12 Search Results for "Roland, Jérémie"

Document
DOI: 10.4230/LIPIcs.FSTTCS.2025.7
Quantum Protocols for Rabin Oblivious Transfer

Authors: Erika Andersson, Akshay Bansal, James T. Peat, Jamie Sikora, and Jiawei Wu

Published in: LIPIcs, Volume 360, 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)

Abstract
Rabin oblivious transfer is the cryptographic task where Alice wishes to receive a bit from Bob but it may get lost with probability 1/2. In this work, we provide protocol designs which yield quantum protocols with improved security. Moreover, we provide a constant lower bound on any quantum protocol for Rabin oblivious transfer. To quantify the security of this task with asymmetric cheating definitions, we introduce the notion of cheating advantage which may be of independent interest in the study of other asymmetric cryptographic primitives.
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Erika Andersson, Akshay Bansal, James T. Peat, Jamie Sikora, and Jiawei Wu. Quantum Protocols for Rabin Oblivious Transfer. In 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 360, pp. 7:1-7:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{andersson_et_al:LIPIcs.FSTTCS.2025.7,
  author =	{Andersson, Erika and Bansal, Akshay and Peat, James T. and Sikora, Jamie and Wu, Jiawei},
  title =	{{Quantum Protocols for Rabin Oblivious Transfer}},
  booktitle =	{45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)},
  pages =	{7:1--7:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-406-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{360},
  editor =	{Aiswarya, C. and Mehta, Ruta and Roy, Subhajit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2025.7},
  URN =		{urn:nbn:de:0030-drops-250866},
  doi =		{10.4230/LIPIcs.FSTTCS.2025.7},
  annote =	{Keywords: quantum cryptography, oblivious transfer, information-theoretic security}
}
Document
DOI: 10.4230/LIPIcs.TQC.2025.1
Quantum Search with In-Place Queries

Authors: Blake Holman, Ronak Ramachandran, and Justin Yirka

Published in: LIPIcs, Volume 350, 20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025)

Abstract
Quantum query complexity is typically characterized in terms of xor queries |x,y⟩ ↦ |x,y⊕ f(x)⟩ or phase queries, which ensure that even queries to non-invertible functions are unitary. When querying a permutation, another natural model is unitary: in-place queries |x⟩↦ |f(x)⟩. Some problems are known to require exponentially fewer in-place queries than xor queries, but no separation has been shown in the opposite direction. A candidate for such a separation was the problem of inverting a permutation over N elements. This task, equivalent to unstructured search in the context of permutations, is solvable with O(√N) xor queries but was conjectured to require Ω(N) in-place queries. We refute this conjecture by designing a quantum algorithm for Permutation Inversion using O(√N) in-place queries. Our algorithm achieves the same speedup as Grover’s algorithm despite the inability to efficiently uncompute queries or perform straightforward oracle-controlled reflections. Nonetheless, we show that there are indeed problems which require fewer xor queries than in-place queries. We introduce a subspace-conversion problem called Function Erasure that requires 1 xor query and Θ(√N) in-place queries. Then, we build on a recent extension of the quantum adversary method to characterize exact conditions for a decision problem to exhibit such a separation, and we propose a candidate problem.
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Blake Holman, Ronak Ramachandran, and Justin Yirka. Quantum Search with In-Place Queries. In 20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 350, pp. 1:1-1:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{holman_et_al:LIPIcs.TQC.2025.1,
  author =	{Holman, Blake and Ramachandran, Ronak and Yirka, Justin},
  title =	{{Quantum Search with In-Place Queries}},
  booktitle =	{20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025)},
  pages =	{1:1--1:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-392-8},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{350},
  editor =	{Fefferman, Bill},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2025.1},
  URN =		{urn:nbn:de:0030-drops-240502},
  doi =		{10.4230/LIPIcs.TQC.2025.1},
  annote =	{Keywords: Quantum algorithms, query complexity, quantum complexity theory, quantum search, Grover’s algorithm, permutation inversion}
}
Document
DOI: 10.4230/LIPIcs.WADS.2025.12
Testing Whether a Subgraph Is Convex or Isometric

