1

September 2017
Journal of the ACM (JACM): Volume 64 Issue 5, October 2017

**Publisher:** ACM

**Bibliometrics**:

Citation Count: 0

Downloads (6 Weeks): 12, Downloads (12 Months): 102, Downloads (Overall): 102

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In 1986, Saks and Wigderson conjectured that the largest separation between deterministic and zero-error randomized query complexity for a total Boolean function is given by the function f on n = 2 k bits defined by a complete binary tree of NAND gates of depth k , which achieves R ...

**Keywords**:
query complexity, Decision trees, quantum algorithms

2

July 2017
CCC '17: Proceedings of the 32nd Computational Complexity Conference

**Publisher:** Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik

The complexity class PPA consists of NP-search problems which are reducible to the parity principle in undirected graphs. It contains a wide variety of interesting problems from graph theory, combinatorics, algebra and number theory, but only a few of these are known to be complete in the class. Before this ...

**Keywords**:
chevalley-warning theorem, combinatorial nullstellensatz, PPA

3

February 2017
Algorithmica: Volume 77 Issue 2, February 2017

**Publisher:** Springer-Verlag New York, Inc.

We show that the quantum query complexity of detecting if an n-vertex graph contains a triangle is $$O(n^{9/7})$$O(n9/7). This improves the previous best algorithm of Belovs (Proceedings of 44th symposium on theory of computing conference, pp 77---84, 2012) making $$O(n^{35/27})$$O(n35/27) queries. For the problem of determining if an operation $$\circ ...

**Keywords**:
Quantum algorithms, Associativity testing, Learning graphs, Query complexity, Triangle testing

4

January 2017
Theoretical Computer Science: Volume 657 Issue PA, January 2017

**Publisher:** Elsevier Science Publishers Ltd.

We present an algorithm to solve a system of diagonal polynomial equations over finite fields when the number of variables is greater than some fixed polynomial of the number of equations whose degree depends only on the degree of the polynomial equations. Our algorithm works in time polynomial in the ...

**Keywords**:
Polynomial equations, Chevalley-Warning theorem, Finite fields, Algorithm, Quantum computing

5

June 2016
STOC '16: Proceedings of the forty-eighth annual ACM symposium on Theory of Computing

**Publisher:** ACM

**Bibliometrics**:

Citation Count: 2

Downloads (6 Weeks): 3, Downloads (12 Months): 48, Downloads (Overall): 115

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In 1986, Saks and Wigderson conjectured that the largest separation between deterministic and zero-error randomized query complexity for a total boolean function is given by the function f on n =2 k bits defined by a complete binary tree of NAND gates of depth k , which achieves R 0 ...

**Keywords**:
Monte Carlo, Randomized algorithms, Deterministic algorithms, Las Vegas, Quantum algorithms

6

November 2015
Journal of Computer and System Sciences: Volume 81 Issue 7, November 2015

**Publisher:** Academic Press, Inc.

Given a linear subspace B of the n í� n matrices over some field F , we consider the following problems: symbolic matrix rank (SMR) asks to determine the maximum rank among matrices in B , while symbolic determinant identity testing (SDIT) asks to decide whether there exists a nonsingular ...

**Keywords**:
Edmonds' problem, Maximum rank matrix completion, Symbolic determinantal identity testing, Wong sequences, Derandomization

7

July 2014
Quantum Information & Computation: Volume 14 Issue 9&10, July 2014

**Publisher:** Rinton Press, Incorporated

We present a new method for solving the hidden polynomial graph problem (HPGP) which is a special case of the hidden polynomial problem (HPP). The new approach yields an efficient quantum algorithm for the bivariate HPGP even when the input consists of several level set superpositions, a more difficult version ...

**Keywords**:
quantum algorithm, hidden polynomial problem

8

January 2013
SODA '13: Proceedings of the twenty-fourth annual ACM-SIAM symposium on Discrete algorithms

**Publisher:** Society for Industrial and Applied Mathematics

**Bibliometrics**:

Citation Count: 5

Downloads (6 Weeks): 2, Downloads (12 Months): 13, Downloads (Overall): 46

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We show that the quantum query complexity of detecting if an n -vertex graph contains a triangle is O ( n 9/7 ). This improves the previous best algorithm of Belovs [2] making O ( n 35/27 ) queries. For the problem of determining if an operation o : S ...

9

June 2012
Algorithmica: Volume 63 Issue 1-2, June 2012

**Publisher:** Springer-Verlag New York, Inc.

The hitting time of a classical random walk (Markov chain) is the time required to detect the presence of—or equivalently, to find —a marked state. The hitting time of a quantum walk is subtler to define; in particular, it is unknown whether the detection and finding problems have the same ...

