William Munizzi

The monogamy of mutual information (MMI) is a quantum entropy inequality that enforces the non-positivity of tripartite information. We investigate the failure of MMI in graph states as a forbidden-subgraph phenomenon, conjecturing that every MMI-violating graph state is local-Clifford equivalent to one whose graph contains a four-star subgraph. We construct a family of star-like graphs whose states fail a specific class of MMI instances, and extend this analysis to general star topologies. Deriving adjacency matrix constraints that fix the MMI evaluation for these instances and interpreting them physically, we prove the forbidden-subgraph conjecture for this family of graphs. Finally, through an exhaustive search over graph representatives for all 8-qubit stabilizer entropy vectors, we establish that MMI failure is not reducible to the cases within our scope.

Practical implementation of quantum error correction is currently limited by near-term quantum hardware. In contrast, quantum error mitigation has demonstrated strong promise for improving the performance of noisy quantum circuits without the requirement of full fault tolerance. In this work, we develop a hybrid error suppression protocol that integrates Pauli twirling, probabilistic error cancellation, and the [[n,n−2,2]] quantum error detecting code. In addition, to reduce overhead from error mitigation components of our method, we modify Pauli twirling by lowering the number of Pauli operators in the twirling set, and apply probabilistic error cancellation at the end of the encoded circuit to remove undetectable errors. Finally, we demonstrate our protocol on a non-Clifford variational quantum eigensolver circuit that estimates the ground state energy of $H_2$ using both qiskit AerSimulator and the IBM quantum processor ibm brussels.

We present a machine learning framework to study the dynamics of entropy vectors and quantum resources, including entanglement and magic, focusing on violations of entropy inequalities. Using a reinforcement learning agent formulated as a Markov decision process, we identify quantum circuits that optimally navigate the entropy vector space to generate violations of Ingleton's inequality. We complement this approach with a classical optimization algorithm to produce arbitrary numbers of Ingleton-violating states, with tunable degrees of violation, and empirically determine the maximal attainable violation for Ingleton's inequality. Our analysis reveals characteristic patterns of quantum resources that accompany Ingleton violation. A comprehensive statistical analysis shows that Ingleton-violating states occupy sharply-defined, isolated regions of the Hilbert space, and are extremely rare. Together, these results establish a unified computational toolkit for studying entropy vector dynamics, tracking quantum resource evolution, and engineering circuits with controlled information-theoretic features.