# Local-in-time error in variational quantum dynamics

## TL;DR

This paper revisits the McLachlan principle for variational quantum dynamics, providing exact local-in-time error expressions and demonstrating their application to improve adaptive schemes in quantum simulations.

## Contribution

It introduces exact formulas for local-in-time errors in variational quantum solutions and discusses their use in developing adaptive, cost-efficient quantum dynamical algorithms.

## Key findings

- Exact expressions for local-in-time error derived
- Application to mean-field and adiabatic quantum dynamics
- Framework for adaptive variational scheme development

## Abstract

The McLachlan "minimum-distance" principle for optimizing approximate solutions of the time-dependent Schrodinger equation is revisited, with a focus on the local-in-time error accompanying the variational solutions. Simple, exact expressions are provided for this error, which are then evaluated in illustrative cases, notably the widely used mean-field approach and the adiabatic quantum molecular dynamics. These findings pave the way for the rigorous development of adaptive schemes that re-size on-the-fly the underlying variational manifold and thus optimize the overall computational cost of a quantum dynamical simulation.