Authors: Sergio Cabello

Published in: LIPIcs, Volume 349, 19th International Symposium on Algorithms and Data Structures (WADS 2025)

Abstract
We consider the following two algorithmic problems: given a graph G and a subgraph H ⊆ G, decide whether H is an isometric or a geodesically convex subgraph of G. It is relatively easy to see that the problems can be solved by computing the distances between all pairs of vertices. We provide a conditional lower bound showing that, for sparse graphs with n vertices and Θ(n) edges, we cannot expect to solve the problem in O(n^{2-ε}) time for any constant ε > 0. We also show that the problem can be solved in subquadratic time for planar graphs and in near-linear time for graphs of bounded treewidth. Finally, we provide a near-linear time algorithm for the setting where G is a plane graph and H is defined by a few cycles in G.
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Sergio Cabello. Testing Whether a Subgraph Is Convex or Isometric. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 12:1-12:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{cabello:LIPIcs.WADS.2025.12,
  author =	{Cabello, Sergio},
  title =	{{Testing Whether a Subgraph Is Convex or Isometric}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{12:1--12:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-398-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{349},
  editor =	{Morin, Pat and Oh, Eunjin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.12},
  URN =		{urn:nbn:de:0030-drops-242439},
  doi =		{10.4230/LIPIcs.WADS.2025.12},
  annote =	{Keywords: convex subgraph, isometric subgraph, plane graph}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.54
Multidimensional Quantum Walks, Recursion, and Quantum Divide & Conquer

Authors: Stacey Jeffery and Galina Pass

Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

Abstract
We introduce an object called a subspace graph that formalizes the technique of multidimensional quantum walks. Composing subspace graphs allows one to seamlessly combine quantum and classical reasoning, keeping a classical structure in mind, while abstracting quantum parts into subgraphs with simple boundaries as needed. As an example, we show how to combine a switching network with arbitrary quantum subroutines, to compute a composed function. As another application, we give a time-efficient implementation of quantum Divide & Conquer when the sub-problems are combined via a Boolean formula. We use this to quadratically speed up Savitch’s algorithm for directed st-connectivity.
Cite as

Stacey Jeffery and Galina Pass. Multidimensional Quantum Walks, Recursion, and Quantum Divide & Conquer. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 54:1-54:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{jeffery_et_al:LIPIcs.STACS.2025.54,
  author =	{Jeffery, Stacey and Pass, Galina},
  title =	{{Multidimensional Quantum Walks, Recursion, and Quantum Divide \& Conquer}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{54:1--54:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2025.54},
  URN =		{urn:nbn:de:0030-drops-228791},
  doi =		{10.4230/LIPIcs.STACS.2025.54},
  annote =	{Keywords: Quantum Divide \& Conquer, Time-Efficient, Subspace Graphs, Quantum Walks, Switching Networks, Directed st-Connectivity}
}
Document
DOI: 10.4230/LIPIcs.TQC.2024.7
Eigenpath Traversal by Poisson-Distributed Phase Randomisation

Authors: Joseph Cunningham and Jérémie Roland

Published in: LIPIcs, Volume 310, 19th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2024)

