Physical Limits of Heat-bath Algorithmic Cooling

Leonard Schulman

California Institute of Technology

The most fundamental experimental challenge to the realization of quantum computers in mixed-state devices (such as NMR) is device initialization. A recent proposal to solve this problem is "heat-bath algorithmic cooling." We study the physical limits of this method and discover a threshold effect: If the bath is above a certain temperature threshold, no cooling procedure can initialize the system sufficiently for quantum computation. Conversely we describe procedures which, below the temperature threshold, create such initialization.

The above-threshold impossibility result holds no matter how much time is allowed for cooling. On the other hand the below-threshold result includes an accounting of the number of cooling steps, and this is shown to be near-optimal. The arguments for these results are not thermodynamic, as the system is open; rather, the arguments depend on the analysis of a certain combinatorial game.

Coauthors: T. Mor and Y. Weinstein

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