On Integrable Quantum and Classical Circuits with Stochastic Boundaries

Explore explicit matrix product solutions for quantum many-body Markov chains in this 57-minute lecture by Tomaz Prosen from the University of Ljubljana, presented at Harvard CMSA's Program on Classical, quantum, and probabilistic integrable systems. The talk examines Yang-Baxter integrable quantum circuits with specific stochastic Kraus processes at their boundaries, explaining how these solutions correspond to steady states of boundary driven Lindbladian dynamics and often produce non-trivial quasi-local conservation laws of integrable spin chains. Particular attention is given to the XXZ and Hubbard chain cases, demonstrating novel interactions and applications in quantum and classical circuits with stochastic boundaries.