Quantum optimization for solving nonconvex problem

Farhi and others~\cite{Farhi} have introduced the notion of solving NP problems using adiabatic quantum computers. We discuss an application of this idea to the problem of integer factorization, together with a technique we call \emph{gluing} which can be used to build adiabatic models of interesting problems. Although adiabatic quantum computers already exist, they are likely to be too small to directly tackle problems of interesting practical sizes for the foreseeable future. Therefore, we discuss techniques for decomposition of large problems, which permits us to fully exploit such hardware as may be available. Numerical results suggest that even simple decomposition techniques may yield acceptable results with subexponential overhead, independent of the performance of the underlying device.

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Heuristic Quantum Optimization for 6G Wireless Communications

IEEE Network ◽

10.1109/mnet.012.2000770 ◽

2021 ◽

Vol 35 (4) ◽

pp. 8-15

Author(s):

Minsung Kim ◽

Srikar Kasi ◽

P. Aaron Lott ◽

Davide Venturelli ◽

John Kaewell ◽

...

Keyword(s):

Wireless Communications ◽

Quantum Optimization

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Fundamentals of Quantum Computing, Quantum Supremacy, and Quantum Machine Learning

Limitations and Future Applications of Quantum Cryptography - Advances in Information Security, Privacy, and Ethics ◽

10.4018/978-1-7998-6677-0.ch002 ◽

2021 ◽

pp. 21-46

Author(s):

Kamaljit I. Lakhtaria ◽

Vrunda Gadesha

Keyword(s):

Machine Learning ◽

Quantum Computing ◽

Quantum Computer ◽

Error Mitigation ◽

Fundamental Goal ◽

Quantum Device ◽

Quantum Machine Learning ◽

Simulation Error ◽

The Difference ◽

Quantum Optimization

When we aim to demonstrate that a programmable quantum device can solve complex problems which cannot be addressed by classic computers, this fundamental goal is known as quantum supremacy. This concept has changed every fundamental rule of computation. In this chapter, the detailed concept of quantum computing and quantum supremacy is explained along with various open source tools and real-time applications of this technology. The major base concepts, quantum computing, the difference between classical and quantum computer on physical level, programing quantum device, and the experiment-quantum supremacy are explained conceptually. This chapter also includes an introduction of the tools Cirq and OpenFermion plus the applications like quantum simulation, error mitigation technique, quantum machine learning, and quantum optimization, which are explained with illustrations.

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Influence of End-Effector Velocities on Robotic Manipulator Dynamic Performance: An Analytical Approach

Volume 2: 29th Design Automation Conference, Parts A and B ◽

10.1115/detc2003/dac-48835 ◽

2003 ◽

Cited By ~ 1

Author(s):

ChangHwan Kim ◽

Alan Bowling

Keyword(s):

Quadratic Forms ◽

Dynamic Performance ◽

Optimal Solution ◽

Problem Formulation ◽

Optimization Techniques ◽

Curve Analysis ◽

Centrifugal Forces ◽

End Effector ◽

Nonconvex Problem ◽

Torque Curve

This article explores the effect that end-effector velocities have on a nonredundant robotic manipulator’s ability to accelerate its end-effector as well as to apply forces/moments to the environment at the end-effector. The velocity effects considered here are the Coriolis and Centrifugal forces, and the reduction of actuator torque with rotor velocity, as described by the speed-torque curve. Analysis of these effects is accomplished using optimization techniques, where the problem formulation consists of a cost function and constraints which are all purely quadratic forms, yielding a nonconvex problem. An analytical solution, based on the dialytic elimination technique, is developed which guarantees that the globally optimal solution can be found. The PUMA 560 manipulator is used as an example to illustrate this methodology.

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