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There is great interest in using near-term quantum computers to simulate and study foundational problems in quantum mechanics and quantum information science, such as the scrambling measured by an out-of-time-ordered correlator (OTOC). Here…

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…

Mathematical Software · Computer Science 2021-03-24 Hannah Morgan , Patrick Sanan , Matthew G. Knepley , Richard Tran Mills

We investigate the dynamics of quantum scrambling, characterized by the out-of-time ordered correlators (OTOCs), in a non-Hermitian quantum kicked rotor subjected to quasi-periodical modulation in kicking potential. Quasi-periodic…

Quantum Physics · Physics 2024-01-23 Liang Huo , Han Ke , Wen-Lei Zhao

We study how probes of quantum scrambling dynamics respond to two kinds of imperfections -- unequal forward and backward evolutions and decoherence -- in a solvable Brownian circuit model. We calculate a ``renormalized'' out-of-time-order…

Quantum Physics · Physics 2025-06-05 Nadie Yiluo LiTenn , Tianci Zhou , Brian Swingle

When a solution to an abstract inverse linear problem on Hilbert space is approximable by finite linear combinations of vectors from the cyclic subspace associated with the datum and with the linear operator of the problem, the solution is…

Functional Analysis · Mathematics 2021-03-01 Noe Angelo Caruso , Alessandro Michelangeli

Flexible Krylov methods are a common standpoint for inverse problems. In particular, they are used to address the challenges associated with explicit variational regularization when it goes beyond the two-norm, for example involving an…

Numerical Analysis · Mathematics 2025-10-22 Malena Sabaté Landman

Despite the rapid development of quantum science and technology, errors are inevitable and play a crucial role in quantum simulation and quantum computation. In quantum chaotic systems, coherent errors arising from imperfect Hamiltonian…

Quantum Physics · Physics 2026-01-09 Zeyu Liu , Pengfei Zhang

Classical quasi-integrable systems are known to have Lyapunov times much shorter than their ergodicity time -- the most clear example being the Solar System -- but the situation for their quantum counterparts is less well understood. As a…

Quantum Physics · Physics 2020-09-02 Tomer Goldfriend , Jorge Kurchan

Out-of-Time-Ordered Commutators (OTOCs), representing a key diagnostic for scrambling as a facet of short-time quantum chaos, have attracted wide-ranging interest, from many-body physics to quantum gravity. By means of a suitable form of…

Chaotic Dynamics · Physics 2025-12-24 Fabian Haneder , Gerrit Caspari , Juan Diego Urbina , Klaus Richter

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 Physics · Physics 2024-09-04 William Kirby

How fast quantum information scrambles such that it becomes inaccessible by local probes turns out to be central to various fields. Motivated by recent works on spin systems with nonlocal interactions, we study information scrambling in…

Quantum Physics · Physics 2023-05-24 Darvin Wanisch , Juan Diego Arias Espinoza , Stephan Fritzsche

Electromigration (EM) induced stress evolution is a major reliability challenge in nanometer-scale VLSI interconnects. Accurate EM analysis requires solving stress-governing partial differential equations over large interconnect trees,…

Hardware Architecture · Computer Science 2026-03-27 Sheldon X. -D. Tan , Haotian Lu

Solving short and long time dynamics of closed quantum many-body systems is one of the main challenges of both atomic and condensed matter physics. For locally interacting closed systems, the dynamics of local observables can always be…

Quantum Physics · Physics 2025-11-20 Nicolas Loizeau , Berislav Buča , Dries Sels

This paper introduces new solvers for the computation of low-rank approximate solutions to large-scale linear problems, with a particular focus on the regularization of linear inverse problems. Although Krylov methods incorporating explicit…

Numerical Analysis · Mathematics 2019-11-05 Silvia Gazzola , Chang Meng , James Nagy

We apply the recently proposed Sample-based Krylov Quantum Diagonalization (SKQD) method to lattice gauge theories, using the Schwinger model with a $\theta$-term as a benchmark. SKQD approximates the ground state of a Hamiltonian,…

In this paper, we investigate the dynamics of a non-Hermitian SSH model that arises out of the no-click limit of a monitored SSH model in the Krylov space. We find that the saturation timescale of the complexity associated with the spread…

Quantum Physics · Physics 2025-07-22 Nilachal Chakrabarti , Neha Nirbhan , Arpan Bhattacharyya

Strongly interacting quantum many-body systems are expected to thermalize, however, some evade thermalization due to symmetries. Quantum synchronization provides one such example of ergodicity breaking, but previous studies have focused on…

Disordered Systems and Neural Networks · Physics 2026-02-13 Nicolas Loizeau , Berislav Buča

We propose a simple complexity indicator of classical Liouvillian dynamics, namely the separability entropy, which determines the logarithm of an effective number of terms in a Schmidt decomposition of phase space density with respect to an…

Chaotic Dynamics · Physics 2015-05-19 Tomaz Prosen

Krylov complexity and Nielsen complexity are successful approaches to quantifying quantum evolution complexity that have been actively pursued without much contact between the two lines of research. The two quantities are motivated by…

Quantum Physics · Physics 2024-04-19 Ben Craps , Oleg Evnin , Gabriele Pascuzzi

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…

High Energy Physics - Theory · Physics 2022-09-14 Vijay Balasubramanian , Pawel Caputa , Javier Magan , Qingyue Wu