Implementing variational optimization on fault-tolerant quantum machines

Determine effective methods for implementing variational optimization on fault-tolerant quantum computers, addressing how such optimization should be carried out under fault-tolerant resource constraints.

Background

The paper argues that variational approaches remain relevant beyond NISQ, for example to prepare good initial states for non-variational subroutines like phase estimation. However, fault-tolerant execution introduces new constraints, such as fine-grained rotation synthesis potentially incurring high T-gate counts and slower logical clock rates that make shot economy crucial.

While techniques like error mitigation for compilation and algorithmic errors, amplitude amplification, and classical shadows may help, concrete best practices for fault-tolerant variational optimization remain unsettled and require further investigation.