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On Exact Quantum Query Complexity

Ashley Montanaro, Richard Jozsa, Graeme Mitchison
2013 Algorithmica  
We present several families of total boolean functions which have exact quantum query complexity which is a constant multiple (between 1/2 and 2/3) of their classical query complexity, and show that optimal  ...  We also characterise the model of nonadaptive exact quantum query complexity in terms of coding theory and completely characterise the query complexity of symmetric boolean functions in this context.  ...  has exact quantum query complexity .  ... 
doi:10.1007/s00453-013-9826-8 fatcat:t6aln47tyzcalmhb3ekkegx2u4

Partial Boolean Functions with Exact Quantum Query Complexity One

Guoliang Xu, Daowen Qiu
2021 Entropy  
We provide two sufficient and necessary conditions to characterize any n-bit partial Boolean function with exact quantum query complexity 1.  ...  Using the first characterization, we present all n-bit partial Boolean functions that depend on n bits and can be computed exactly by a 1-query quantum algorithm.  ...  with exact quantum query complexity 1.  ... 
doi:10.3390/e23020189 pmid:33546475 pmcid:PMC7913633 fatcat:xpbyo3ajojexplw6bleujrabae

Characterization of exact one-query quantum algorithms (ii): for partial functions [article]

Zekun Ye, Lvzhou Li
2020 arXiv   pre-print
A. 101, 02232 (2020)) the problem: what functions can be computed by an exact one-query quantum algorithm?  ...  Usually, quantum advantages are revealed by presenting a quantum algorithm that has a better query complexity than its classical counterpart.  ...  The exact quantum query complexity of f , denoted by Q E (f ), is the minimum number of queries that a quantum query algorithm needs to compute f .  ... 
arXiv:2008.11998v3 fatcat:44ywqj2norbhpevr3zkhnwtufe

Properties and Application of Nondeterministic Quantum Query Algorithms [article]

Alina Dubrovska Vasilieva
2006 arXiv   pre-print
We examine properties of such algorithms and prove relations with exact and nondeterministic quantum query algorithm complexity.  ...  As in the classical version of decision trees, different kinds of quantum query algorithms are possible: exact, zero-error, bounded-error and even nondeterministic.  ...  We introduce the notion of dual nondeterministic quantum query algorithm and study the relations between exact, nondeterministic and dual nondeterministic quantum query algorithm complexity.  ... 
arXiv:quant-ph/0606248v1 fatcat:po3ytkopfffdbofg5wpi2tkqiq

Exact quantum query complexity of EXACT and THRESHOLD [article]

Andris Ambainis, Jānis Iraids, Juris Smotrovs
2013 arXiv   pre-print
A quantum algorithm is exact if it always produces the correct answer, on any input.  ...  Coming up with exact quantum algorithms that substantially outperform the best classical algorithm has been a quite challenging task.  ...  . , x n ) with the deterministic query complexity n and the exact quantum query complexity O(n .8675... ) was constructed.  ... 
arXiv:1302.1235v1 fatcat:uxv7xflj2reenftd7qq3fhfghe

Exact Quantum Query Complexity of EXACT and THRESHOLD

Andris Ambainis, Janis Iraids, Juris Smotrovs, Marc Herbstritt
2013 Theory of Quantum Computation, Communication, and Cryptography  
A quantum algorithm is exact if it always produces the correct answer, on any input.  ...  ACM Subject Classification F.2 Analysis of Algorithms and Problem Complexity  ...  . , x n ) with the deterministic query complexity n and the exact quantum query complexity O(n .8675... ) was constructed.  ... 
doi:10.4230/lipics.tqc.2013.263 dblp:conf/tqc/AmbainisIS13 fatcat:sns6gyomd5fl3j5wlp76zxaxz4

Quantum Query Algorithm Constructions for Computing AND, OR and MAJORITY Boolean Functions [article]

Alina Vasilieva
2009 arXiv   pre-print
First, we present several exact quantum query algorithms for certain problems that are better than classical counterparts.  ...  Finally, we propose quantum algorithm designing methods. Given algorithms for the set of sub-functions, our methods use them to design a more complex one, based on algorithms described before.  ...  Deterministic complexity: D(PAIR_EQUALITY 4 )=4, by sensitivity on accepting input. Algorithm 2. Exact quantum query algorithm for PAIR_EQUALITY 4 is presented in figure 2.  ... 
arXiv:0710.5592v2 fatcat:fkin6ztltfc77bgracxpf3ihku

Quantum Query Algorithms for Certain Problems and Generalization of Algorithm Designing Techniques [article]

