Efficiently Cooling Quantum Systems with Finite Resources: Insights from Thermodynamic Geometry

Landauer's limit on heat dissipation during information erasure is critical as devices shrink, requiring optimal pure-state preparation to minimise errors. However, Nernst's third law states this demands infinite resources in energy, time, or control complexity. We address the challenge of cooling quantum systems with finite resources. Using Markovian collision models, we explore resource trade-offs and present efficient cooling protocols (that are optimal for qubits) for coherent and incoherent control. Leveraging thermodynamic length, we derive bounds on heat dissipation for swap-based strategies and discuss the limitations of preparing pure states efficiently.