Quantum and evolutionary approaches to computational learning

Variational quantum algorithms (VQAs) employ parametrized quantum circuits optimized using classical methods to minimize a cost function. While VQAs have found broad applications, certain challenges persist. Notably, a significant computational burden arises during parameter optimization. The prevailing ``parameter shift rule'' mandates a double evaluation of the cost function for each parameter. In this paper, we introduce an optimization approach named ``learning to learn with an evolutionary strategy'' (LLES). LLES unifies ``learning to learn'' and ``evolutionary strategy'' methods. Learning to learn treats optimization as a learning problem, utilizing recurrent neural networks to iteratively propose VQA parameters. Conversely, evolutionary strategy employs gradient searches to estimate function gradients. Our optimization method is applied to two distinct tasks: determining the ground state of an Ising Hamiltonian and training a quantum neural network. The obtained results underscore the efficacy of this approach. Additionally, we identify a key hyperparameter that significantly influences gradient estimation using the evolutionary strategy method.Variational quantum algorithms (VQAs) employ parametrized quantum circuits optimized using classical methods to minimize a cost function. While VQAs have found broad applications, certain challenges persist. Notably, a significant computational burden arises during parameter optimization. The prevailing ``parameter shift rule'' mandates a double evaluation of the cost function for each parameter. In this paper, we introduce an optimization approach named ``learning to learn with an evolutionary strategy'' (LLES). LLES unifies ``learning to learn'' and ``evolutionary strategy'' methods. Learning to learn treats optimization as a learning problem, utilizing recurrent neural networks to iteratively propose VQA parameters. Conversely, evolutionary strategy employs gradient searches to estimate function gradients. Our optimization method is applied to two distinct tasks: determining the ground state of an Ising Hamiltonian and training a quantum neural network. The obtained results underscore the efficacy of this approach. Additionally, we identify a key hyperparameter that significantly influences gradient estimation using the evolutionary strategy method.

Physical Review AFeb 27, 20254 citations

Learning to learn with an evolutionary strategy applied to variational quantum algorithms

Lucas Friedrich, Jonas Maziero

Variational Quantum Algorithms (VQAs) employ quantum circuits parameterized by $U$ , optimized using classical methods to minimize a cost function. While VQAs have found broad applications, certain challenges persist. Notably, a significant computational burden arises during parameter optimization. The prevailing ``parameter shift rule'' mandates a double evaluation of the cost function for each parameter. In this article, we introduce a novel optimization approach named ``Learning to Learn with an Evolutionary Strategy'' (LLES). LLES unifies ``Learning to Learn'' and ``Evolutionary Strategy'' methods. ``Learning to Learn'' treats optimization as a learning problem, utilizing recurrent neural networks to iteratively propose VQA parameters. Conversely, ``Evolutionary Strategy'' employs gradient searches to estimate function gradients. Our optimization method is applied to two distinct tasks: determining the ground state of an Ising Hamiltonian and training a quantum neural network. Results underscore the efficacy of this novel approach. Additionally, we identify a key hyperparameter that significantly influences gradient estimation using the ``Evolutionary Strategy'' method.Variational Quantum Algorithms (VQAs) employ quantum circuits parameterized by $U$, optimized using classical methods to minimize a cost function. While VQAs have found broad applications, certain challenges persist. Notably, a significant computational burden arises during parameter optimization. The prevailing ``parameter shift rule'' mandates a double evaluation of the cost function for each parameter. In this article, we introduce a novel optimization approach named ``Learning to Learn with an Evolutionary Strategy'' (LLES). LLES unifies ``Learning to Learn'' and ``Evolutionary Strategy'' methods. ``Learning to Learn'' treats optimization as a learning problem, utilizing recurrent neural networks to iteratively propose VQA parameters. Conversely, ``Evolutionary Strategy'' employs gradient searches to estimate function gradients. Our optimization method is applied to two distinct tasks: determining the ground state of an Ising Hamiltonian and training a quantum neural network. Results underscore the efficacy of this novel approach. Additionally, we identify a key hyperparameter that significantly influences gradient estimation using the ``Evolutionary Strategy'' method.

arXiv:2310.17402Oct 26, 20232 citations

Variational Quantum Algorithms (VQAs) employ quantum circuits parameterized by

U

, optimized using classical methods to minimize a cost function. While VQAs have found broad applications, certain challenges persist. Notably, a significant computational burden arises during parameter optimization. The prevailing ``parameter shift rule'' mandates a double evaluation of the cost function for each parameter. In this article, we introduce a novel optimization approach named ``Learning to Learn with an Evolutionary Strategy'' (LLES). LLES unifies ``Learning to Learn'' and ``Evolutionary Strategy'' methods. ``Learning to Learn'' treats optimization as a learning problem, utilizing recurrent neural networks to iteratively propose VQA parameters. Conversely, ``Evolutionary Strategy'' employs gradient searches to estimate function gradients. Our optimization method is applied to two distinct tasks: determining the ground state of an Ising Hamiltonian and training a quantum neural network. Results underscore the efficacy of this novel approach. Additionally, we identify a key hyperparameter that significantly influences gradient estimation using the ``Evolutionary Strategy'' method.