Dissipative State Preparation and the Dissipative Quantum Eigensolver

Explore a groundbreaking lecture on the Dissipative Quantum Eigensolver (DQE), a novel quantum algorithm for preparing ground states of quantum many-body systems. Delve into the complexities of finding ground states, from NP-hard classical problems to QMA-hard quantum Hamiltonians. Examine various quantum algorithms proposed for tackling this challenge, including quantum phase estimation, adiabatic state preparation, and the variational quantum eigensolver. Learn how the DQE algorithm overcomes limitations of previous methods, offering unconditional convergence to the ground state subspace without prior information or variational optimization. Discover the algorithm's unique advantages, such as monotonic increase in ground state overlap, low circuit depth implementation, and inherent fault-resilience. Gain insights into the mathematical analysis behind DQE, utilizing non-commutative generalizations of classical probability theory methods.