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Even though probabilistic treatments of neural networks have a long history, they have not found widespread use in practice. Sampling approaches are often too slow already for simple networks. The size of the inputs and the depth of typical…

Considering recent advancements and successes in the development of efficient quantum algorithms for electronic structure calculations --- alongside impressive results using machine learning techniques for computation --- hybridizing…

Essentials of the scientific discovery process have remained largely unchanged for centuries: systematic human observation of natural phenomena is used to form hypotheses that, when validated through experimentation, are generalized into…

Quantum state tomography is a fundamental task in quantum computing, involving the reconstruction of an unknown quantum state from measurement outcomes. Although essential, it is typically introduced at the graduate level due to its…

Quantized deep neural networks (QDNNs) are necessary for low-power, high throughput, and embedded applications. Previous studies mostly focused on developing optimization methods for the quantization of given models. However, quantization…

It is widely known that Boltzmann machines are capable of representing arbitrary probability distributions over the values of their visible neurons, given enough hidden ones. However, sampling -- and thus training -- these models can be…

Learning in neural networks critically hinges on the intricate geometry of the loss landscape associated with a given task. Traditionally, most research has focused on finding specific weight configurations that minimize the loss. In this…

Quantum neural networks generalize classical artificial neural networks into the quantum domain. They are formulated as parameterized quantum circuits which are optimized by measuring and minimizing a suitably chosen loss function. The core…

Tensor networks were developed in the context of many-body physics as compressed representations of multiparticle quantum states. These representations mitigate the exponential complexity of many-body systems by capturing only the most…

The entanglement resource required for quantum information processing comes in a variety of forms, from Bell states to multipartite GHZ states or cluster states. Purifying these resources after their imperfect generation is an indispensable…

Unsupervised machine learning models build an internal representation of their training data without the need for explicit human guidance or feature engineering. This learned representation provides insights into which features of the data…

In this survey the possible approaches to the description of the evolution of states of quantum many-particle systems by means of the possible modifications of the density operator which kernel known as density matrix are considered. In…

Data collection in economically constrained countries often necessitates using approximate and biased measurements due to the low-cost of the sensors used. This leads to potentially invalid predictions and poor policies or decision making.…

In quantum information technology, crucial information is regularly encoded in different quantum states. To extract information, the identification of one state from the others is inevitable. However, if the states are non-orthogonal and…

Students in quantum mechanics class are taught that the wave function contains all knowable information about an isolated system. Later in the course, this view seems to be contradicted by the mysterious density matrix, which introduces a…

Virtually all aspects of many-body atomic physics are challenging: experiments are technically demanding, datasets have become enormous, and the memory and CPU requirements for classical simulation of generic quantum systems often scale…

Restricted Boltzmann machines (RBMs) are a class of neural networks that have been successfully employed as a variational ansatz for quantum many-body wave functions. Here, we develop an analytic method to study quantum many-body spin…

Quantum state tomography, the task of learning an unknown quantum state, is a fundamental problem in quantum information. In standard settings, the complexity of this problem depends significantly on the type of quantum state that one is…

The random purification channel, which, given $n$ copies of an unknown mixed state $\rho$, prepares $n$ copies of an associated random purification, has proved to be an extremely valuable tool in quantum information theory. In this work, we…

Image tokenizers play a central role in modern generative models, where the structure of the latent space critically determines the downstream generation performance. A key but underexplored property of effective latent representations is…