Optimal Algorithmic Cooling of Spins

Algorithmic cooling (AC) is a recent spin-cooling approach that employs entropy compression methods in open systems. AC reduces the entropy of spins on suitable molecules beyond Shannon's bound on the degree of entropy compression by reversible manipulations. Remarkably, AC makes use of thermalization, a generally destructive facet of spin systems, as an integral part of the cooling scheme. AC is capable of cooling spins to very low temperatures and provides significant cooling for molecules containing as few as 5–7 spins. Application of AC to slightly larger molecules could lead to breakthroughs in high-sensitivity NMR spectroscopy in the near future. Furthermore, AC may be germane to the development of scalable NMR quantum computers. We introduce here a new practicable algorithm, “PAC3”, and several new exhaustive cooling algorithms, such as the Tribonacci and k-bonacci algorithms. In particular, we present the “all-bonacci” algorithm, which appears to reach the maximal degree of cooling obtainable by the optimal AC approach. AC is potentially beneficial for NMR-derived biomedical applications, which involve bio-molecules with isotope enrichments, such as ¹³ C- and ¹⁵ N-labeled amino acids. We briefly survey AC experiments, including a recent 3-spin experiment in which Shannon's bound was bypassed. The difficulties associated with cooling molecules bearing a greater number of spins are explained. Finally, the potential of selected cooling algorithms (practicable, exhaustive, and optimal algorithms) is illustrated with regard to a highly relevant bio-medical target— ¹³ C-labeled glucose.