Validating quantum systems in the presence of errors

Sourabh Lahiri, Arun M. Jayannavar

It has recently been shown that the Jarzynski equality gets modified, when there are experimental errors in computing work. This modified result also holds good in presence of feedback. In this work, we use a simple toy model, that of a Szilard engine, to prove these results both in the presence and in absence of feedback.

Sarah Sheldon

Fangjun Hu, Xun Gao

Tackling output sampling noise due to finite shots of quantum measurement is an unavoidable challenge when extracting information in machine learning with physical systems. A technique called Eigentask Learning was developed recently as a framework for learning with infinite input training data in the presence of output sampling noise. In the work of Eigentask Learning, numerical evidence was presented that extracting low-noise contributions of features can practically improve performance for machine learning tasks, displaying robustness to overfitting and increasing generalization accuracy. However, it remains unsolved to quantitatively characterize generalization errors in situations where the training dataset is finite, while output sampling noise still exists. In this study, we use methodologies from statistical mechanics to calculate the training and generalization errors of a generic quantum machine learning system when the input training dataset and output measurement sampling shots are both finite. Our analytical findings, supported by numerical validation, offer solid justification that Eigentask Learning provides optimal learning in the sense of minimizing generalization errors.

Vassilios Constantoudis, Nikos Theodorakopoulos

Two fundamental quantum signatures of classically chaotic behaviour, large second derivatives and the logarithmic time barrier separating classical from quantum dynamics, have been observed near the separatrix of an integrable spin system. A systematic study in the neighbourhood of the separatrix reveals that the error in semiclassical eigenvalues (measured in units of the quantum level spacing) approaches a finite value at the classical limit. The generic factor which limits the validity of the correspondence principle is the presence of classical instabilities; chaotic behaviour is one such case; the separatrix of an integrable system is another.

Megan Dahlhauser, Robin Blume-Kohout, Timothy J Proctor +1 more