Related papers: Quantum Cellular Automata, Tensor Networks, and Ar…
To address Quantum Artificial Neural Networks as quantum dynamical computing systems, a formalization of quantum artificial neural networks as dynamical systems is developed, expanding the concept of unitary map to the neural computation…
The complexity of cellular automata is traditionally measured by their computational capacity. However, it is difficult to choose a challenging set of computational tasks suitable for the parallel nature of such systems. We study the…
Tensor network algorithms seek to minimize correlations to compress the classical data representing quantum states. Tensor network algorithms and similar tools---called tensor network methods---form the backbone of modern numerical methods…
(i) We point out that every local unitary circuit of depth smaller than the linear system size is easily distinguished from a global Haar random unitary if there is a conserved quantity that is a sum of local operators. This is always the…
The theory of cellular automata in operational probabilistic theories is developed. We start introducing the composition of infinitely many elementary systems, and then use this notion to define update rules for such infinite composite…
Quantum cellular automata (QCA) evolve qubits in a quantum circuit depending only on the states of their neighborhoods and model how rich physical complexity can emerge from a simple set of underlying dynamical rules. For instance,…
We demonstrate that the concept of a conservation law can be naturally extended from deterministic to probabilistic cellular automata (PCA) rules. The local function for conservative PCA must satisfy conditions analogous to conservation…
The entanglement area law is a universal principle that characterizes the information structure in quantum many-body systems and serves as the foundation for modern algorithms based on tensor network representations. Historically, the area…
Quantum machine learning has the potential to enable advances in artificial intelligence, such as solving problems intractable on classical computers. Some fundamental ideas behind quantum machine learning are similar to kernel methods in…
Modeling joint probability distributions over sequences has been studied from many perspectives. The physics community developed matrix product states, a tensor-train decomposition for probabilistic modeling, motivated by the need to…
Monitored quantum circuits host a rich variety of exotic non-equilibrium phases. Among the most representative examples are measurement-induced phase transitions between distinct area-law entangled states. However, because these transitions…
Probabilistic cellular automata describe the dynamics of classical spin models, which, for sufficiently small temperature $T$, can serve as classical memory capable of storing information even in the presence of nonzero external magnetic…
Algorithms developed to solve many-body quantum problems, like tensor networks, can turn into powerful quantum-inspired tools to tackle problems in the classical domain. In this work, we focus on matrix product operators, a prominent…
Unital quantum channels, defined by their property of leaving the maximally mixed state invariant, form an important class of quantum operations. A distinguished subset of these channels can be represented as a probabilistic mixture of…
Quantum entanglement plays a crucial role in quantum information processing tasks and quantum mechanics, hence quantifying unknown entanglement is a fundamental task. However, this is also challenging, as entanglement cannot be measured by…
Probabilistic cellular automata with deterministic updating are quantum systems. We employ the quantum formalism for an investigation of random probabilistic cellular automata, which start with a probability distribution over initial…
Quantum mechanics permits nonlocality - both nonlocal correlations and nonlocal equations of motion - while respecting relativistic causality. Is quantum mechanics the unique theory that reconciles nonlocality and causality? We consider two…
We show that quantum cellular automata naturally form the degree-zero part of a coarse homology theory. The recent result of Ji and Yang that the space of QCA forms an Omega-spectrum in the sense of algebraic topology is a direct…
We focus on using an architecture similar to the $\beta$-Variational Autoencoder ($\beta$-VAE) to discriminate if a quantum state is entangled or separable based on measurements. We split the data into two sets, the set of local and…
The set of Entanglement Saving (ES) quantum channels is introduced and characterized. These are completely positive, trace preserving transformations which when acting locally on a bipartite quantum system initially prepared into a…