相关论文: Quantum complexity and localization in random and …

We calculate the frame potential for Brownian clusters of $N$ spins or fermions with time-dependent all-to-all interactions. In both cases the problem can be mapped to an effective statistical mechanics problem which we study using a path…

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 establish a direct connection between spread complexity and quantum circuit complexity by demonstrating that spread complexity emerges as a limiting case of a circuit complexity framework built from two fundamental operations:…

We study information scrambling -- a spread of initially localized quantum information into the system's many degree of freedom -- in discrete-time quantum walks. We consider out-of-time-ordered correlators (OTOC) and K-complexity as a…

We study Krylov complexity in various models of quantum field theory: free massive bosons and fermions on flat space and on spheres, holographic models, and lattice models with the UV-cutoff. In certain cases we find asymptotic behavior of…

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…

We investigate how quantum localization encodes the hierarchical stickiness that governs transport in mixed classical phase spaces. Using the periodically driven kicked top, we show that the participation ratio (PR) of coherent states in…

We show that quantum circuit complexity for the unitary time evolution operator of any time-independent Hamiltonian is bounded by linear growth at early times, independent of any choices of the fundamental gates or cost metric. Deviations…

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…

We study the quantum complexity of time evolution in large-$N$ chaotic systems, with the SYK model as our main example. This complexity is expected to increase linearly for exponential time prior to saturating at its maximum value, and is…

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…

This paper is devoted to the study of the evolution of holographic complexity after a local perturbation of the system at finite temperature. We calculate the complexity using both the complexity=action(CA) and the complexity=volume(CA)…

We investigate circuit complexity of unitaries generated by time evolution of randomly chosen strongly interacting Hamiltonians in finite dimensional Hilbert spaces. Specifically, we focus on two ensembles of random generators -- the so…

The concept of quantum complexity has far-reaching implications spanning theoretical computer science, quantum many-body physics, and high energy physics. The quantum complexity of a unitary transformation or quantum state is defined as the…

We investigate the complexity of states and operators evolved with the modular Hamiltonian by using the Krylov basis. In the first part, we formulate the problem for states and analyse different examples, including quantum mechanics,…

Randomness generation through quantum-chaotic evolution underpins foundational questions in statistical mechanics and applications across quantum information science, including benchmarking, tomography, metrology, and demonstrations of…

Thermalization of chaotic quantum many-body systems under unitary time evolution is related to the growth in complexity of initially simple Heisenberg operators. Operator growth is a manifestation of information scrambling and can be…

Building upon recent research in spin systems with non-local interactions, this study investigates operator growth using the Krylov complexity in different non-local versions of the Ising model. We find that the non-locality results in a…

In this work, we investigate the impact of conserved charges on the dynamics of spread complexity of quantum states. Building on the notion of symmetry-resolved Krylov complexity [1], we extend the framework to general quantum states and…

We consider the statistics of the results of a measurement of the spreading operator in the Krylov basis generated by the Hamiltonian of a quantum system starting from a specified initial pure state. We first obtain the probability…