# Heat-Bath Algorithmic Cooling with correlated qubit-environment interactions

## TL;DR

This paper demonstrates that incorporating correlated qubit-environment interactions in heat-bath algorithmic cooling enhances qubit purification, surpassing previous methods by exploiting system-bath correlations to more effectively remove entropy.

## Contribution

The authors introduce a generalized relaxation model with system-bath correlations and develop improved cooling algorithms that achieve higher qubit purity than prior approaches.

## Key findings

- Enhanced qubit purity through correlated relaxation.
- Introduction of the 'state-reset' cooling tool.
- Relation of results to the Nuclear Overhauser Effect.

## Abstract

Controlled preparation of highly pure quantum states is at the core of practical applications of quantum information science, from the state initialization of most quantum algorithms to a reliable supply of ancilla qubits that satisfy the fault-tolerance threshold for quantum error correction. Heat-bath algorithmic cooling has been shown to purify qubits by controlled redistribution of entropy and multiple contact with a bath, not only for ensemble implementations but also for technologies with strong but imperfect measurements. However, an implicit restriction about the interaction with the bath has been assumed in previous work. In this paper, we show that better purification can be achieved by removing that restriction. More concretely, we include correlations between the system and the bath, and we take advantage of these correlations to pump entropy out of the system into the bath. We introduce a tool for cooling algorithms, which we call "state-reset", obtained when the coupling to the environment is generalized from individual-qubits relaxation to correlated-qubit relaxation. We present improved cooling algorithms which lead to an increase of purity beyond all the previous work, and relate our results to the Nuclear Overhauser Effect.