Learning Orthogonal Random Unitary Channels with Contracted Quantum Approaches and Simplex Optimization

Abstract: Random (mixed) unitary channels describe an important subset of quantum channels, which are commonly used in quantum information, noise modeling, and quantum error mitigation. Despite their usefulness, there is substantial complexity in characterizing or identifying generic random unitary channels. We present a procedure for learning a class of random unitary channels on orthogonal unitary bases on a quantum computer utilizing Pauli learning and a contracted quantum learning procedure. Our approach involves a multi-objective, Pauli- and unitary-based minimization, and allows for learning locally equivalent channels. We demonstrate our approach for varying degrees of noise and investigate the scalability of these approaches, particularly with sparse noise models.