Quantum-enhanced data science, also known as quantum machine learning (QML), is of growing interest as an application of near-term quantum computers. Variational QML algorithms have the potential to solve practical problems on real hardware, particularly when involving quantum data. However, training these algorithms can be challenging and calls for tailored optimization procedures. Specifically, QML applications can require a large shot-count overhead due to the large datasets involved. In this work, we advocate for simultaneous random sampling over both the dataset as well as the measurement operators that define the loss function. We consider a highly general loss function that encompasses many QML applications, and we show how to construct an unbiased estimator of its gradient. This allows us to propose a shot-frugal gradient descent optimizer called Refoqus (REsource Frugal Optimizer for QUantum Stochastic gradient descent). Our numerics indicate that Refoqus can save several orders of magnitude in shot cost, even relative to optimizers that sample over measurement operators alone.
In this work, we design a novel game-theoretical framework capable of capturing the defining aspects of quantum theory. We introduce an original model and an algorithmic procedure that enables to express measurement scenarios encountered in quantum mechanics as multiplayer games and to translate physical notions of causality, correlation, and contextuality to particular aspects of game theory. Furthermore, inspired by the established correspondence, we investigate the causal consistency of games in extensive form with imperfect information from the quantum perspective and we conclude that counterfactual dependencies should be distinguished from causation and correlation as a separate phenomenon of its own. Most significantly, we deduce that Nashian free choice game theory is non-contextual and hence is in contradiction with the Kochen-Specker theorem. Hence, we propose that quantum physics should be analysed with toolkits from non-Nashian game theory applied to our suggested model.
We propose a framework for Quantum Field Theory studies that allows to represent field excitations as quantum channels and hence to examine them from a quantum information perspective. We demonstrate inner-workings of the proposed scheme for two universal states: the vacuum state of 1D harmonic chain being the regularization of one spatial dimension QFT system and the latticeregulated Thermofield Double State of two identical free QFTs. We investigate actions of unitary and non-unitary Bosonic Gaussian channels (including Petz recovery maps). To evaluate and quantify the character of channel static action and channel induced dynamics we calculate quantum entropies and fidelities.
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