Related papers: Exploring quantum ergodicity of unitary evolution …
We introduce the concept of ergodicity and explore its deviation caused by quantum scars in an isolated quantum system, employing a pedagogical approach based on a toy model. Quantum scars, originally identified as traces of classically…
The understanding of how classical dynamics can emerge in closed quantum systems is a problem of fundamental importance. Remarkably, while classical behavior usually arises from coupling to thermal fluctuations or random spectral noise, it…
Control over the quantum dynamics of chaotic kicked rotor systems is demonstrated. Specifically, control over a number of quantum coherent phenomena is achieved by a simple modification of the kicking field. These include the enhancement of…
The separation of the Schr\"{o}dinger equation into a Markovian and an interference term provides a new insight in the quantum dynamics of classically chaotic systems. The competition between these two terms determines the localized or…
Recent work highlighted the importance of higher-order correlations in quantum dynamics for a deeper understanding of quantum chaos and thermalization. The full Eigenstate Thermalization Hypothesis, the framework encompassing correlations,…
Quantum annealers play a major role in the ongoing development of quantum information processing and in the advent of quantum technologies. Their functioning is underpinned by the many-body adiabatic evolution connecting the ground state of…
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…
We propose a class of randomized quantum Krylov diagonalization (rQKD) algorithms capable of solving the eigenstate estimation problem with modest quantum resource requirements. Compared to previous real-time evolution quantum Krylov…
In this work we study the relationship between quantum random walks on graphs and Krylov/spread complexity. We show that the latter's definition naturally emerges through a canonical method of reducing a graph to a chain, on which we can…
We develop a geometric approach to operator growth and Krylov complexity in many-body quantum systems governed by symmetries. We start by showing a direct link between a unitary evolution with the Liouvillian and the displacement operator…
This work aims at giving Trotter errors in digital quantum simulation (DQS) of collective spin systems an interpretation in terms of quantum chaos of the kicked top. In particular, for DQS of such systems, regular dynamics of the kicked top…
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…
Statistical mechanics is founded on the assumption that all accessible configurations of a system are equally likely. This requires dynamics that explore all states over time, known as ergodic dynamics. In isolated quantum systems, however,…
Krylov methods have reappeared recently, connecting physically sensible notions of complexity with quantum chaos and quantum gravity. In these developments, the Hamiltonian and the Liouvillian are tridiagonalized so that…
While classical chaos has been successfully characterized with consistent theories and intuitive techniques, such as with the use of Lyapunov exponents, quantum chaos is still poorly understood, as well as its relation with multi-partite…
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…
Using the fact that any linear representation of a group can be embedded into permutations, we propose a constructive description of quantum behavior that provides, in particular, a natural explanation of the appearance of complex numbers…
Weak ergodicity breaking, particularly through quantum many-body scars (QMBS), has become a significant focus in many-body physics. Krylov state complexity quantifies the spread of quantum states within the Krylov basis and serves as a…
Krylov complexity has recently been proposed as a quantum probe of chaos. The Krylov exponent characterising the exponential growth of Krylov complexity is conjectured to upper-bound the Lyapunov exponent. We compute the Krylov and the…
Krylov space methods provide an efficient framework for analyzing the dynamical aspects of quantum systems, with tridiagonal matrices playing a key role. Despite their importance, the behavior of such matrices from chaotic to integrable…