Enabling large-depth simulation of noisy quantum circuits with positive tensor networks

Understand

Matrix product density operators (MPDOs) are tensor network representations of locally purified density matrices where each physical degree of freedom is associated to an environment degree of freedom.

• MPDOs have interesting properties for mixed state representations: guaranteed positivity by construction, efficient conservation of the trace and computation of local observables.
• However, they have been challenging to use for noisy quantum circuit simulation, as the application of noise increases the dimension of the environment Hilbert space, leading to an exponential growth of bond dimensions.
• MPDOs also lack a unique canonical form, due to the freedom in the choice of basis for the environment Hilbert space, which leads to a vast variation of bond dimensions.