Digital Quantum Simulation, Learning of the Floquet Hamiltonian, and Quantum Chaos of the Kicked Top
arXiv:2208.13837 · doi:10.1088/1751-8121/ac8087
Abstract
The kicked top is one of the paradigmatic models in the study of quantum chaos~[F.~Haake et al., \emph{Quantum Signatures of Chaos (Springer Series in Synergetics vol 54)} (2018)]. Recently it has been shown that the onset of quantum chaos in the kicked top can be related to the proliferation of Trotter errors in digital quantum simulation (DQS) of collective spin systems. Specifically, the proliferation of Trotter errors becomes manifest in expectation values of few-body observables strongly deviating from the target dynamics above a critical Trotter step, where the spectral statistics of the Floquet operator of the kicked top can be predicted by random matrix theory. In this work, we study these phenomena in the framework of Hamiltonian learning (HL). We show how a recently developed Hamiltonian learning protocol can be employed to reconstruct the generator of the stroboscopic dynamics, i.e., the Floquet Hamiltonian, of the kicked top. We further show how the proliferation of Trotter errors is revealed by HL as the transition to a regime in which the dynamics cannot be approximately described by a low-order truncation of the Floquet-Magnus expansion. This opens up new experimental possibilities for the analysis of Trotter errors on the level of the generator of the implemented dynamics, that can be generalized to the DQS of quantum many-body systems in a scalable way. This paper is in memory of our colleague and friend Fritz Haake.
References in corpus (56)
- Random Matrix Theories in Quantum Physics: Common Concepts
- Localization of interacting fermions at high temperature
- The Magnus expansion and some of its applications
- An Open-System Quantum Simulator with Trapped Ions
- The distribution of the ratio of consecutive level spacings in random matrix ensembles
- Engineered 2D Ising interactions on a trapped-ion quantum simulator with hundreds of spins
- Programmable Quantum Simulations of Spin Systems with Trapped Ions
- Real-time dynamics of lattice gauge theories with a few-qubit quantum computer
- Scalable Quantum Simulation of Molecular Energies
- Universal digital quantum simulation with trapped ions
- Measuring out-of-time-order correlations and multiple quantum spectra in a trapped ion quantum magnet
- Equilibrium states of generic quantum systems subject to periodic driving
- Long-time behavior of periodically driven isolated interacting lattice systems
- A Theory of Trotter Error
- Digitized adiabatic quantum computing with a superconducting circuit
- Floquet-Magnus Theory and Generic Transient Dynamics in Periodically Driven Many-Body Quantum Systems
- Exponentially slow heating in periodically driven many-body systems
- Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems
- Effective Hamiltonians, prethermalization and slow energy absorption in periodically driven many-body systems
- Digital quantum simulation of fermionic models with a superconducting circuit
- Quantum certification and benchmarking
- Ergodic dynamics and thermalization in an isolated quantum system
- Gate count estimates for performing quantum chemistry on small quantum computers
- Diagrammatic method of integration over the unitary group, with applications to quantum transport in mesoscopic systems
- Rényi Entropies from Random Quenches in Atomic Hubbard and Spin Models
- Does a single eigenstate encode the full Hamiltonian?
- Digital quantum simulation of spin models with circuit quantum electrodynamics
- Random Matrices and Chaos in Nuclear Physics: Nuclear Reactions
- Experimentally simulating the dynamics of quantum light and matter at ultrastrong coupling
- Nearly optimal lattice simulation by product formulas
- Learning a local Hamiltonian from local measurements
- Higher Order Decompositions of Ordered Operator Exponentials
- Determining a local Hamiltonian from a single eigenstate
- Sample-efficient learning of quantum many-body systems
- Quantum localization bounds Trotter errors in digital quantum simulation
- Quantum Phase Transition of Ground-state Entanglement in a Heisenberg Spin Chain Simulated in an NMR Quantum Computer
- Heating and many-body resonances in a periodically driven two-band system
- Unitary -designs via random quenches in atomic Hubbard and Spin models: Application to the measurement of Rényi entropies
- Probing scrambling using statistical correlations between randomized measurements
- Digital Quantum Simulation, Trotter Errors, and Quantum Chaos of the Kicked Top
- Quantum-enhanced sensing using non-classical spin states of a highly magnetic atom
- Computational inverse method for constructing spaces of quantum models from wave functions
- Theoretical and Experimental Perspectives of Quantum Verification
- Sufficient conditions for the convergence of the Magnus expansion
- Asymptotic Prethermalization in Periodically Driven Classical Spin Chains
- Hamiltonian Tomography via Quantum Quench
- Convergence of the Magnus series
- Realization of a Strongly Interacting Fermi Gas of Dipolar Atoms
- Digital Quantum Simulation with Rydberg Atoms
- Exponentially Slow Heating in Short and Long-range Interacting Floquet Systems
- Absence of dynamical localization in interacting driven systems
- Floquet Thermalization: Symmetries and Random Matrix Ensembles
- Learning the dynamics of open quantum systems from their steady states
- NMR studies of quantum chaos in a two-qubit kicked top
- Exploring quantum chaos with a single nuclear spin
- Efficient Product Formulas for Commutators and Applications to Quantum Simulation