Abstract
We present a framework for quantum computation, similar to Adiabatic Quantum Computation (AQC), that is based on the quantum Zeno effect. By performing randomised dephasing operations at intervals determined by a Poisson process, we are able to track the eigenspace associated to a particular eigenvalue. We derive a simple differential equation for the fidelity, leading to general theorems bounding the time complexity of a whole class of algorithms. We also use eigenstate filtering to optimise the scaling of the complexity in the error tolerance ε. In many cases the bounds given by our general theorems are optimal, giving a time complexity of O(1/Δ_m) with Δ_m the minimum of the gap. This allows us to prove optimal results using very general features of problems, minimising the problem-specific insight necessary. As two applications of our framework, we obtain optimal scaling for the Grover problem (i.e. O(√N) where N is the database size) and the Quantum Linear System Problem (i.e. O(κlog(1/ε)) where κ is the condition number and ε the error tolerance) by direct applications of our theorems.
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Joseph Cunningham and Jérémie Roland. Eigenpath Traversal by Poisson-Distributed Phase Randomisation. In 19th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 310, pp. 7:1-7:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{cunningham_et_al:LIPIcs.TQC.2024.7,
  author =	{Cunningham, Joseph and Roland, J\'{e}r\'{e}mie},
  title =	{{Eigenpath Traversal by Poisson-Distributed Phase Randomisation}},
  booktitle =	{19th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2024)},
  pages =	{7:1--7:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-328-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{310},
  editor =	{Magniez, Fr\'{e}d\'{e}ric and Grilo, Alex Bredariol},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2024.7},
  URN =		{urn:nbn:de:0030-drops-206779},
  doi =		{10.4230/LIPIcs.TQC.2024.7},
  annote =	{Keywords: Randomisation method, Non-unitary adiabatic theorems, Grover problem, Quantum linear systems problem}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2023.32
Certificate Games

Authors: Sourav Chakraborty, Anna Gál, Sophie Laplante, Rajat Mittal, and Anupa Sunny

Published in: LIPIcs, Volume 251, 14th Innovations in Theoretical Computer Science Conference (ITCS 2023)

Abstract
We introduce and study Certificate Game complexity, a measure of complexity based on the probability of winning a game where two players are given inputs with different function values and are asked to output some index i such that x_i≠ y_i, in a zero-communication setting. We give upper and lower bounds for private coin, public coin, shared entanglement and non-signaling strategies, and give some separations. We show that complexity in the public coin model is upper bounded by Randomized query and Certificate complexity. On the other hand, it is lower bounded by fractional and randomized certificate complexity, making it a good candidate to prove strong lower bounds on randomized query complexity. Complexity in the private coin model is bounded from below by zero-error randomized query complexity. The quantum measure highlights an interesting and surprising difference between classical and quantum query models. Whereas the public coin certificate game complexity is bounded from above by randomized query complexity, the quantum certificate game complexity can be quadratically larger than quantum query complexity. We use non-signaling, a notion from quantum information, to give a lower bound of n on the quantum certificate game complexity of the OR function, whose quantum query complexity is Θ(√n), then go on to show that this "non-signaling bottleneck" applies to all functions with high sensitivity, block sensitivity or fractional block sensitivity. We also consider the single-bit version of certificate games, where the inputs of the two players are restricted to having Hamming distance 1. We prove that the single-bit version of certificate game complexity with shared randomness is equal to sensitivity up to constant factors, thus giving a new characterization of sensitivity. On the other hand, the single-bit version of certificate game complexity with private randomness is equal to λ², where λ is the spectral sensitivity.
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Sourav Chakraborty, Anna Gál, Sophie Laplante, Rajat Mittal, and Anupa Sunny. Certificate Games. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 32:1-32:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{chakraborty_et_al:LIPIcs.ITCS.2023.32,
  author =	{Chakraborty, Sourav and G\'{a}l, Anna and Laplante, Sophie and Mittal, Rajat and Sunny, Anupa},
  title =	{{Certificate Games}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{32:1--32:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-263-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{251},
  editor =	{Tauman Kalai, Yael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.32},
  URN =		{urn:nbn:de:0030-drops-175353},
  doi =		{10.4230/LIPIcs.ITCS.2023.32},
  annote =	{Keywords: block sensitivity, boolean function complexity, certificate complexity, query complexity, sensitivity, zero-communication two-player games}
}
Document
DOI: 10.4230/LIPIcs.STACS.2022.35
Improved Quantum Lower and Upper Bounds for Matrix Scaling

Authors: Sander Gribling and Harold Nieuwboer

Published in: LIPIcs, Volume 219, 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)

