相关论文: Engineering Quantum Reservoirs through Krylov Comp…
We demonstrate that time-evolved operators can construct a Krylov space to compute Operator complexity and introduce Krylov observability as a measure of effective phase space dimension in quantum systems. We test Krylov observability in…
Quantum reservoir computing algorithms recently emerged as a standout approach in the development of successful methods for the NISQ era, because of its superb performance and compatibility with current quantum devices. By harnessing the…
Krylov complexity is a novel measure of operator complexity that exhibits universal behavior and bounds a large class of other measures. In this letter, we generalize Krylov complexity from a closed system to an open system coupled to a…
This paper investigates the notion of Krylov complexity, a measure of operator growth, within the framework of 1-matrix quantum mechanics (1-MQM). Krylov complexity quantifies how an operator evolves over time by expanding it in a series of…
Krylov complexity provides a powerful framework for characterizing the dynamical evolution of quantum systems through the spreading of states in Krylov space. The motivation for this is rooted in the optimality of the Krylov basis for the…
Quantum reservoir computing is a computing approach which aims at utilising the complexity and high-dimensionality of small quantum systems, together with the fast trainability of reservoir computing, in order to solve complex tasks. The…
Reservoir computing is a machine learning framework that uses artificial or physical dissipative dynamics to predict time-series data using nonlinearity and memory properties of dynamical systems. Quantum systems are considered as promising…
Quantum complexity, suitably defined, has been suggested as an important probe of late-time dynamics of black holes, particularly in the context of AdS/CFT. A notion of quantum complexity can be effectively captured by quantifying the…
Krylov complexity is a novel approach to study how an operator spreads over a specific basis. Recently, it has been stated that this quantity has a long-time saturation that depends on the amount of chaos in the system. Since this quantity…
Reservoir computing with optical devices offers an energy-efficient approach for time-series forecasting. Quantum dot lasers with feedback are modelled in this paper to explore the extent to which increased complexity in the charge carrier…
In this work, we collect data from runs of Krylov subspace methods and pipelined Krylov algorithms in an effort to understand and model the impact of machine noise and other sources of variability on performance. We find large variability…
Quantum reservoir computing is a machine learning framework that offers ease of training compared to other quantum neural networks, as it does not rely on gradient-based optimization. Learning is performed in a single step on the output…
In this work, we propose a quantum-mechanically measurable basis for the computation of spread complexity. Current literature focuses on computing different powers of the Hamiltonian to construct a basis for the Krylov state space and the…
Krylov complexity is a measure of operator growth in quantum systems, based on the number of orthogonal basis vectors needed to approximate the time evolution of an operator. In this paper, we study the Krylov complexity of a…
We introduce and review a new complexity measure, called `Krylov complexity', which takes its origins in the field of quantum-chaotic dynamics, serving as a canonical measure of operator growth and spreading. Krylov complexity, underpinned…
We investigate the relationship between Krylov complexity and operator quantum speed limits (OQSLs) of the complexity operator and level repulsion in random/integrable matrices and many-body systems. An enhanced level-repulsion corresponds…
Quantum reservoir computing (QRC) is an emerging framework for near-term quantum machine learning that offers in-memory processing, platform versatility across analogue and digital systems, and avoids typical trainability challenges such as…
This work provides a nonasymptotic error analysis of quantum Krylov algorithms based on real-time evolutions, subject to generic errors in the outputs of the quantum circuits. We prove upper and lower bounds on the resulting ground state…
Quantum reservoir computing (QRC) harnesses driven quantum dynamics for time-series processing, yet the mechanisms behind the differing performance levels across its many implementations remain unclear. We show that apparently unrelated…
Reservoir computing is a framework which is primarily used for temporal information processing, using the intrinsic dynamics of an underlying physical system. The framework, in a quantum setup, is implemented using ergodic dynamics…