Mario Collura
(SISSA)

 

After a pedagogical introduction to Matrix Product State (MPS) and stabilizer formalisms, I will present a novel approach for assessing the non-stabilizer characteristics of an N-qubit MPS wave function. Initially, I demonstrate the evaluation of recently introduced Stabilizer Renyi Entropies (SREs) through perfect sampling of the many-body wave function across Pauli string configurations. This sampling employs an innovative MPS technique, enabling efficient computation with a computational cost of O(N χ^3), and is exemplified with practical cases.

Subsequently, I delve into the challenging task of learning the stabilizer group of an MPS. This involves modifying the earlier algorithm, biasing the sampling scheme to favor the extraction of strings within the stabilizer group. To comprehensively map the entire group, the sampling iterates over modified states obtained by applying Clifford transformations to the original MPS. The algorithm's output includes a set of stabilizer generators and an estimate of the stabilizer dimension for the state.

Benchmarking the algorithm is performed on T-doped states for rigorous evaluation and validation of its effectiveness.
 

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