Abstract
Matrix scaling is a simple to state, yet widely applicable linear-algebraic problem: the goal is to scale the rows and columns of a given non-negative matrix such that the rescaled matrix has prescribed row and column sums. Motivated by recent results on first-order quantum algorithms for matrix scaling, we investigate the possibilities for quantum speedups for classical second-order algorithms, which comprise the state-of-the-art in the classical setting. We first show that there can be essentially no quantum speedup in terms of the input size in the high-precision regime: any quantum algorithm that solves the matrix scaling problem for n × n matrices with at most m non-zero entries and with 𝓁₂-error ε = Θ~(1/m) must make Ω(m) queries to the matrix, even when the success probability is exponentially small in n. Additionally, we show that for ε ∈ [1/n,1/2], any quantum algorithm capable of producing ε/100-𝓁₁-approximations of the row-sum vector of a (dense) normalized matrix uses Ω(n/ε) queries, and that there exists a constant ε₀ > 0 for which this problem takes Ω(n^{1.5}) queries. To complement these results we give improved quantum algorithms in the low-precision regime: with quantum graph sparsification and amplitude estimation, a box-constrained Newton method can be sped up in the large-ε regime, and outperforms previous quantum algorithms. For entrywise-positive matrices, we find an ε-𝓁₁-scaling in time O~(n^{1.5}/ε²), whereas the best previously known bounds were O~(n²polylog(1/ε)) (classical) and O~(n^{1.5}/ε³) (quantum).
Cite as

Sander Gribling and Harold Nieuwboer. Improved Quantum Lower and Upper Bounds for Matrix Scaling. In 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 219, pp. 35:1-35:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{gribling_et_al:LIPIcs.STACS.2022.35,
  author =	{Gribling, Sander and Nieuwboer, Harold},
  title =	{{Improved Quantum Lower and Upper Bounds for Matrix Scaling}},
  booktitle =	{39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)},
  pages =	{35:1--35:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-222-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{219},
  editor =	{Berenbrink, Petra and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2022.35},
  URN =		{urn:nbn:de:0030-drops-158458},
  doi =		{10.4230/LIPIcs.STACS.2022.35},
  annote =	{Keywords: Matrix scaling, quantum algorithms, lower bounds}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2020.59
A Tight Lower Bound For Non-Coherent Index Erasure

Authors: Nathan Lindzey and Ansis Rosmanis

Published in: LIPIcs, Volume 151, 11th Innovations in Theoretical Computer Science Conference (ITCS 2020)

Abstract
The index erasure problem is a quantum state generation problem that asks a quantum computer to prepare a uniform superposition over the image of an injective function given by an oracle. We prove a tight Ω(√n) lower bound on the quantum query complexity of the non-coherent case of the problem, where, in addition to preparing the required superposition, the algorithm is allowed to leave the ancillary memory in an arbitrary function-dependent state. This resolves an open question of Ambainis, Magnin, Roetteler, and Roland (CCC 2011), who gave a tight bound for the coherent case, the case where the ancillary memory must return to its initial state. To prove our main result, we first extend the so-called automorphism principle (Høyer et al. STOC 2007) to the general adversary method for state conversion problems (Lee et al. STOC 2011), which allows one to exploit the symmetries of these problems to lower bound their quantum query complexity. Using this method, we establish a strong connection between the quantum query complexity of non-coherent symmetric state generation problems and the well-known Krein parameters of association schemes. Krein parameters are usually hard to determine, nevertheless, we give a novel way of computing certain Krein parameters of a commutative association scheme defined over partial permutations. We believe the study of this association scheme may also be of independent interest.
Cite as

Nathan Lindzey and Ansis Rosmanis. A Tight Lower Bound For Non-Coherent Index Erasure. In 11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 151, pp. 59:1-59:37, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{lindzey_et_al:LIPIcs.ITCS.2020.59,
  author =	{Lindzey, Nathan and Rosmanis, Ansis},
  title =	{{A Tight Lower Bound For Non-Coherent Index Erasure}},
  booktitle =	{11th Innovations in Theoretical Computer Science Conference (ITCS 2020)},
  pages =	{59:1--59:37},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-134-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{151},
  editor =	{Vidick, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2020.59},
  URN =		{urn:nbn:de:0030-drops-117446},
  doi =		{10.4230/LIPIcs.ITCS.2020.59},
  annote =	{Keywords: General Adversary Method, Quantum Query Complexity, Association Schemes, Krein Parameters, Representation Theory}
}
Document
DOI: 10.4230/LIPIcs.TQC.2016.5
Robust Bell Inequalities from Communication Complexity

