Abstract
Classical machine learning algorithms can provide insights on high-dimensional processes that are hardly accessible with conventional approaches. As a notable example, t-distributed Stochastic Neighbor Embedding (t-SNE) represents the state of the art for visualization of data sets of large dimensionality. An interesting question is then if this algorithm can provide useful information also in quantum experiments with very large Hilbert spaces. Leveraging these considerations, in this work we apply t-SNE to probe the spatial distribution of n-photon events in m-dimensional Hilbert spaces, showing that its findings can be beneficial for validating genuine quantum interference in boson sampling experiments. In particular, we find that nonlinear dimensionality reduction is capable to capture distinctive features in the spatial distribution of data related to multi-photon states with different evolutions. We envisage that this approach will inspire further theoretical investigations, for instance for a reliable assessment of quantum computational advantage.
Highlights
Motivated by the recent achievements enabled by machine learning, the last decades have seen a flowering of novel approaches developed to tackle hard problems
The manuscript is structured in two parts: first, after a short introduction on boson sampling and its validation, we introduce t-distributed Stochastic Neighbor Embedding algorithm (t-SNE) as a promising tool to study multi-particle interference
In this work we tackle this challenge by leveraging machine learning techniques, with an approach that naturally fits in photonic applications
Summary
Motivated by the recent achievements enabled by machine learning, the last decades have seen a flowering of novel approaches developed to tackle hard problems. Machine learning algorithms are conveniently divided in three classes [2]: (i) supervised, when they are trained on labeled examples, (ii) unsupervised, when they infer patterns in data with no labels, and (iii) reinforcement learning, when training aims at maximizing a reward Beyond this classification, other statistical tools are employed to prepare [3] or to explore [4] the input data, usually spread in very large domains, or to test a statistical model [5]. Other statistical tools are employed to prepare [3] or to explore [4] the input data, usually spread in very large domains, or to test a statistical model [5] Within these techniques, visualizing high-dimensional points would naturally represent a critical advantage for data analysis. T-distributed Stochastic Neighbor Embedding algorithm (t-SNE) [7] has established itself as the new state of the art for this task in several fields [8,9,10,11,12]
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