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Center for Nonlinear Studies |
Abstract: In this talk I will show how to efficiently investigate the optimization landscape of a variational quantum algorithm with information content. I will start by showing that the information content of any optimization landscape is connected to the average norm of the gradient, and the robust bounds we calculate on the estimator of the average norm of the gradient from information content. Next, I will describe how to efficiently computed this value with only a linear (in the number of parameters) number of queries to a quantum computer. Finally, I will demonstrate the power of this method when applied to an instance of the barren plateau problem, for which we are able to estimate its scaling pre-factors. If time allows, I will share some very recent results on the application of a simple persistent homology data analysis, the sublevel set, to the barren plateau problem, and show how to use sublevel sets to estimate the probability distribution of the eigenvalues of a quantum observable.
Dr Bonet-Monroig received his PhD in November 2022 from the University of Leiden under the supervision of Carlo Beenakker and Tom O'Brien. He is currently a postdoc at the same institute within the Quantum Delta NL consortium. During his PhD he has studied all aspects of variational quantum algorithms in near-term hardware: error mitigation, measurement scheduling of quantum states, and optimization of parametrized quantum circuits. His work focuses mostly on application of near-term quantum algorithms for quantum physics and chemistry problems such as ground and excited state calculations and energy derivatives. More recently, he has been interested in studying the computational complexity of variational algorithms from a computer science point of view, using data-driven methods to see whether a hybrid quantum-classical computer is more powerful than a classical computer.
Host: Andrew Sornborger (CCS-3)