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Title: Quantum Optical Experiments Modeled by Long Short-Term Memory

Paper content:
We demonstrate how machine learning is able to model experiments in quantum physics.
Quantum entanglement is a cornerstone for upcoming quantum technologies such as quantum computation and quantum cryptography.
Of particular interest are complex quantum states with more than two particles and a large number of entangled quantum levels.
Given such a multiparticle high-dimensional quantum state, it is usually impossible to reconstruct an experimental setup that produces it.
To search for interesting experiments, one thus has to randomly create millions of setups on a computer and calculate the respective output states.
In this work, we show that machine learning models can provide significant improvement over random search.
We demonstrate that a long short-term memory (LSTM) neural network can successfully learn to model quantum experiments by correctly predicting output state characteristics for given setups without the necessity of computing the states themselves.
This approach not only allows for faster search but is also an essential step towards automated design of multiparticle high-dimensional quantum experiments using generative machine learning models.
In the past decade, artificial neural networks have been applied to a plethora of scientific disciplines, commercial applications, and every-day tasks with outstanding performance in, e.g., medical diagnosis, self-driving, and board games (Esteva et al., 2017; Silver et al., 2017) .
In contrast to standard feedforward neural networks, long short-term memory (LSTM) (Hochreiter, 1991; Hochreiter & Schmidhuber, 1997) architectures have recurrent connections, which allow them to process sequential data such as text and speech (Sutskever et al., 2014) .
Such sequence-processing capabilities can be particularly useful for designing complex quantum experiments, since the final state of quantum particles depends on the sequence of elements, i.e. the experimental setup, these particles pass through.
For instance, in quantum optical experiments, photons may traverse a sequence of wave plates, beam splitters, and holographic plates.
Highdimensional quantum states are important for multiparticle and multisetting violations of local realist models as well as for applications in emerging quantum technologies such as quantum communication and error correction in quantum computers (Shor, 2000; Kaszlikowski et al., 2000) .
Already for three photons and only a few quantum levels, it becomes in general infeasible for humans to determine the required setup for a desired final quantum state, which makes automated design procedures for this inverse problem necessary.
One example of such an automated procedure is the algorithm MELVIN , which uses a toolbox of optical elements, randomly generates sequences of these elements, calculates the resulting quantum state, and then checks whether the state is interesting, i.e. maximally entangled and involving many quantum levels.
The setups proposed by MELVIN have been realized in laboratory experiments Erhard et al., 2018b) .
Recently, also a reinforcement learning approach has been applied to design new experiments (Melnikov et al., 2018) .
Inspired by these advances, we investigate how LSTM networks can learn quantum optical setups and predict the characteristics of the resulting quantum states.
We train the neural networks using millions of setups generated by MELVIN.
The huge amount of data makes deep learning approaches the first choice.
We use cluster cross validation (Mayr et al., 2016) to evaluate the models.
We have shown that an LSTM-based neural network can be trained to successfully predict certain characteristics of high-dimensional multiparticle quantum states from the experimental setup without any explicit knowledge of quantum mechanics.
The network performs well even on unseen data beyond the training distribution, proving its extrapolation capabilities.
This paves the way to automated design of complex quantum experiments using generative machine learning models.

assistant: text: We demonstrate how machine learning is able to model experiments in quantum physics.