Method for solving hypergraph Ramsey number based on adiabatic quantum algorithm

A quantum and adiabatic technology, applied in the field of calculating Ramsey numbers of hypergraphs based on adiabatic quantum algorithms, it can solve problems such as the difficulty of solving Ramsey numbers, and achieve strong fault tolerance and outstanding decoherence resistance

Pending Publication Date: 2020-04-07
TIANJIN UNIV
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It is very difficult to solve the Ra

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  • Method for solving hypergraph Ramsey number based on adiabatic quantum algorithm
  • Method for solving hypergraph Ramsey number based on adiabatic quantum algorithm
  • Method for solving hypergraph Ramsey number based on adiabatic quantum algorithm

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[0040] Below in conjunction with accompanying drawing, technical scheme of the present invention is described in further detail:

[0041] The present invention is a method for calculating hypergraph Ramsey numbers based on an adiabatic quantum algorithm, and the specific flow chart is shown in Figure 1. Its implementation has the following steps:

[0042] (1) By studying the r-dimensional adjacency matrix representation corresponding to the r-homogeneous hypergraph, the mapping rule g between the r-homogeneous hypergraph and the binary string is given N,r (G), the Ramsey number R(m,n;r) of the r-homogeneous hypergraph is mapped to a combinatorial optimization problem. The specific method is as follows:

[0043] For a given N and r, an r-homogeneous complete hypergraph of N vertices and {0,1} can be built B(N,r) There is a one-to-one correspondence between them, where B is defined as the binomial coefficient. For convenience, define the sequence of N vertices as V≡{1,2,...,...

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Abstract

The invention discloses a method for calculating the Ramsey number of an r-homogeneous hypergraph based on an adiabatic quantum algorithm. The method comprises the following steps: researching an r-dimensional adjacency matrix representation form corresponding to an r-homogeneous hypergraph, giving a mapping rule gN, r (G) between the r-homogeneous hypergraph and a binary string, and mapping a Ramsey number R (m, n, r) of the r-homogeneous hypergraph into a combined optimization problem; solving a cost function of the combined optimization problem; defining a final-state Hamiltonian quantity of the adiabatic quantum algorithm by utilizing the solved cost function; the adiabatic quantum algorithm evolves the state of the L-bit register from the ground state of the initialized Hamiltonian tothe ground state of the final Hamiltonian; and after adiabatic evolution is finished, adopting a proper measurement method to measure the final state of the system, so that the solution of the combinatorial optimization problem can be obtained with a relatively high probability. The invention provides a method for solving an r-homogeneous hypergraph Ramsey number combination optimization problemby using an adiabatic quantum algorithm. The method has an acceleration effect on solving the Ramsey number of the graph compared with a classical algorithm.

Description

technical field [0001] The invention relates to the field of hypergraphs and adiabatic quantum algorithms, in particular to a method for calculating hypergraph Ramsey numbers based on adiabatic quantum algorithms. Background technique [0002] Quantum computing and quantum information are an interdisciplinary subject that combines the principles of quantum mechanics and computer theory. Due to the limitations of existing computers in quickly processing large amounts of information, quantum information science, with quantum computing and quantum communication as the main research content, is an interdisciplinary science and technology that has developed rapidly in recent years. It has important basic theoretical functions and promotes high-tech develop rapidly. Quantum computers provide a new computing method based on algorithms based on quantum principles, namely quantum algorithms. [0003] The adiabatic quantum algorithm is a new quantum computing algorithm that has attr...

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Application Information

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IPC IPC(8): G06N10/00
CPCG06N10/00
Inventor 蒋亚菊曲日王娟鲍彦茹张鹏
Owner TIANJIN UNIV
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