Practical limitations of the switching theorem for adiabatic state preparation

TL;DR

This paper investigates how modifications at the endpoints of Hamiltonian evolution can reduce errors in adiabatic quantum computation, but may require impractically long times to achieve the ideal asymptotic error scaling.

Contribution

It analyzes the effects of endpoint modifications on the transition from adiabatic to hyperadiabatic regimes in simple Hamiltonians, highlighting practical limitations.

Findings

Endpoint modifications can significantly reduce errors for long evolution times.

Such modifications may require excessively long times to reach the asymptotic regime.

Practical implementations face limitations due to the transition dynamics.

Abstract

The viability of adiabatic quantum computation depends on the slow evolution of the Hamiltonian. The adiabatic switching theorem provides an asymptotic series for error estimates in $1/T$, based on the lowest non-zero derivative of the Hamiltonian and its eigenvalues at the endpoints. Modifications at the endpoints in practical implementations can modify this scaling behavior, suggesting opportunities for error reduction by altering endpoint behavior while keeping intermediate evolution largely unchanged. Such modifications can significantly reduce errors for long evolution times, but they may also require exceedingly long timescales to reach the hyperadiabatic regime, limiting their practicality. This paper explores the transition between the adiabatic and hyperadiabatic regimes in simple low-dimensional Hamiltonians, highlighting the impact of modifications of the endpoints on approaching the asymptotic behavior described by the switching theorem.