Beyond Unitary Quantum Simulation: Open-System Approaches to Quantum Chemistry toward Quantum Advantage

Quantum simulation is widely regarded as one of the most promising routes to genuine quantum advantage, yet most existing approaches to quantum chemistry are formulated in terms of closed-system, unitary dynamics and ground-state preparation within the Born--Oppenheimer approximation. In this review, we discuss a broader perspective motivated by the observation that naturally occurring quantum systems are rarely isolated and often reach physically relevant states only through relaxation, decoherence, and thermalization. We first examine what is and is not known about exponential quantum advantage in chemistry, emphasizing that coherent Hamiltonian simulation provides the clearest formal case for speed-up, while many open questions remain for realistic problems. We then discuss how dissipation might ideally be integrated into quantum chemistry on a fault-tolerant quantum computer, using recent proposals for chemically motivated dynamical simulation as a guiding vision. More generally, we highlight the practical appeal of this approach to enhancing the robustness of quantum algorithms.