The scaling of NMR ensemble computers is currently one of the main obstacles to building larger-scale quantum computing devices. To achieve scalability, one needs a large number of highly polarized spins in liquid nuclear-spin systems at finite temperature. In quantum computing terminology, such spin-half states are (almost) pure qubit states. Producing highly polarized spins (almost pure qubit states) out of non-polarized spins (non-pure qubit states) is sometimes called "purification". From a thermodynamic point of view, purification can be viewed as cooling spins to a very low temperature. In this preliminary work, we study the optimality of purification as a tradeoff between the number of cooled spins and the closeness of their quantum state to the ideal pure state.
The scaling of NMR ensemble computers is currently one of the main obstacles to building larger-scale quantum computing devices. To achieve scalability, one needs a large number of highly polarized spins in liquid nuclear-spin systems at finite temperature. In quantum computing terminology, such spin-half states are (almost) pure qubit states. Producing highly polarized spins (almost pure qubit states) out of non-polarized spins (non-pure qubit states) is sometimes called "purification". From a thermodynamic point of view, purification can be viewed as cooling spins to a very low temperature. In this preliminary work, we study the optimality of purification as a tradeoff between the number of cooled spins and the closeness of their quantum state to the ideal pure state.
To achieve scalability of NMR computers, one needs a large number of highly polarized spins in liquid nuclearspin systems at finite temperature. In quantum computing terminology, such spin-half states are (almost) pure qubit states. Producing highly polarized spins (almost pure qubit states) out of non-polarized spins (non-pure qubit states) is sometimes called "purification". From a thermodynamic point of view, purification can be viewed as cooling spins to a very low temperature. In this work, we study how classical data compression codes can be used to design cooling algorithms for both short and long molecules. We argue that so designed cooling (purification) algorithms potentially outperform other methods in terms of the closeness of the output state to the ideal pure state, which in turn implies lower output temperature. We also analyze how the mismatch of the algorithm's computational basis and the actual eigenbasis of the spins' density matrix will affect the cooling (purification) performance.
To achieve scalability of NMR computers, one needs a large number of highly polarized spins in liquid nuclear-spin systems at finite temperature. In quantum computing terminology, such spin-half states are (almost) pure qubit states. Producing highly polarized spins (almost pure qubit states) out of non-polarized spins (non-pure qubit states) is sometimes called "purification ". From a thermodynamic point of view, purification can be viewed as cooling spins to a very low temperature and can be achieved via data compression algorithms on spins. In this work, we study how classical data compression codes can be used to design cooling algorithms. Specifically, we utilize fixed-rate block compression codes for long molecules and variable-rate lossless compression codes for short molecules and and provide a rudimentary analysis of cooling performance for both short and long molecules.
We present here algorithmic cooling (via polarization heat bath)-a powerful method for obtaining a large number of highly polarized spins in liquid nuclear-spin systems at finite temperature. Given that spin-half states represent (quantum) bits, algorithmic cooling cleans dirty bits beyond the Shannon's bound on data compression, by using a set of rapidly thermal-relaxing bits. Such auxiliary bits could be implemented by using spins that rapidly get into thermal equilibrium with the environment, e.g., electron spins. Interestingly, the interaction with the environment, usually a most undesired interaction, is used here to our benefit, allowing a cooling mechanism. Cooling spins to a very low temperature without cooling the environment could lead to a breakthrough in NMR experiments, and our "spin-refrigerating" method suggests that this is possible. The scaling of NMR ensemble computers is currently one of the main obstacles to building larger-scale quantum computing devices, and our spin-refrigerating method suggests that this problem can be resolved.
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) 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 (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.