Locally Purified Density Operators for Noisy Quantum Circuits

Explore the efficient representation of mixed states generated from noisy quantum circuits using locally purified density operators (LPDOs) in this comprehensive conference talk. Delve into a novel mapping from LPDOs of N qubits to projected entangled-pair states and discover a unified method for managing virtual and Kraus bonds. Examine the numerical validation of this approach using noisy random quantum circuits with depths up to d=40, focusing on fidelity and entanglement entropy as accuracy measures. Analyze the effectiveness of LPDO representation in describing mixed states within quantum and classical regions, while understanding its limitations at the quantum-classical critical point. Compare the LPDO approach with matrix product operator (MPO) representation, noting the latter's success in characterizing entanglement trends but potential issues with positivity conditions. Gain valuable insights into efficient mixed-state representation in open quantum systems and the entanglement structure of noisy quantum circuits, advancing your understanding of this crucial area in quantum computing research.