This paper shows that many quantum systems where every particle can interact with many others — so-called all-to-all k-local systems — settle to thermal equilibrium at a rate that does not slow down as the system grows, provided the temperature is high enough. In plain terms, the authors prove that a standard model of thermalization in open quantum systems has a spectral gap that stays bounded away from zero even as the number of particles increases. A spectral gap here measures how fast the system forgets its initial state and approaches the thermal or Gibbs state.

The authors study n quantum d-level particles (qudits) with terms in the energy operator (Hamiltonian) that each act on at most k particles. They assume the interaction degree (how many partners each particle couples to) and a suitable measure of interaction strength are bounded so these quantities do not grow with n. They analyze a specific continuous-time thermalization model (a Lindbladian generator introduced in earlier work) and prove that this generator has a system-size independent gap whenever the inverse temperature β is below a threshold β_c. Concretely, the threshold scales like β_c = [c · q · k · d · J]^{-1} for a universal constant c, where q is the local dimension, k the locality, d the degree, and J the interaction strength. At high temperatures (small β) the bound applies.

Why this matters: a size-independent spectral gap implies efficient ways to approximate thermal quantities on a quantum computer. The paper shows that, under the same high-temperature condition, one can estimate the partition function (a normalizing constant that encodes thermodynamic information) and global expectation values to fixed accuracy in time polynomial in n and 1/ε. In the authors’ analysis the time to get within ε in trace distance satisfies t_mix(ε) = O(n + log(1/ε)), so the result yields an efficient state-preparation route by simulating the Lindbladian dynamics. For the common case of two-level systems with pairwise interactions, the threshold β_c becomes a universal constant; the authors note this is believed to be essentially optimal given known hardness results for related counting problems.