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.

arXiv comment20 pages, 4 figures

References in corpus (36)

• Quantum Computing in the NISQ era and beyond
• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Quantum Machine Learning
• A variational eigenvalue solver on a quantum processor
• Quantum Simulation
• Probing many-body dynamics on a 51-atom quantum simulator
• Simulated Quantum Computation of Molecular Energies
• Observation of a Many-Body Dynamical Phase Transition with a 53-Qubit Quantum Simulator
• Quantum Phases of Matter on a 256-Atom Programmable Quantum Simulator
• Floquet Time Crystals
• Quantum Time Crystals
• Real-time dynamics of lattice gauge theories with a few-qubit quantum computer
• Programmable quantum simulation of 2D antiferromagnets with hundreds of Rydberg atoms
• Discrete time crystals: rigidity, criticality, and realizations
• Toward the first quantum simulation with quantum speedup
• A Theory of Trotter Error
• Chaos and complexity by design
• Quantum-Classical Computation of Schwinger Model Dynamics using Quantum Computers
• Dynamical Quantum Phase Transitions in Spin Chains with Long-Range Interactions: Merging different concepts of non-equilibrium criticality
• Floquet time crystal in the Lipkin-Meshkov-Glick model
• Does scrambling equal chaos?
• Quantum localization bounds Trotter errors in digital quantum simulation
• Energy gaps in quantum first-order mean-field-like transitions: The problems that quantum annealing cannot solve
• Digital Quantum Simulation, Trotter Errors, and Quantum Chaos of the Kicked Top
• Excited-state quantum phase transitions in many-body systems with infinite-range interaction: Localization, dynamics, and bifurcation
• Curie-Weiss magnet: a simple model of phase transition
• On quantum mean-field models and their quantum annealing
• Quantum ergodicity and entanglement in kicked coupled-tops
• Quantum phase transitions in fully connected spin models: an entanglement perspective
• Saddle-point scrambling without thermalisation
• Quantum annealing correction at finite temperature: ferromagnetic $p$-spin models
• Nonlinear dynamics and quantum chaos of a family of kicked $p$-spin models
• Simulation of complex dynamics of mean-field $p$-spin models using measurement-based quantum feedback control
• Quantifying the sensitivity to errors in analog quantum simulation
• 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

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• Macroproperties vs. Microstates in the Classical Simulation of Critical Phenomena in Quench Dynamics of 1D Ising Models
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• 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