Nonadiabatic Self-Healing of Trotter Errors in Digitized Counterdiabatic Dynamics

TL;DR

This paper demonstrates that self-healing of Trotter errors in digitized quantum dynamics persists at finite times when nonadiabatic errors are compensated, enhancing high-fidelity quantum state preparation.

Contribution

It reveals the finite-time self-healing mechanism in digitized counterdiabatic protocols, extending understanding beyond the long-time adiabatic regime.

Findings

Self-healing persists at finite evolution times with error compensation.

Analytic upper bounds on Trotter errors derived from Fourier analysis.

Guidance for high-fidelity quantum state preparation on gate-based processors.

Abstract

Trotter errors in digitized quantum dynamics arise from approximating time-ordered evolution under noncommuting Hamiltonian terms with a product formula. In the adiabatic regime, such errors are known to exhibit long-time self-healing [Phys. Rev. Lett. \textbf{131}, 060602 (2023)], where discretization effects are effectively suppressed. Here we show that self-healing persists at finite evolution times once nonadiabatic errors induced by finite-speed ramps are compensated. Using counterdiabatic driving to cancel diabatic transitions and isolate discretization effects, we study both noninteracting and interacting spin models and characterize the finite-time scaling with the Trotter steps and the total evolution time. In the instantaneous eigenbasis of the driven Hamiltonian, the leading digital error maps to an effective harmonic perturbation whose dominant Fourier component yields an analytic upper bound on the finite-time Trotter error and reveals the phase-cancellation mechanism underlying self-healing. Our results establish finite-time self-healing as a generic feature of digitized counterdiabatic protocols, clarify its mechanism beyond the long-time adiabatic limit, and provide practical guidance for high-fidelity state preparation on gate-based quantum processors.