Spectral Gap of Davies Generator Scales with Qubit Count

Researchers have discovered a surprising stability in the rate of thermalization for quantum systems as their size increases. Joao Basso, Thiago Bergamaschi, Lin Lin, Michael Ragone, and Kevin D. Stubbs report that for inverse temperatures below 2, the spectral gap remains constant as the number of qubits increases. This challenges the expectation that increasing qubits would always complicate a system and slow down this process. The team also found that above inverse temperatures of 2, the spectral gap decreases proportionally to 1 divided by the number of qubits. This slowdown is linked to the “total magnetization order parameter,” suggesting a fundamental connection between symmetry and this behavior.

The Davies generator spectral gap at noncritical temperatures exhibits behavior as complexity increases. For inverse temperatures below 2, the gap is constant, meaning it does not change regardless of the number of qubits added. Above inverse temperatures of 2, the gap decreases proportionally to 1 divided by the number of qubits, establishing a quantifiable link between system size and dynamic properties.

The behavior of quantum systems exhibits unexpected stability linked to underlying symmetries, according to research into the mean-field Heisenberg ferromagnet. Their approach utilizes auxiliary generators to bound dissipation and a decomposition of observables into spherical tensor operators to reveal monotonicity. This research provides insight into the relationship between symmetry and the thermalization of quantum systems.