Although the performance of hybrid quantum-classical algorithms is highly dependent on the selection of the classical optimizer and the circuit ansatz, a robust and thorough assessment on-hardware of such features has been missing to date.
From the optimizer perspective, the primary challenge lies in the solver's stochastic nature, and their significant variance over the random initialization.
Therefore, a robust comparison requires that one perform several training curves for each solver before one can reach conclusions about their typical performance.
Since each of the training curves requires the execution of thousands of quantum circuits in the quantum computer, such a robust study remained a steep challenge for most hybrid platforms available today.
Robust Implementation of Generative Modeling with Parametrized Quantum Circuits · Around
Alberto Peruzzo, Jarrod McClean, Peter Shadbolt, Man-Hong Yung, Xiao-Qi Zhou, Peter J. Love, Alán Aspuru-Guzik, and Jeremy L. O’Brien, “A variational eigenvalue solver on a photonic quantum processor,” Nature Communications 5
Jarrod R McClean, Jonathan Romero, Ryan Babbush, and Alán Aspuru-Guzik, “The theory of variational hybrid quantum-classical algorithms,” New Journal of Physics 18
Abhinav Kandala, Antonio Mezzacapo, Kristan Temme, Maika Takita, Markus Brink, Jerry M. Chow, and Jay M. Gambetta, “Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets,” Nature 549
E. F. Dumitrescu, A. J. McCaskey, G. Hagen, G. R. Jansen, T. D. Morris, T. Papenbrock, R. C. Pooser, D. J. Dean, and P. Lougovski, “Cloud quantum computing of an atomic nucleus,” Phys. Rev. Lett. 120
Oscar Perdomo, Vicente Leyton-Ortega, and Alejandro Perdomo-Ortiz, “A stochastic variation of the hill climbing method,” In preparation (2019a)
Cited in the paper.
Oscar Perdomo, Vicente Leyton-Ortega, and Alejandro Perdomo-Ortiz, “Upgrading the bloch sphere: Projective space foliated by klein bottles as a geometrical representation of two-qubit states and their entanglement,” In preparation (2019b)