Authors: Sophie Laplante, Mathieu Laurière, Alexandre Nolin, Jérémie Roland, and Gabriel Senno

Published in: LIPIcs, Volume 61, 11th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2016)

Abstract
The question of how large Bell inequality violations can be, for quantum distributions, has been the object of much work in the past several years. We say a Bell inequality is normalized if its absolute value does not exceed 1 for any classical (i.e. local) distribution. Upper and (almost) tight lower bounds have been given in terms of number of outputs of the distribution, number of inputs, and the dimension of the shared quantum states. In this work, we revisit normalized Bell inequalities together with another family: inefficiency-resistant Bell inequalities. To be inefficiency-resistant, the Bell value must not exceed 1 for any local distribution, including those that can abort. Both these families of Bell inequalities are closely related to communication complexity lower bounds. We show how to derive large violations from any gap between classical and quantum communication complexity, provided the lower bound on classical communication is proven using these lower bounds. This leads to inefficiency-resistant violations that can be exponential in the size of the inputs. Finally, we study resistance to noise and inefficiency for these Bell inequalities.
Cite as

Sophie Laplante, Mathieu Laurière, Alexandre Nolin, Jérémie Roland, and Gabriel Senno. Robust Bell Inequalities from Communication Complexity. In 11th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 61, pp. 5:1-5:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{laplante_et_al:LIPIcs.TQC.2016.5,
  author =	{Laplante, Sophie and Lauri\`{e}re, Mathieu and Nolin, Alexandre and Roland, J\'{e}r\'{e}mie and Senno, Gabriel},
  title =	{{Robust Bell Inequalities from Communication Complexity}},
  booktitle =	{11th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2016)},
  pages =	{5:1--5:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-019-4},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{61},
  editor =	{Broadbent, Anne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2016.5},
  URN =		{urn:nbn:de:0030-drops-66867},
  doi =		{10.4230/LIPIcs.TQC.2016.5},
  annote =	{Keywords: Communication complexity, Bell inequalities, nonlocality, detector efficiency}
}
Document
DOI: 10.4230/LIPIcs.TQC.2015.163
A Universal Adiabatic Quantum Query Algorithm

Authors: Mathieu Brandeho and Jérémie Roland

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

Abstract
Quantum query complexity is known to be characterized by the so-called quantum adversary bound. While this result has been proved in the standard discrete-time model of quantum computation, it also holds for continuous-time (or Hamiltonian-based) quantum computation, due to a known equivalence between these two query complexity models. In this work, we revisit this result by providing a direct proof in the continuous-time model. One originality of our proof is that it draws new connections between the adversary bound, a modern technique of theoretical computer science, and early theorems of quantum mechanics. Indeed, the proof of the lower bound is based on Ehrenfest's theorem, while the upper bound relies on the adiabatic theorem, as it goes by constructing a universal adiabatic quantum query algorithm. Another originality is that we use for the first time in the context of quantum computation a version of the adiabatic theorem that does not require a spectral gap.
Cite as

Mathieu Brandeho and Jérémie Roland. A Universal Adiabatic Quantum Query Algorithm. In 10th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 44, pp. 163-179, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{brandeho_et_al:LIPIcs.TQC.2015.163,
  author =	{Brandeho, Mathieu and Roland, J\'{e}r\'{e}mie},
  title =	{{A Universal Adiabatic Quantum Query Algorithm}},
  booktitle =	{10th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2015)},
  pages =	{163--179},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2015.163},
  URN =		{urn:nbn:de:0030-drops-55556},
  doi =		{10.4230/LIPIcs.TQC.2015.163},
  annote =	{Keywords: Quantum Algorithms, Query Complexity, Adiabatic Quantum Computation, Adversary Method}
}
Document
DOI: 10.4230/LIPIcs.STACS.2013.434
Explicit relation between all lower bound techniques for quantum query complexity

