Related papers: Machine Learns Quantum Complexity
Krylov complexity and Nielsen complexity are successful approaches to quantifying quantum evolution complexity that have been actively pursued without much contact between the two lines of research. The two quantities are motivated by…
Continuing the previous initiatives arXiv: 2207.05347 and arXiv: 2212.06180, we pursue the exploration of operator growth and Krylov complexity in dissipative open quantum systems. In this paper, we resort to the bi-Lanczos algorithm…
Machine learning models are used for pattern recognition analysis of big data, without direct human intervention. The task of unsupervised learning is to find the probability distribution that would best describe the available data, and…
Machine learning is widely believed to be one of the most promising practical applications of quantum computing. Existing quantum machine learning schemes typically employ a quantum-classical hybrid approach that relies crucially on…
Solving the ground state and the ground-state properties of quantum many-body systems is generically a hard task for classical algorithms. For a family of Hamiltonians defined on an $m$-dimensional space of physical parameters, the ground…
We apply a notion of quantum complexity, called "Krylov complexity", to study the evolution of systems from integrability to chaos. For this purpose we investigate the integrable XXZ spin chain, enriched with an integrability breaking…
In this paper we present a deep learning method to predict the temporal evolution of dissipative dynamic systems. We propose using both geometric and thermodynamic inductive biases to improve accuracy and generalization of the resulting…
In the vicinity of a phase transition ergodicity can be broken. Here, different initial many-body configurations evolve towards one of several fixed points, which are macroscopically distinguishable through an order parameter. This…
Impurities in quantum materials have provided successful strategies for learning properties of complex states, ranging from unconventional superconductors to topological insulators. In quantum magnetism, inferring the Hamiltonian of an…
Quantum extreme learning machines (QELMs) are unconventional computing architectures that bear remarkable promise in both classical and quantum machine-learning tasks, such as the estimate of quantum state properties. However, the…
Quantifying complexity in quantum systems has witnessed a surge of interest in recent years, with Krylov-based measures such as Krylov complexity ($C_K$) and Spread complexity ($C_S$) gaining prominence. In this study, we investigate their…
Quantum subspace diagonalization (QSD) algorithms have emerged as a competitive family of algorithms that avoid many of the optimization pitfalls associated with parameterized quantum circuit algorithms. While the vast majority of the QSD…
Quantum machine learning (QML) is rapidly transitioning from theoretical promise to practical relevance across data-intensive scientific domains. In this Review, we provide a structured overview of recent advances that bridge foundational…
We show how complexity theory can be introduced in machine learning to help bring together apparently disparate areas of current research. We show that this new approach requires less training data and is more generalizable as it shows…
Machine learning techniques have led to broad adoption of a statistical model of computing. The statistical distributions natively available on quantum processors are a superset of those available classically. Harnessing this attribute has…
In this work, we explore in detail, the time evolution of Krylov complexity. We demonstrate, through analytical computations, that in finite many-body systems, while ramp and plateau are two generic features of Krylov complexity, the manner…
Quantum neural networks (QNNs) have been a promising framework in pursuing near-term quantum advantage in various fields, where many applications can be viewed as learning a quantum state that encodes useful data. As a quantum analog of…
We study operator spreading in many-body quantum systems by its potential to generate an informationally complete measurement record in quantum tomography. We adopt continuous weak measurement tomography for this purpose. We generate the…
We study thermalization in closed non-integrable quantum systems using the Krylov basis. We demonstrate that for thermalization to occur, the matrix representation of typical local operators in the Krylov basis should exhibit a specific…
Understanding the complexity of quantum many-body systems has been attracting much attention recently for its fundamental importance in characterizing complex quantum phases beyond the scope of quantum entanglement. Here, we investigate…