Algorithmic Cooling

Algorithmic Cooling is an information processing protocol that aims to reduce the entropy in some target subsystem, whilst increasing the entropy in the complementary system. This is done by separating a system into a target subsystem to be cooled and a thermal machine to facilitate the cooling. This joint system then interacts with a thermal bath.

Lin et al. (2024) define a unified framework for coherent control algorithmic cooling.

let $\rho_t$ be the target system, $\rho_m$ the thermal machine and $\tau$ a thermal state from a bath at temperature $T$ such that

Coherent control algorithmic cooling protocols consist of two subroutines: a unitary control step and a thermalisation step.

1. Unitary Control Step: A unitary, $U_{s,m}$ that acts on both the target and machine subsystems. This step does not need to conserve energy in the system.
2. Thermalisation Step: a thermal operation, $\mathcal{E}$, that acts on the joint target and machine state such that

where $\rho_{s,m}$ is the joint state of the system and thermal machine after a unitary control step and $[V_{s,m,b}, H_{s} + H_m + H_b]=0$.

A coherent control algorithmic cooling protocol is then defined as a methodical sequence which alternative between a unitary control step and a thermalisation step with the aim to reduce the entropy in the target system.