Trotter errors from dynamical structural instabilities of Floquet maps in quantum simulation

Abstract

We study the behavior of errors in the quantum simulation of spin systems with long-range multi-body 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 (Sieberer et al., npj Quantum Information 5, 1 (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.

20 pages, 4 figures

References in corpus (10)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Probing many-body dynamics on a 51-atom quantum simulator
• Simulated Quantum Computation of Molecular Energies
• Energy gaps in quantum first-order mean-field-like transitions: The problems that quantum annealing cannot solve
• On quantum mean-field models and their quantum annealing
• Quantum phase transitions in fully connected spin models: an entanglement perspective
• Quantum annealing correction at finite temperature: ferromagnetic $p$-spin models
• Nonlinear dynamics and quantum chaos of a family of kicked $p$-spin models
• An efficient quantum algorithm for generative machine learning
• Route to Extend the Lifetime of a Discrete Time Crystal in a Finite Spin Chain Without Disorder

Cited by in corpus (14)

• Probing confinement in a ${\mathbb{Z}}_2$ lattice gauge theory on a quantum computer
• Quantum Simulation of Z2 Lattice Gauge theory with minimal resources
• Floquet time crystals in driven spin systems with all-to-all $p$-body interactions
• Krylov complexity and Trotter transitions in unitary circuit dynamics
• State-dependent Trotter Limits and their approximations
• Probing Dynamical Sensitivity of a Non-KAM System Through Out-of-Time-Order Correlators
• Generalized hydrodynamics of integrable quantum circuits
• Entangled states from sparsely coupled spins for metrology with neutral atoms
• Macroproperties vs. Microstates in the Classical Simulation of Critical Phenomena in Quench Dynamics of 1D Ising Models
• Robustness of near-thermal dynamics on digital quantum computers
• Quantum simulation of fermionic non-Abelian lattice gauge theories in $(2+1)$D with built-in gauge protection
• Information acquisition, scrambling, and sensitivity to errors in quantum chaos
• Trotter transition in BCS pairing dynamics
• Quantum Chaos and Universal Trotterisation Behaviours in Digital Quantum Simulations