Scalable stochastic classification of quantum states of matter
Vittorio Vitale (Pasqal)
Quantum computers and simulators, in the noisy intermediate-scale quantum era, offer a unique ability to control and probe individual quantum states at the many-body level. This capability allows for wave function snapshots via collective projective measurements, which are key to understanding the power of quantum computations. However, the connection between these snapshots and many-body collective properties remains poorly understood. We develop a network theory framework to link quantum phases of matter to their snapshots. First, we identify a minimal-complexity basis by analyzing the information compressibility of snapshots over different basis. Then, we build a wave-function network to study correlations in this basis. This approach reveals a stochastic classification of quantum states in one dimension: low-complexity networks correspond to paramagnetic and symmetry-broken phases, while high-complexity networks characterize conformal and topological phases. The latter can be distinguished by their network structures – which are either scale-free or Erdős–Rényi.
We corroborate this classification using extensive tensor network numerical experiments, complemented with state-of-the-art network theory analysis. The classification is of immediate experimental relevance, and draws a clear connection between probability distribution sampling and physical properties that is uncovered by network theory.