Quantum versus Classical Online Streaming Algorithms with Logarithmic Size of Memory

Khadiev, Kamil; Khadieva, Aliya; Kravchenko, Dmitry V.; Rivosh, Alexander; Yamilov, Ramis; Mannapov, Ilnaz

doi:10.48550/arxiv.1710.09595

Cited by 3 publications

(5 citation statements)

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“…A similar result was proven in [21]. At the same time, the problem that was considered in [21] has one restriction.…”

Section: Our Resultssupporting

confidence: 67%

“…A similar result was proven in [21]. At the same time, the problem that was considered in [21] has one restriction. It is not defined for all inputs and requires a pre-validation to check whether an input is permissible.…”

Section: Our Resultssupporting

confidence: 67%

“…The first one is sublogarithmic size of memory [8]. The second case is polylogarithmic size of memory [21]. Note that if an algorithm can use the linear size of memory, then it can store the whole input in memory.…”

Section: Introductionmentioning

confidence: 99%

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Quantum and Classical Log-Bounded Automata for the Online Disjointness Problem

Khadiev

Khadieva

2022

Mathematics

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We consider online algorithms with respect to the competitive ratio. In this paper, we explore one-way automata as a model for online algorithms. We focus on quantum and classical online algorithms. For a specially constructed online minimization problem, we provide a quantum log-bounded automaton that is more effective (has less competitive ratio) than classical automata, even with advice, in the case of the logarithmic size of memory. We construct an online version of the well-known Disjointness problem as a problem. It was investigated by many researchers from a communication complexity and query complexity point of view.

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“…A similar result was proven in [21]. At the same time, the problem that was considered in [21] has one restriction.…”

Section: Our Resultssupporting

confidence: 67%

Section: Our Resultssupporting

confidence: 67%

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Quantum and Classical Log-Bounded Automata for the Online Disjointness Problem

Khadiev

Khadieva

2022

Mathematics

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“…This measure is an analog of a number of states for finite automaton and OBDDs can be seen as nonuniform finite automata (see for example [4]). As for many other computation models, it is possible to consider quantum OBDDs, and during the last decade they have been studied vividly [1,5,43,48,47,2,24,23,20,19,21,31,30].…”

Section: Introductionmentioning

confidence: 99%

Exponential Separation between Quantum and Classical Ordered Binary Decision Diagrams, Reordering Method and Hierarchies

Khadiev¹,

Khadieva²,

Knop³

2022

Preprint

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In this paper, we study quantum Ordered Binary Decision Diagrams(OBDD) model; it is a restricted version of read-once quantum branching programs, with respect to "width" complexity. It is known that the maximal gap between deterministic and quantum complexities is exponential. But there are few examples of functions with such a gap. We present a new technique ("reordering") for proving lower bounds and upper bounds for OBDD with an arbitrary order of input variables if we have similar bounds for the natural order. Using this transformation, we construct a total function REQ such that the deterministic OBDD complexity of it is at least 2 Ω(n/ log n) , and the quantum OBDD complexity of it is at most O(n 2 / log n). It is the biggest known gap for explicit functions not representable by OBDDs of a linear width. Another function(shifted equality function) allows us to obtain a gap 2 Ω(n) vs O(n 2 ). Moreover, we prove the bounded error quantum and probabilistic OBDD width hierarchies for complexity classes of Boolean functions. Additionally, using "reordering" method we extend a hierarchy for read-k-times Ordered Binary Decision Diagrams (k-OBDD) of polynomial width, for k = o(n/ log 3 n). We prove a similar hierarchy for bounded error probabilistic k-OBDDs of polynomial, superpolynomial and subexponential width.

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“…Superior of quantum over classical was shown for different computational models like query model, streaming processing models, communication models and others [12,7,6,5,4,3,30,25,20,35,24]. Different versions of online quantum algorithms were considered in [30,3] including quantum streaming algorithms as online algorithms [29,26], quantum online algorithms with restricted memory [27,28], quantum online algorithms with repeated test [40]. In these papers, authors show examples of problems that have quantum online algorithms with better competitive ratio comparing to classical online algorithms.…”

Section: Introductionmentioning

confidence: 99%

Quantum Request-Answer Game with Buffer Model for Online Algorithms

Khadiev

2020

Preprint

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We consider online algorithms as a request-answer game. An adversary that generates input requests, and an online algorithm answers. We consider a generalized version of the game that has a buffer of limited size. The adversary loads data to the buffer, and the algorithm has random access to elements of the buffer. We consider quantum and classical (deterministic or randomized) algorithms for the model. In the paper, we provide a specific problem (The Most Frequent Keyword Problem) and a quantum algorithm that works better than any classical (deterministic or randomized) algorithm in terms of competitive ratio. At the same time, for the problem, classical online algorithms in the standard model are equivalent to the classical algorithms in the request-answer game with buffer model.

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Quantum versus Classical Online Streaming Algorithms with Logarithmic Size of Memory

Cited by 3 publications

References 0 publications

Quantum and Classical Log-Bounded Automata for the Online Disjointness Problem

Quantum and Classical Log-Bounded Automata for the Online Disjointness Problem

Exponential Separation between Quantum and Classical Ordered Binary Decision Diagrams, Reordering Method and Hierarchies

Quantum Request-Answer Game with Buffer Model for Online Algorithms

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