STRETCHING NATURE'S LAWS

L.D. LANDAU, Efrat Lifshitz

Ferenc Oravecz

We define a natural transformation of certain symmetric probability measures, and show that it brings the Gaussian-law as well as several deformed analogue of it to the Poisson-law or to the corresponding deformed Poisson-law, respectively. An important example is the q-Gaussian-law with its transform being the q-Poisson-law of Saitoh and Yoshida. By analogy we define an even more general class of deformed Poisson distributions, and show that, as in the classical and the q-case, these deformed Poisson-laws can be achieved as the distributions of certain operators.

Zeyi Tao, Jindi Wu, Qi Xia +1 more

Variational quantum algorithms (VQAs) have recently received much attention due to their promising performance in Noisy Intermediate-Scale Quantum computers (NISQ). However, VQAs run on parameterized quantum circuits (PQC) with randomly initialized parameters are characterized by barren plateaus (BP) where the gradient vanishes exponentially in the number of qubits. In this paper, we proposed a Look Around Warm-Start (LAWS) quantum natural gradient (QNG) algorithm to mitigate the widespread existing BP issues. LAWS is a combinatorial optimization strategy taking advantage of model parameter initialization and fast convergence of QNG. LAWS repeatedly reinitializes parameter search space for the next iteration parameter update. The reinitialized parameter search space is carefully chosen by sampling the gradient close to the current optimal. Moreover, we present a unified framework (WS-SGD) for integrating parameter initialization techniques into the optimizer. We provide the convergence proof of the proposed framework for both convex and non-convex objective functions based on Polyak-Lojasiewicz (PL) condition. Our experiment results show that the proposed algorithm could mitigate the BP and have better generalization ability in quantum classification problems.

Melinda Baldwin