Related papers: Quantum Dynamics in Krylov Space: Methods and Appl…
In the Wigner-Weyl phase space formulation of quantum mechanics, we analyse the problem of the spreading of an initial state or an initial operator under time evolution when described in terms of the Krylov basis. After constructing the…
Information scrambling refers to the phenomenon in which local quantum information in a many-body system becomes dispersed throughout the entire system under unitary evolution. It has been extensively studied in closed quantum systems,…
This work addresses how the growth of invariant operators is influenced by their underlying symmetry structure. For this purpose, we introduce the symmetry-resolved Krylov complexity, which captures the time evolution of each block into…
The spreading of quantum information in closed systems, often termed scrambling, is a hallmark of many-body quantum dynamics. In open systems, scrambling competes with noise, errors and decoherence. Here, we provide a universal framework…
The complexity of quantum states under dynamical evolution can be investigated by studying the spread with time of the state over a pre-defined basis. It is known that this complexity is minimised by choosing the Krylov basis, thus defining…
Krylov complexity has recently emerged as a new paradigm to characterize quantum chaos in many-body systems. However, which features of Krylov complexity are prerogative of quantum chaotic systems and how they relate to more standard…
The Krylov subspace methods, being one category of the most important classical numerical methods for linear algebra problems, can be much more powerful when generalised to quantum computing. However, quantum Krylov subspace algorithms are…
Identifying the real and imaginary parts of wave functions with coordinates and momenta, quantum evolution may be mapped onto a classical Hamiltonian system. In addition to the symplectic form, quantum mechanics also has a positive-definite…
Recently, Krylov complexity was proposed as a measure of complexity and chaoticity of quantum systems. We consider the stadium billiard as a typical example of the quantum mechanical system obtained by quantizing a classically chaotic…
Recent advances in quantum technologies and related experiments have created a need for highly accurate, versatile, and computationally efficient simulation techniques for the dynamics of open quantum systems. Long-lived correlation effects…
Quantum simulation of complex many-body systems beyond classical computational capabilities provides a promising route toward understanding novel quantum phases and their transitions. In particular, analog quantum simulators with global…
In this paper we study the notion of complexity under time evolution in chaotic quantum systems with holographic duals. Continuing on from our previous work, we turn our attention to the issue of Krylov complexity upon the insertion of a…
We shortly review the progress in the domain of deterministic chaos for quantum dynamical systems. With the appropriately extended definition of quantum Lyapunov exponent we analyze various quantum dynamical maps. It is argued that, within…
We investigate the phase transitions from chaotic to nonchaotic dynamics in a quantum spin chain with a local non-Hermitian disorder, which can be realized with a Rydberg atom array setting. As the disorder strength increases, the emergence…
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 computers provide new avenues to access ground and excited state properties of systems otherwise difficult to simulate on classical hardware. New approaches using subspaces generated by real-time evolution have shown efficiency in…
Krylov complexity (K-complexity) is a measure of quantum state complexity that minimizes wavefunction spreading across all the possible bases. It serves as a key indicator of operator growth and quantum chaos. In this work, K-complexity and…
The ability to harness the dynamics of quantum information and entanglement is necessary for the development of quantum technologies and the study of complex quantum systems. On the theoretical side the dynamics of quantum information is a…
This paper is devoted to the description of the evolution of states of quantum many-particle systems within the framework of a one-particle density operator, which enables to construct the kinetic equations in scaling limits in the presence…
We propose a measure of quantum state complexity defined by minimizing the spread of the wave-function over all choices of basis. Our measure is controlled by the "survival amplitude" for a state to remain unchanged, and can be efficiently…