Alina Dubrovska Vasilieva, Taisia Mischenko-Slatenkova
2006 arXiv   pre-print
We present several exact quantum query algorithms for certain problems that are better than classical counterparts.  ...  In this paper we concentrate on quantum query algorithm designing tasks. The main aim of research was to find new efficient algorithms and develop general algorithm designing techniques.  ...  advantage of quantum query complexity over deterministic one as PARITY function does.  ... 
arXiv:quant-ph/0611213v1 fatcat:yct6e5bu5jgtfpl2mnqbdadtou

What can exact one-query quantum algorithms do? [article]

Weijiang Chen, Zekun Ye, Lvzhou li
2019 arXiv   pre-print
In this paper, we characterize the computational power of exact one-query quantum algorithms.  ...  Quantum query models are one of the most important models in quantum computing.  ...  The classical deterministic query complexity of f is denoted by D(f ), and the quantum query complexity in the exact setting is denoted by Q E (f ).  ... 
arXiv:1912.03493v1 fatcat:35n5lfathfhi3ispwiwq2ln5fa

Partial Boolean functions with exact quantum 1-query complexity [article]

Guoliang Xu, Daowen Qiu
2020 arXiv   pre-print
Using the first characterization, we present all n-bit partial Boolean functions that depend on n bits and have exact quantum 1-query complexity.  ...  We provide two sufficient and necessary conditions to characterize any n-bit partial Boolean function with exact quantum 1-query complexity.  ...  n-bit partial Boolean functions that depend on k (k ≤ n) bits and have exact quantum 1-query complexity.  ... 
arXiv:2007.10924v3 fatcat:ycmnscdtlfglnjhs465waulhpy

Quantum versus Classical Learnability [article]

Rocco A. Servedio, Steven J. Gortler
2000 arXiv   pre-print
We consider quantum versions of two well-studied classical learning models: Angluin's model of exact learning from membership queries and Valiant's Probably Approximately Correct (PAC) model of learning  ...  For both the model of exact learning from membership queries and the PAC model, we show that under a widely held computational hardness assumption for classical computation (the intractability of factoring  ...  The quantum sample complexity of a quantum exact learning algorithm for C is T (n), where T (n) is the query complexity of N n .  ... 
arXiv:quant-ph/0007036v1 fatcat:jkia4oqhyjcxhj3fvhtadiw2qy

Exact quantum query complexity of computing Hamming weight modulo powers of two and three [article]

Arjan Cornelissen and Nikhil S. Mande and Maris Ozols and Ronald de Wolf
2021 arXiv   pre-print
We show that the exact quantum query complexity of this problem is ⌈ n(1 - 1/m) ⌉.  ...  ., the parity of the input bits), and a new 2-query quantum algorithm to compute the Hamming weight of a 3-bit string mod 3.  ...  Ambainis, Iraids and Smotrovs [AIS13] showed a tight bound on the exact quantum query complexity of EXACT k (the Boolean function that outputs 1 iff the Hamming weight of the input equals k) for all  ... 
arXiv:2112.14682v1 fatcat:vi4vd3mtufhjvkk7quo7s6gn3q

Exact quantum query complexity for total Boolean functions [article]

Gatis Midrijanis
2004 arXiv   pre-print
We will show that if there exists a quantum query algorithm that exactly computes some total Boolean function f by making T queries, then there is a classical deterministic algorithm A that exactly computes  ...  f making O(T^3) queries.  ...  We will focus on exact quantum query algorithms. There are two general methods how to show quantum lower bounds.  ... 
arXiv:quant-ph/0403168v2 fatcat:4iiwins24fg4rp56coh3es2j3a

On Quantum Versions of the Yao Principle [article]

Mart de Graaf, Ronald de Wolf
2001 arXiv   pre-print
For both principles, we prove that the quantum bounded-error complexity is a lower bound on the quantum analogues of max mu D_epsilon^mu(f).  ...  On the other hand, as a positive result we prove that the "weak" version holds up to a constant factor for the query complexity of all symmetric Boolean functions  ...  Acknowledgments We thank Harry Buhrman for initiating this research, for coming up with the counterexample of Theorem 2, and for useful comments on a preliminary version of this paper.  ... 
arXiv:quant-ph/0109070v1 fatcat:n7tmoaj365cb7cfoaioajwfh2u

Optimal Separation in Exact Query Complexities for Simon's Problem [article]

Guangya Cai, Daowen Qiu
2017 arXiv   pre-print
Simon's problem is one of the most important problems demonstrating the power of quantum computers, which achieves a large separation between quantum and classical query complexities.  ...  In this paper, we propose another exact quantum algorithm for solving Simon's problem with O(n) queries, which is simple, concrete and does not rely on special query oracles.  ...  With previously established results on exact quantum query complexity, we can get the optimal separation in exact query complexities for Simon's problem: Θ(n) versus Θ( √ 2 n ).  ... 
arXiv:1610.01920v5 fatcat:l6kpwez2gzhqpdvbkrgb2a3bq4
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