William Cruz-Santos's Books

Approximability of Optimization Problems through Adiabatic Quantum Computation

By: William Cruz-Santos,Guillermo Morales-Luna

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Approximability of Optimization Problems through Adiabatic Quantum Computation

By: William Cruz-Santos,Guillermo Morales-Luna

The adiabatic quantum computation (AQC) is based on the adiabatic theorem to approximate solutions of the Schrödinger equation. The design of an AQC algorithm involves the construction of a Hamiltonian that describes the behavior of the quantum system. This Hamiltonian is expressed as a linear interpolation of an initial Hamiltonian whose ground state is easy to compute, and a final Hamiltonian whose ground state corresponds to the solution of a given combinatorial optimization problem. The adiabatic theorem asserts that if the time evolution of a quantum system described by a Hamiltonian is large enough, then the system remains close to its ground state. An AQC algorithm uses the adiabatic theorem to approximate the ground state of the final Hamiltonian that corresponds to the solution of the given optimization problem. In this book, we investigate the computational simulation of AQC algorithms applied to the MAX-SAT problem. A symbolic analysis of the AQC solution is given in order to understand the involved computational complexity of AQC algorithms. This approach can be extended to other combinatorial optimization problems and can be used for the classical simulation of an AQC algorithm where a Hamiltonian problem is constructed. This construction requires the computation of a sparse matrix of dimension 2n × 2n, by means of tensor products, where n is the dimension of the quantum system. Also, a general scheme to design AQC algorithms is proposed, based on a natural correspondence between optimization Boolean variables and quantum bits. Combinatorial graph problems are in correspondence with pseudo-Boolean maps that are reduced in polynomial time to quadratic maps. Finally, the relation among NP-hard problems is investigated, as well as its logical representability, and is applied to the design of AQC algorithms. It is shown that every monadic second-order logic (MSOL) expression has associated pseudo-Boolean maps that can be obtained by expanding the given expression, and also can be reduced to quadratic forms. Table of Contents: Preface / Acknowledgments / Introduction / Approximability of NP-hard Problems / Adiabatic Quantum Computing / Efficient Hamiltonian Construction / AQC for Pseudo-Boolean Optimization / A General Strategy to Solve NP-Hard Problems / Conclusions / Bibliography / Authors' Biographies

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Page Count

105

Publisher

Springer Nature

Published Date

ISBN 10

3031025199

ISBN 13

9783031025198

Fruitless Trees

Portuguese Conservation and Brazil’s Colonial Timber

By: Shawn William Miller

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Fruitless Trees

Portuguese Conservation and Brazil’s Colonial Timber

By: Shawn William Miller

By and large, Brazil's forests were not simply harvested by the Portugese colonists, but rather annihilated, and relatively little was extracted for the benefit of Brazilians, a tragedy perhaps worse than deforestation alone. Fruitless Trees aims to make sense of what at first glance appears to be the senseless destruction of Brazil's incomparable timber as a result of Portuguese colonial policies.

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Page Count

352

Publisher

Stanford University Press

Published Date

ISBN 10

0804733961

ISBN 13

9780804733960

Approximability of Optimization Problems through Adiabatic Quantum Computation

By: William Cruz-Santos,Guillermo Morales-Luna

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Approximability of Optimization Problems through Adiabatic Quantum Computation

By: William Cruz-Santos,Guillermo Morales-Luna

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Page Count

115

Publisher

Morgan & Claypool Publishers

Published Date

ISBN 10

1627055576

ISBN 13

9781627055574

Book's by William Cruz-Santos

Approximability of Optimization Problems through Adiabatic Quantum Computation

Approximability of Optimization Problems through Adiabatic Quantum Computation

Fruitless Trees

Fruitless Trees

Approximability of Optimization Problems through Adiabatic Quantum Computation

Approximability of Optimization Problems through Adiabatic Quantum Computation

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