Quantum-over-Classical Advantage in Solving Multiplayer Games

Kravchenko, Dmitry; Khadiev, Kamil; Serov, Danil; Kapralov, Ruslan

doi:10.1007/978-3-030-61739-4_6

Cited by 7 publications

(3 citation statements)

References 26 publications

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“…It is a kind of Nim game, which belongs to combination games [16]. Nim games are notable games in game theory, and they have similar definitions to subtraction games [17]. Following the definition of subtraction games introduced by Kravchenko et al [18], there are two players, a heap of tokens and a strategy matrix Γ, in a subtraction game.…”

Section: Introductionmentioning

confidence: 99%

A linear algorithm for the restricted subtraction games

Yang

He²,

Li³

et al. 2022

Front. Phys.

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The subtraction game is a well-known problem in the field of game theory, which is often called a one-heap Nim game. There are two players, a heap of tokens, and a strategy matrix, in this game. It is called a restricted subtraction game if some constraints are imposed on the strategy matrix. The subtraction game could be solved by a classical algorithm with a query complexity no less than O(N2) and computed by an O(N32logN) quantum query algorithm with an error probability ϵ≤1N. The restricted subtraction game proposed by Huang et al. can be computed by an exact quantum algorithm with O(N32) queries. They also proved that the classical exact query complexity is Θ(N2). In this study, we use an array and an adjacency list to replace the strategy matrix and propose another more general subtraction game than the one introduced by Huang et al. Based on dynamic programming and the replaced game strategy, two linear classical query algorithms are designed to solve the restricted subtraction game proposed by Huang and this study, respectively.

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Section: Introductionmentioning

confidence: 99%

A linear algorithm for the restricted subtraction games

Yang

He²,

Li³

et al. 2022

Front. Phys.

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“…There are many problems where quantum algorithms outperform the best-known classical algorithms. Some of them can be founded here [32,15,19,23,18,10]. Problems for strings are examples of such problems [17,20,30,9,1,27].…”

Section: Introductionmentioning

confidence: 99%

Quantum Algorithm for the Shortest Superstring Problem

Khadiev¹,

Machado²

2021

Preprint

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In this paper, we consider the "Shortest Superstring Problem"(SSP) or the "Shortest Common Superstring Problem"(SCS). The problem is as follows. For a positive integer n, a sequence of n strings S = (s 1 , . . . , s n ) is given. We should construct the shortest string t (we call it superstring) that contains each string from the given sequence as a substring. The problem is connected with the sequence assembly method for reconstructing a long DNA sequence from small fragments. We present a quantum algorithm with running time O * (1.728 n ). Here O * notation does not consider polynomials of n and the length of t.

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“…There are many problems where quantum algorithms outperform the best known classical ones [12], and one of the most important performance metrics in this regard is query complexity. We refer to [3] for a nice survey on the quantum query complexity, and to [14,13,16,15,9] for the more recent progress.…”

Section: Introductionmentioning

confidence: 99%

Quantum algorithm for Dyck Language with Multiple Types of Brackets

Khadiev¹,

Kravchenko²

2021

Preprint

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We consider the recognition problem of the Dyck Language generalized for multiple types of brackets. We provide an algorithm with quantum query complexity O( √ n(log n) 0.5k ), where n is the length of input and k is the maximal nesting depth of brackets. Additionally, we show the lower bound for this problem which is O( √ nc k ) for some constant c. Interestingly, classical algorithms solving the Dyck Language for multiple types of brackets substantially differ form the algorithm solving the original Dyck language. At the same time, quantum algorithms for solving both kinds of the Dyck language are of similar nature and requirements.

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Quantum-over-Classical Advantage in Solving Multiplayer Games

Cited by 7 publications

References 26 publications

A linear algorithm for the restricted subtraction games

A linear algorithm for the restricted subtraction games

Quantum Algorithm for the Shortest Superstring Problem

Quantum algorithm for Dyck Language with Multiple Types of Brackets

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