Numerical study of computational cost of maintaining adiabaticity for long paths

TL;DR

This paper numerically investigates how the computational cost of maintaining adiabaticity scales with path length, confirming that for simple systems, the key quantity grows roughly as L log L, indicating superlinear scaling.

Contribution

It demonstrates through numerical analysis that the dimensionless quantity Q_D scales approximately as L log L for simple Hamiltonian systems, supporting the conjecture of superlinear scaling.

Findings

Q_D grows approximately as L log L for studied systems

Supports the conjecture of superlinear scaling of computational cost

Numerical evidence for the behavior of adiabaticity maintenance

Abstract

Recent work argued that the scaling of a dimensionless quantity $Q_D$ with path length is a better proxy for quantifying the scaling of the computational cost of maintaining adiabaticity than the timescale. It also conjectured that generically the scaling will be superlinear (although special cases exist in which it is linear). The quantity $Q_D$ depends only on the properties of ground states along the Hamiltonian path and the rate at which the path is followed. In this paper, we demonstrate that this conjecture holds for simple Hamiltonian systems that can be studied numerically. In particular, the systems studied exhibit the behavior that $Q_D$ grows approximately as $L \log L$ where $L$ is the path length when the threshold error is fixed.