Enhancement of quantum annealing via n-local catalysts

TL;DR

This paper demonstrates that n-local catalysts can significantly enhance quantum annealing by reopening energy gaps, improving efficiency, and reducing circuit complexity for solving NP-complete problems like MWIS.

Contribution

It introduces the use of n-local catalysts to improve gap scaling and efficiency in quantum annealing, providing analytical and circuit-based evidence of their advantages.

Findings

n-local catalysts exponentially improve gap scaling

They can replace direct tunneling in certain scenarios

Circuit implementation reduces depth and gate count

Abstract

The potential quantum speedup in solving optimization problems via adiabatic quantum annealing is often hindered by the closing of the energy gap during the anneal, especially when this gap scales exponentially with system size. In this work, we alleviate this bottleneck by demonstrating that for the NP-complete Maximum Weighted Independent Set (MWIS) problem, an informed choice of $n-$local catalysts (operators involving $n$ qubits) can re-open the gap during the annealing process. By analyzing first-order phase transitions in toy instances of the MWIS problem, we first identify direct-tunneling catalysts that effectively eliminate the transition and provide an analytical discussion on when the sign of the catalyst influences its impact. We then reveal that $n-$local catalysts exponentially improve gap scaling and in certain scenarios are as effective as direct tunnel coupling between two minima. Utilizing this understanding, we show that they also increase the efficiency of ground state preparation via adiabatic quantum annealing in random graphs and analytically demonstrate the necessity of their placement across unfrustrated loops in the graph for effective performance in MWIS problems. Additionally, using a circuit implementation of the $n$-local catalyst (requiring $2n$ nearest-neighbour gates), we demonstrate that both the circuit depth and the total number of gates required to solve the problem are reduced by several orders of magnitude when compared to the discrete-time version of traditional quantum annealing using local drivers. Our analysis suggests that non-local quantum fluctuations entangling multiple qubits as a catalyst are key to achieving the desired quantum advantage.