A dissipative environment may improve the quantum annealing performances of the ferromagnetic p-spin model

TL;DR

This study shows that a carefully engineered dissipative environment can enhance quantum annealing efficiency in the ferromagnetic p-spin model, especially at intermediate coupling and low temperatures, challenging the notion that dissipation is always detrimental.

Contribution

It demonstrates that dissipation can improve quantum annealing performance in the ferromagnetic p-spin model, revealing a potential method to optimize quantum algorithms via environment engineering.

Findings

Dissipative environment can speed up annealing at intermediate coupling.

Performance improvement persists even at zero temperature.

Enhancement is due to correlated spin-bath states, not thermal fluctuations.

Abstract

We investigate the quantum annealing of the ferromagnetic $ p $-spin model in a dissipative environment ($ p = 5 $ and $ p = 7 $). This model, in the large $ p $ limit, codifies the Grover's algorithm for searching in an unsorted database. The dissipative environment is described by a phonon bath in thermal equilibrium at finite temperature. The dynamics is studied in the framework of a Lindblad master equation for the reduced density matrix describing only the spins. Exploiting the symmetries of our model Hamiltonian, we can describe many spins and extrapolate expected trends for large $ N $, and $ p $. While at weak system bath coupling the dissipative environment has detrimental effects on the annealing results, we show that in the intermediate coupling regime, the phonon bath seems to speed up the annealing at low temperatures. This improvement in the performance is likely not due to thermal fluctuation but rather arises from a correlated spin-bath state and persists even at zero temperature. This result may pave the way to a new scenario in which, by appropriately engineering the system-bath coupling, one may optimize quantum annealing performances below either the purely quantum or classical limit.