 1 Theory of computation → Expander graphs and randomness extractors
  • 1 Theory of computation → Quantum complexity theory

  • Refine by Keyword
  • 2 expander graphs
  • 1 Graph lifts
  • 1 Lie algebras
  • 1 QCMA
  • 1 derandomization
  • Show More...

  • Refine by Type
  • 3 document

  • Refine by Publication Year
  • 2 2022
  • 1 2023

Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH Imprint Privacy Contact