Authors: Loïck Magnin and Jérémie Roland

Published in: LIPIcs, Volume 20, 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)

Abstract
The polynomial method and the adversary method are the two main techniques to prove lower bounds on quantum query complexity, and they have so far been considered as unrelated approaches. Here, we show an explicit reduction from the polynomial method to the multiplicative adversary method. The proof goes by extending the polynomial method from Boolean functions to quantum state generation problems. In the process, the bound is even strengthened. We then show that this extended polynomial method is a special case of the multiplicative adversary method with an adversary matrix that is independent of the function. This new result therefore provides insight on the reason why in some cases the adversary method is stronger than the polynomial method. It also reveals a clear picture of the relation between the different lower bound techniques, as it implies that all known techniques reduce to the multiplicative adversary method.
Cite as

Loïck Magnin and Jérémie Roland. Explicit relation between all lower bound techniques for quantum query complexity. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 434-445, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)

Copy BibTex To Clipboard

@InProceedings{magnin_et_al:LIPIcs.STACS.2013.434,
  author =	{Magnin, Lo\"{i}ck and Roland, J\'{e}r\'{e}mie},
  title =	{{Explicit relation between all lower bound techniques for quantum query complexity}},
  booktitle =	{30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
  pages =	{434--445},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-50-7},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{20},
  editor =	{Portier, Natacha and Wilke, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.434},
  URN =		{urn:nbn:de:0030-drops-39548},
  doi =		{10.4230/LIPIcs.STACS.2013.434},
  annote =	{Keywords: Quantum computation, lower bound, adversary method, polynomial method}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2009.2322
Non-Local Box Complexity and Secure Function Evaluation

Authors: Marc Kaplan, Iordanis Kerenidis, Sophie Laplante, and Jérémie Roland

Published in: LIPIcs, Volume 4, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (2009)

Abstract
A non-local box is an abstract device into which Alice and Bob input bits $x$ and $y$ respectively and receive outputs $a$ and $b$ respectively, where $a,b$ are uniformly distributed and $a \oplus b = x \wedge y$. Such boxes have been central to the study of quantum or generalized non-locality as well as the simulation of non-signaling distributions. In this paper, we start by studying how many non-local boxes Alice and Bob need in order to compute a Boolean function $f$. We provide tight upper and lower bounds in terms of the communication complexity of the function both in the deterministic and randomized case. We show that non-local box complexity has interesting applications to classical cryptography, in particular to secure function evaluation, and study the question posed by Beimel and Malkin \cite{BM} of how many Oblivious Transfer calls Alice and Bob need in order to securely compute a function $f$. We show that this question is related to the non-local box complexity of the function and conclude by greatly improving their bounds. Finally, another consequence of our results is that traceless two-outcome measurements on maximally entangled states can be simulated with 3 \nlbs, while no finite bound was previously known.
Cite as

Marc Kaplan, Iordanis Kerenidis, Sophie Laplante, and Jérémie Roland. Non-Local Box Complexity and Secure Function Evaluation. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 4, pp. 239-250, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

Copy BibTex To Clipboard

@InProceedings{kaplan_et_al:LIPIcs.FSTTCS.2009.2322,
  author =	{Kaplan, Marc and Kerenidis, Iordanis and Laplante, Sophie and Roland, J\'{e}r\'{e}mie},
  title =	{{Non-Local Box Complexity and Secure Function Evaluation}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
  pages =	{239--250},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-13-2},
  ISSN =	{1868-8969},
  year =	{2009},
  volume =	{4},
  editor =	{Kannan, Ravi and Narayan Kumar, K.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2009.2322},
  URN =		{urn:nbn:de:0030-drops-23226},
  doi =		{10.4230/LIPIcs.FSTTCS.2009.2322},
  annote =	{Keywords: Communication complexity, non-locality, non-local boxes, secure function evaluation}
}
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