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Chinni, Karthik

Publications and source records attributed to Chinni, Karthik.

4 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Scrambling and quantum chaos indicators from long-time properties of operator distributions

Scrambling is a key concept in the analysis of nonequilibrium properties of quantum many-body systems. Most studies focus on its characterization via out-of-time-ordered correlation (OTOC) functions, particularly through the early-time decay of the OTOC. However, scrambling is a complex process which involves operator spreading and operator entanglement, and a full characterization requires one to access more refined information on the operator dynamics at several timescales. In this work we analyze operator scrambling by expanding the target operator in a complete basis and studying the structure of the expansion coefficients treated as a coarse-grained probability distribution in the space of operators. Here we study different features of this distribution, such as its mean, variance, and participation ratio, for the Ising model with longitudinal and transverse fields, kicked collective spin models, and random circuit models. We show that the long-time properties of the operator distribution display common features across these cases and discuss how these properties can be used as a proxy for the onset of quantum chaos. Finally, we discuss the connection with OTOCs and analyze the cost of probing the operator distribution experimentally using these correlation functions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Trotter Errors from Dynamical Structural Instabilities of Floquet Maps in Quantum Simulation

We study the behavior of errors in the quantum simulation of spin systems with long-range multibody interactions resulting from the Trotter-Suzuki decomposition of the time-evolution operator. We identify a regime where the Floquet operator underlying the Trotter decomposition undergoes sharp changes even for small variations in the simulation step size. This results in a time evolution operator that is very different from the dynamics generated by the targeted Hamiltonian, which leads to a proliferation of errors in the quantum simulation. These regions of sharp change in the Floquet operator, referred to as structural instability regions, appear typically at intermediate Trotter step sizes and in the weakly interacting regime, and are thus complementary to recently revealed quantum chaotic regimes of the Trotterized evolution [L. M. Sieberer et al. npj Quantum Inf. 5, 78 (2019); M. Heyl, P. Hauke, and P. Zoller, Sci. Adv. 5, eaau8342 (2019)]. We characterize these structural instability regimes in p-spin models, transverse-field Ising models with all-to-all p-body interactions, and analytically predict their occurrence based on unitary perturbation theory. We further show that the effective Hamiltonian associated with the Trotter decomposition of the unitary time-evolution operator, when the Trotter step size is chosen to be in the structural instability region, is very different from the target Hamiltonian, which explains the large errors that can occur in the simulation in the regions of instability. These results have implications for the reliability of near-term gate-based quantum simulators, and reveal an important interplay between errors and the physical properties of the system being simulated.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