Algorithmic Cooling (AC) of Spins is potentially the first near-future application of quantum computing devices. Straightforward quantum algorithms combined with novel entropy manipulations can result in a method to improve the identification of molecules. We introduce here 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.
Algorithmic Cooling (AC) of Spins is potentially the first near-future application of quantum computing devices. Straightforward quantum algorithms combined with novel entropy manipulations can result in a method to improve the identification of molecules. We introduce here 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.
Abstract Algorithmic cooling (AC)is a recent spin‐cooling approach that employs entropy compression methods inopen 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 andk‐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.
An efficient technique to generate ensembles of spins that are highly polarized by external magnetic fields is the Holy Grail in Nuclear Magnetic Resonance (NMR) spectroscopy. Since spin-half nuclei have steady-state polarization biases that increase inversely with temperature, spins exhibiting high polarization biases are considered cool, even when their environment is warm. Existing spin-cooling techniques are highly limited in their efficiency and usefulness. Algorithmic cooling is a promising new spin-cooling approach that employs data compression methods in open systems. It reduces the entropy of spins on long molecules to a point far beyond Shannon's bound on reversible entropy manipulations, thus increasing their polarization. Here we present an efficient and experimentally feasible algorithmic cooling technique that cools spins to very low temperatures even on short molecules. This practicable algorithmic cooling could lead to breakthroughs in high-sensitivity NMR spectroscopy in the near future, and to the development of scalable NMR quantum computers in the far future. Moreover, while the cooling algorithm itself is classical, it uses quantum gates in its implementation, thus representing the first short-term application of quantum computing devices.
Algorithmic cooling (AC) of spins applies entropy manipulation algorithms in open spin systems in order to cool spins far beyond Shannon's entropy bound. Algorithmic cooling of nuclear spins was demonstrated experimentally and may contribute to nuclear magnetic resonance spectroscopy. Several cooling algorithms were suggested in recent years, including practicable algorithmic cooling (PAC) and exhaustive AC. Practicable algorithms have simple implementations, yet their level of cooling is far from optimal; exhaustive algorithms, on the other hand, cool much better, and some even reach (asymptotically) an optimal level of cooling, but they are not practicable. We introduce here semioptimal practicable AC (SOPAC), wherein a few cycles (typically two to six) are performed at each recursive level. Two classes of SOPAC algorithms are proposed and analyzed. Both attain cooling levels significantly better than PAC and are much more efficient than the exhaustive algorithms. These algorithms are shown to bridge the gap between PAC and exhaustive AC. In addition, we calculated the number of spins required by SOPAC in order to purify qubits for quantum computation. As few as 12 and 7 spins are required (in an ideal scenario) to yield a mildly pure spin (60% polarized) from initial polarizations of 1% and 10%, respectively. In the latter case, about five more spins are sufficient to produce a highly pure spin (99.99% polarized), which could be relevant for fault-tolerant quantum computing.
Algorithmic cooling (AC) is a method to purify quantum systems, such as ensembles of nuclear spins, or cold atoms in an optical lattice. When applied to spins, AC produces ensembles of highly polarized spins, which enhance the signal strength in nuclear magnetic resonance (NMR). According to this cooling approach, spin-half nuclei in a constant magnetic field are considered as bits, or more precisely, quantum bits, in a known probability distribution. Algorithmic steps on these bits are then translated into specially designed NMR pulse sequences using common NMR quantum computation tools. The algorithmic cooling of spins is achieved by alternately combining reversible, entropy-preserving manipulations (borrowed from data compression algorithms) with selectivereset, the transfer of entropy from selected spins to the environment. In theory, applying algorithmic cooling to sufficiently large spin systems may produce polarizations far beyond the limits due to conservation of Shannon entropy. Here, only selective reset steps are performed, hence we prefer to call this process "heat-bath" cooling, rather than algorithmic cooling. We experimentally implement here two consecutive steps of selective reset that transfer entropy from two selected spins to the environment. We performed such cooling experiments with commercially-available labeled molecules, on standard liquid-state NMR spectrometers. Our experiments yielded polarizations that bypassShannon′sentropy-conservationbound, so that the entire spin-system was cooled. This paper was initially submitted in 2005, first to Science and then to PNAS, and includes additional results from subsequent years (e.g. for resubmission in 2007). The Postscriptum includes more details.
Algorithmic cooling is a novel technique to generate ensembles of highly polarized spins, which could significantly improve the signal strength in Nuclear Magnetic Resonance (NMR) spectroscopy. It combines reversible (entropy-preserving) manipulations and irreversible controlled interactions with the environment, using simple quantum computing techniques to increase spin polarization far beyond the Shannon entropy-conservation bound. Notably, thermalization is beneficially employed as an integral part of the cooling scheme, contrary to its ordinary destructive implications. We report the first cooling experiments bypassing Shannon's entropy-conservation bound, performed on a standard liquid-state NMR spectrometer. We believe that this experimental success could pave the way for the first near-future application of quantum computing devices.
Algorithmic cooling (AC) is a method to purify quantum systems, such as ensembles of nuclear spins, or cold atoms in an optical lattice. When applied to spins, AC produces ensembles of highly polarized spins, which enhance the signal strength in nuclear magnetic resonance (NMR). According to this cooling approach, spin-half nuclei in a constant magnetic field are considered as bits, or more precisely quantum bits, in a known probability distribution. Algorithmic steps on these bits are then translated into specially designed NMR pulse sequences using common NMR quantum computation tools. The algorithmic cooling of spins is achieved by alternately combining reversible, entropy-preserving manipulations (borrowed from data compression algorithms) with selective reset , the transfer of entropy from selected spins to the environment. In theory, applying algorithmic cooling to sufficiently large spin systems may produce polarizations far beyond the limits due to conservation of Shannon entropy. Here, only selective reset steps are performed, hence we prefer to call this process “heat-bath” cooling, rather than algorithmic cooling. We experimentally implemented two consecutive steps of selective reset, thus transferring entropy from two selected spins to the environment. We performed such cooling experiments, with commercially available labeled molecules, on standard liquid-state NMR spectrometers. We report in particular on our original experiment, unpublished until now except on the arXiv (quant-ph/0511156) in 2005, which was, to the best of our knowledge, the world’s first experiment that yielded polarizations results that bypassed Shannon’s entropy-conservation bound , so that the entire spin-system was cooled.