Locally purified maximally mixed states at scale: Entanglement pruning and symmetries

Abstract

Locally Purified Density Operators (LPDOs) are state-of-the-art tensor network ansatze candidates that efficiently represent mixed quantum states. However, given their non-uniqueness, their representational complexity is generally sub-optimal in practical computations. In this work we perform an comprehensive numerical and analytical analysis and resolve this issue in the experimentally relevant limit where noise depolarizes the density operator into a maximally mixed state. To resolve the sub-optimality issue we combine two numerical tools with one analytic proof and detail the relations between them. The numerical tools used are fidelity-preserving truncations and isometric gauge transformations leveraging Riemannian optimizations over entropic objective functions. In addition, by invoking the injectivity and symmetry constraints of the maximally mixed LPDO, we also present analytical closed-form expressions for the disentangler and discuss their relation to numerical optimizers. Our work shows how, by minimizing the resources required to represent key states of practical interest in experiment, the efficiency of tensor network algorithms can be substantially increased. This paves the path for uncovering tensor network’s fundamental scalability limits and latent potential in representing the wide locus of mixed quantum states that near-term quantum architectures and devices provide the scientific community access to.