Necessity of phase-transition crossing for improved mixing in complex systems

Determine whether the adiabatically dressed quantum‑enhanced Markov chain Monte Carlo protocol, which uses a time‑symmetric transverse‑field ramp to generate symmetric quantum proposals, can achieve the improved spectral‑gap scaling observed in the one‑dimensional Ising chain without crossing a quantum phase transition when applied to more complex classical spin systems in which efficient mixing requires non‑local update proposals.

Background

In the one‑dimensional Ising model, the authors show that an adiabatically dressed quantum proposal can improve the Markov chain’s spectral gap and that this improvement can be achieved without crossing the quantum phase transition, owing to the locality of effective proposals.

For more complex systems—such as models where local updates are insufficient and efficient mixing requires non‑local moves—it is uncertain whether the same improvement without crossing a phase transition can be obtained with the adiabatically dressed protocol. Clarifying this would determine whether the mechanism that avoids phase-transition crossing in the Ising case extends to broader classes of problems.