Compression of Matrix Product Density Operators (MPDO) and application to noisy quantum computer emulation.

Matrix Product Density Operators (MPDO) are tensor network representations of density matrices with interesting properties for noisy quantum computer emulation. In practice however, noisy circuits produce an explosion of the memory footprint of MPDOs, making them unusable after only a few layers of gates.

In this work we overcame this obstacle by designing a method to compress MPDOs in a systematic way. As MPDOs really represent purifications of mixed states, the method boils down to finding a purification of the state with a low enough entanglement entropy and auxiliary Hilbert space dimension, using only local operations.

This compression method is adapted to control MPDO's memory footprint in the emulation of noisy quantum circuits, and allows to take the full benefit of MPDO's nice properties: guaranteed positivity by construction, easy conservation of the trace and computation of local observables.