Diagonal Catalysts in Quantum Adiabatic Optimization

TL;DR

This paper introduces a diagonal catalyst protocol in quantum adiabatic optimization that can remove first-order phase transitions, improving efficiency when biasing towards correlated low-energy states, but may worsen performance otherwise.

Contribution

It proposes a novel diagonal catalyst method for quantum adiabatic optimization that can eliminate phase transitions and analyzes its effectiveness and limitations.

Findings

Diagonal catalyst removes first-order phase transitions in certain problems.

Biasing towards states correlated with the ground state improves success.

Biasing towards distant low-energy states can worsen performance.

Abstract

We propose a protocol for quantum adiabatic optimization, whereby an intermediary Hamiltonian that is diagonal in the computational basis is turned on and off during the interpolation. This `diagonal catalyst' serves to bias the energy landscape towards a given spin configuration, and we show how this can remove the first-order phase transition present in the standard protocol for the ferromagnetic $p$-spin and the Weak-Strong Cluster problems. The success of the protocol also makes clear how it can fail: biasing the energy landscape towards a state only helps in finding the ground state if the Hamming distance from the ground state and the energy of the biased state are correlated. We present examples where biasing towards low energy states that are nonetheless very far in Hamming distance from the ground state can severely worsen the efficiency of the algorithm compared to the standard protocol. Our results for the diagonal catalyst protocol are analogous to results exhibited by adiabatic reverse annealing, so our conclusions should apply to that protocol as well.