Related papers: Engineering Quantum Reservoirs through Krylov Comp…
With the exponentially faster computation for certain problems, quantum computing has garnered significant attention in recent years. Variational quantum algorithms are crucial methods to implement quantum computing, and an appropriate…
In closed quantum systems, Krylov complexity admits a geometric description; operator growth is equivalent to Hamiltonian flow in an emergent phase space whose structure is fixed by the Lanczos coefficients. We show that this picture…
Biological neural networks can perform complex computations to predict their environment, far above the limited predictive capabilities of individual neurons. While conventional approaches to understanding these computations often focus on…
Quantum reservoir computing (QRC) and quantum extreme learning machines (QELM) are two emerging approaches that have demonstrated their potential both in classical and quantum machine learning tasks. They exploit the quantumness of physical…
Quantum Reservoir Computing (QRC) uses quantum dynamics to efficiently process temporal data. In this work, we investigate a QRC framework based on two coupled Kerr nonlinear oscillators, a system well-suited for time-series prediction…
Realistic quantum devices are inherently open and often involve environments with memory. Here, we investigate quantum resource generation in two classes of random circuits, namely, memoryless open and memoryful open random circuits, and…
Quantum computing and neural networks show great promise for the future of information processing. In this paper we study a quantum reservoir computer (QRC), a framework harnessing quantum dynamics and designed for fast and efficient…
Kubernetes is a container management system that has many automated functionalities. Those functionalities are managed by configuring objects and resources in the control plane. Since most objects change their state depending on other…
We analyze the properties of Krylov state complexity in qubit dynamics, considering a single qubit and a qubit pair. A geometrical picture of the Krylov complexity is discussed for the single-qubit case, whereas it becomes non-trivial for…
Quantum reservoir computing is a class of quantum machine learning algorithms involving a reservoir of an echo state network based on a register of qubits, but the dependence of its memory capacity on the hyperparameters is still rather…
Heisenberg time evolution under a chaotic many-body Hamiltonian $H$ transforms an initially simple operator into an increasingly complex one, as it spreads over Hilbert space. Krylov complexity, or `K-complexity', quantifies this growth…
In this paper, we study the Krylov complexity ($K$) from the planar/inflationary patch of the de Sitter space using the two mode squeezed state formalism in the presence of an effective field having sound speed $c_s$. From our analysis, we…
Devices based on arrays of interconnected magnetic nano-rings with emergent magnetization dynamics have recently been proposed for use in reservoir computing applications, but for them to be computationally useful it must be possible to…
We investigate the effects of application of random time-shifts to the readouts of a reservoir computer in terms of both accuracy (training error) and performance (testing error.) For different choices of the reservoir parameters and…
Accumulating evidences show that the cerebral cortex is operating near a critical state featured by power-law size distribution of neural avalanche activities, yet evidence of this critical state in artificial neural networks mimicking the…
Reservoir Computing is an Unconventional Computation model to perform computation on various different substrates, such as recurrent neural networks or physical materials. The method takes a 'black-box' approach, training only the outputs…
This paper explores the problem of quantum measurement complexity. In computability theory, the complexity of a problem is determined by how long it takes an effective algorithm to solve it. This complexity may be compared to the difficulty…
Reservoir computing is a powerful framework for modeling dynamical systems due to its universality and computational efficiency. However, a major challenge is achieving a forecast with accurate long-time statistics, or climate, which is…
The growth of simple operators is essential for the emergence of chaotic dynamics and quantum thermalization. Recent studies have proposed different measures, including the out-of-time-order correlator and Krylov complexity. It is…
In contrast to entropy, which increases monotonically, the "complexity" or "interestingness" of closed systems seems intuitively to increase at first and then decrease as equilibrium is approached. For example, our universe lacked complex…