Quantum second-order optimization algorithm for general polynomials

Gao, Pan; Li, Keren; Wei, Shijie; Long, Gui‐Lu

doi:10.1007/s11433-021-1725-9

Cited by 19 publications

(8 citation statements)

References 51 publications

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“…This work focused on the first-order optimization method, but the second-order optimization method (the Newton method) [88] may also be used in the preparation of NESS. Aside from the preparation of NESS, it is possible to simulate the dynamics of quantum open systems on a doubledimension Hilbert space.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Quantum gradient descent algorithms for nonequilibrium steady states and linear algebraic systems

Liang,

Wei,

Fei

2022

Preprint

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The gradient descent approach is the key ingredient in variational quantum algorithms and machine learning tasks, which is an optimization algorithm for finding a local minimum of an objective function. The quantum versions of gradient descent have been investigated and implemented in calculating molecular ground states and optimizing polynomial functions. Based on the quantum gradient descent algorithm and Choi-Jamiolkowski isomorphism, we present approaches to simulate efficiently the nonequilibrium steady states of Markovian open quantum many-body systems. Two strategies are developed to evaluate the expectation values of physical observables on the nonequilibrium steady states. Moreover, we adapt the quantum gradient descent algorithm to solve linear algebra problems including linear systems of equations and matrix-vector multiplications, by converting these algebraic problems into the simulations of closed quantum systems with well-defined Hamiltonians. Detailed examples are given to test numerically the effectiveness of the proposed algorithms for the dissipative quantum transverse Ising models and matrix-vector multiplications.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Quantum gradient descent algorithms for nonequilibrium steady states and linear algebraic systems

Liang,

Wei,

Fei

2022

Preprint

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“…The Hamiltonian simulated in our numerical experiments is from 13 C-labeled Crotonic acid dissolved in d6-acetone, which is usually employed as a four-qubit quantum system for NMR-based quantum information processing [18].…”

Section: Hamiltonian Of Crotonic Acidmentioning

confidence: 99%

“…For example, complexity of t -time analog Hamiltonian evolution is

. Furthermore, certain digital algorithms were proposed for hermitian matrices’ evolution, which produce quantum speedups in many scenarios, such as simulation algorithms, quantum principal component analysis, quantum matrix inversion, and their generalizations [ 9 , 10 , 11 , 12 , 13 , 14 , 15 ]. However, deep quantum circuits and inaccessible oracles are required, which hinder their applications on near term devices.…”

Section: Introductionmentioning

confidence: 99%

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A NISQ Method to Simulate Hermitian Matrix Evolution

Gao

2022

Entropy

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As a universal quantum computer requires millions of error-corrected qubits, one of the current goals is to exploit the power of noisy intermediate-scale quantum (NISQ) devices. Based on a NISQ module–layered circuit, we propose a heuristic protocol to simulate Hermitian matrix evolution, which is widely applied as the core for many quantum algorithms. The two embedded methods, with their own advantages, only require shallow circuits and basic quantum gates. Capable to being deployed in near future quantum devices, we hope it provides an experiment-friendly way, contributing to the exploitation of power of current devices.

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“…First-order optimization techniques are generally time-saving and straightforward calculation methods that converge quickly for large datasets. Second-order optimization algorithms [ 29 ]: In these algorithms, error functions (or objective functions)

are maximized or minimized using a second-order derivative, also known as the Hessian. The Hessian of a matrix can be considered the partial derivative of the second order of the same matrix.…”

Section: Introductionmentioning

confidence: 99%

A Systematic Review of Optimization Algorithms for Structural Health Monitoring and Optimal Sensor Placement

Hassani

Dackermann

2023

Sensors

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In recent decades, structural health monitoring (SHM) has gained increased importance for ensuring the sustainability and serviceability of large and complex structures. To design an SHM system that delivers optimal monitoring outcomes, engineers must make decisions on numerous system specifications, including the sensor types, numbers, and placements, as well as data transfer, storage, and data analysis techniques. Optimization algorithms are employed to optimize the system settings, such as the sensor configuration, that significantly impact the quality and information density of the captured data and, hence, the system performance. Optimal sensor placement (OSP) is defined as the placement of sensors that results in the least amount of monitoring cost while meeting predefined performance requirements. An optimization algorithm generally finds the “best available” values of an objective function, given a specific input (or domain). Various optimization algorithms, from random search to heuristic algorithms, have been developed by researchers for different SHM purposes, including OSP. This paper comprehensively reviews the most recent optimization algorithms for SHM and OSP. The article focuses on the following: (I) the definition of SHM and all its components, including sensor systems and damage detection methods, (II) the problem formulation of OSP and all current methods, (III) the introduction of optimization algorithms and their types, and (IV) how various existing optimization methodologies can be applied to SHM systems and OSP methods. Our comprehensive comparative review revealed that applying optimization algorithms in SHM systems, including their use for OSP, to derive an optimal solution, has become increasingly common and has resulted in the development of sophisticated methods tailored to SHM. This article also demonstrates that these sophisticated methods, using artificial intelligence (AI), are highly accurate and fast at solving complex problems.

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Quantum second-order optimization algorithm for general polynomials

Cited by 19 publications

References 51 publications

Quantum gradient descent algorithms for nonequilibrium steady states and linear algebraic systems

Quantum gradient descent algorithms for nonequilibrium steady states and linear algebraic systems

A NISQ Method to Simulate Hermitian Matrix Evolution

A Systematic Review of Optimization Algorithms for Structural Health Monitoring and Optimal Sensor Placement

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