**Keywords**:
Quantum hitting time, Random walk, Hitting time, Quantum walk

10

February 2012
Algorithmica: Volume 62 Issue 1-2, February 2012

**Publisher:** Springer-Verlag New York, Inc.

In this paper we show that the hidden subgroup problem in nil-2 groups, that is in groups of nilpotency class at most 2, can be solved efficiently by a quantum procedure. The algorithm is an extension of our earlier method for extraspecial groups in Ivanyos et al. (Proceedings of the ...

**Keywords**:
Hidden subgroup problem, Nilpotent group, Efficient algorithm

11

December 2011
WINE'11: Proceedings of the 7th international conference on Internet and Network Economics

**Publisher:** Springer-Verlag

We extend the study of the complexity of computing an <em>ε</em> -approximate Nash equilibrium in symmetric congestion games from the case of positive delay functions to delays of arbitrary sign. Our results show that with this extension the complexity has a richer structure, and it depends on the exact nature ...

12

July 2011
ICALP'11: Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I

**Publisher:** Springer-Verlag

We consider the randomized decision tree complexity of the recursive 3-majority function. For evaluating height h formulae, we prove a lower bound for the δ-two-sided-error randomized decision tree complexity of (1 - 2δ)(5/2) h , improving the lower bound of (1 - 2δ)(7/3) h given by Jayram, Kumar, and Sivakumar ...

13

February 2011
SIAM Journal on Computing: Volume 40 Issue 1, February 2011

**Publisher:** Society for Industrial and Applied Mathematics

We propose a new method for designing quantum search algorithms for finding a “marked” element in the state space of a classical Markov chain. The algorithm is based on a quantum walk à la Szegedy [ Quantum speed-up of Markov chain based algorithms , in Proceedings of the 45th IEEE ...

**Keywords**:
hitting time, amplitude amplification, quantum walk, Markov chain, phase estimation, search

14

September 2010
Information Processing Letters: Volume 110 Issue 20, September, 2010

**Publisher:** Elsevier North-Holland, Inc.

A Direct Sum Theorem holds in a model of computation, when for every problem solving some k input instances together is k times as expensive as solving one. We show that Direct Sum Theorems hold in the models of deterministic and randomized decision trees for all relations. We also note ...

**Keywords**:
Direct sum, Computational complexity, Decision tree complexity

15

June 2010
CSR'10: Proceedings of the 5th international conference on Computer Science: theory and Applications

**Publisher:** Springer-Verlag

Many classical search problems can be cast in the following abstract framework: Given a finite set X and a subset M ⊆ X of marked elements, detect if M is empty or not, or find an element in M if there is any. When M is not empty, a naive ...

16

July 2009
Theory of Computing Systems: Volume 45 Issue 3, July 2009

**Publisher:** Springer-Verlag New York, Inc.

We present several results on the complexity of various forms of Sperner’s Lemma in the black-box model of computing. We give a deterministic algorithm for Sperner problems over pseudo-manifolds of arbitrary dimension. The query complexity of our algorithm is linear in the separation number of the skeleton graph of the ...

**Keywords**:
Deterministic algorithm, Probabilistic and quantum lower bound, Query complexity, Sperner’s lemma

17

June 2009
Algorithmica - Special Issue: Quantum Computation; Guest Editors: Frédéric Magniez and Ashwin Nayak: Volume 55 Issue 3, June 2009

**Publisher:** Springer-Verlag New York, Inc.

Let f be an integer valued function on a finite set V . We call an undirected graph G ( V , E ) a neighborhood structure for f . The problem of finding a local minimum for f can be phrased as: for a fixed neighborhood structure G ( ...

**Keywords**:
Local search, Quantum computing, Query complexity

18

April 2009
Fundamenta Informaticae - Machines, Computations and Universality, Part II: Volume 91 Issue 2, April 2009

**Publisher:** IOS Press

We construct efficient or query efficient quantum property testers for two existential group properties which have exponential query complexity both for their decision problem in the quantum and for their testing problem in the classical model of computing. These are periodicity in groups and the common coset range property of ...

**Keywords**:
Property Testing, Quantum Computing

19

April 2009
Fundamenta Informaticae - Machines, Computations and Universality, Part II: Volume 91 Issue 2, April 2009

**Publisher:** IOS Press

We construct efficient or query efficient quantum property testers for two existential group properties which have exponential query complexity both for their decision problem in the quantum and for their testing problem in the classical model of computing. These are periodicity in groups and the common coset range property of ...

**Keywords**:
Property Testing, Quantum Computing

20

January 2009
SODA '09: Proceedings of the twentieth annual ACM-SIAM symposium on Discrete algorithms

**Publisher:** Society for Industrial and Applied Mathematics

**Bibliometrics**:

Citation Count: 6

Downloads (6 Weeks): 2, Downloads (12 Months): 14, Downloads (Overall): 212

Full text available:

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The hitting time of a classical random walk (Markov chain) is the time required to detect the presence of -- or equivalently, to find -- a marked state. The hitting time of a quantum walk is subtler to define; in particular, it is unknown whether the detection and finding problems ...