We show that deterministic quantumcomputing with a single bit can determine whether the classical limit of a quantum system is chaotic or integrable using O(N) physical resources, where N is the dimension of the Hilb...
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We show that deterministic quantumcomputing with a single bit can determine whether the classical limit of a quantum system is chaotic or integrable using O(N) physical resources, where N is the dimension of the Hilbert space of the system under study. This is a square-root improvement over all known classical procedures. Our study relies strictly on the random matrix conjecture. We also present numerical results for the nonlinear kicked top.
In this article, we focus on the communication costs of three symmetric matrix computations: i) multiplying a matrix with its transpose, known as a symmetric rank-k update (SYRK) ii) adding the result of the multiplic...
In this article, we focus on the communication costs of three symmetric matrix computations: i) multiplying a matrix with its transpose, known as a symmetric rank-k update (SYRK) ii) adding the result of the multiplication of a matrix with the transpose of another matrix and the transpose of that result, known as a symmetric rank-2k update (SYR2K) iii) performing matrix multiplication with a symmetric input matrix (SYMM). All three computations appear in the Level 3 Basic Linear Algebra Subroutines (BLAS) and have wide use in applications involving symmetric matrices. We establish communication lower bounds for these kernels using sequential and distributed-memory parallel computational models, and we show that our bounds are tight by presenting communication-optimal algorithms for each setting. Our lower bound proofs rely on applying a geometric inequality for symmetric computations and analytically solving constrained nonlinear optimization problems. The symmetric matrix and its corresponding computations are accessed and performed according to a triangular block partitioning scheme in the optimal algorithms.
This book constitutes the thoroughly refereed workshop proceedings of the 9th International Workshop on Structured Object-Oriented Formal Language and Method, SOFL+MSVL 2019, held in Shenzhen, China, in November 2019....
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ISBN:
(数字)9783030414184
ISBN:
(纸本)9783030414177
This book constitutes the thoroughly refereed workshop proceedings of the 9th International Workshop on Structured Object-Oriented Formal Language and Method, SOFL+MSVL 2019, held in Shenzhen, China, in November 2019. The 23 revised full papers included in the volume were carefully reviewed and selected from 43 submissions. They are organized in the following topical sections: testing and debugging, formal verification, problem solving, software analysis and evolution, and software analysis and testing.
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