A variational eigenvalue solver on a photonic quantum processor, Alberto Peruzzo, Jeremy McClean, Peter Shadbolt, M. H. Yung, Xiao-Qi Zhou, Peter J. Love, Alán Aspuru-Guzik, Jeremy L. O'Brien, 2014Nature Communications, Vol. 5DOI: 10.1038/ncomms5213 - Introduces the Variational Quantum Eigensolver (VQE), a foundational algorithm that uses a classical optimizer to minimize a quantum expectation value, establishing the VQA framework.
Supervised Learning with Quantum Computers, Maria Schuld, Francesco Petruccione, 2018 (Springer)DOI: 10.1007/978-3-319-96424-9 - A comprehensive textbook on quantum machine learning, detailing how cost functions are constructed from quantum measurements for various supervised learning tasks.
Barren plateaus in quantum neural network training landscapes, Jarrod R. McClean, Sergio Boixo, Vadim N. Smelyanskiy, Ryan Babbush, Hartmut Neven, 2018Nature Communications, Vol. 9DOI: 10.1038/s41467-018-07090-4 - Identifies the phenomenon of barren plateaus in variational quantum algorithms, a significant challenge where cost function gradients vanish exponentially, hindering optimization.
Quantum machine learning, Jacob Biamonte, Peter Wittek, Nicola Pancotti, Patrick Rebentrost, Nathan Wiebe, Seth Lloyd, 2017Nature, Vol. 549DOI: 10.1038/nature23474 - A widely cited review providing an overview of quantum machine learning paradigms and algorithms, including the role of cost functions in quantum learning tasks.