**Molecular Scale Heat Engines and Scalable Quantum Computation **
Leonard Schulman

We describe a quantum mechanical heat engine. Like its classical counterpart introduced by Carnot, this engine carries out a reversible process in which an input of energy to the system results in a separation of cold and hot regions. The method begins with a reinterpretation in thermodynamic terms of a simple step introduced by von Neumann to extract fair coin flips from sequences of biased coin flips. Some of the experimental set-ups proposed for implementation of quantum computers, begin with the quantum bits of the computer initially in a mixed state. Each qubit is $\epsilon$ polarized --- in the state $\ket{0}$ with probability $\frac{1+\epsilon}\{2}$, and in the state $\ket{1}$ with probability $\frac{1-\epsilon}\{2}$, independently (or nearly so) of all other bits. The heat engine may be used to transform this initial collection of $n$ qubits into a state in which a near-optimal $m=n[{1+\ep \over 2} \lg (1+\ep) +{1-\ep \over 2} \lg (1-\ep) -o(1)]$ qubits are in the joint state $\ket{0^m}$. These qubits can then be used as the registers for a quantum computation. The heat engine is described at the level of an algorithm implementable in any quantum system capable of massive coherent states. A particular implementation is also described for a system of nuclear spins arranged in a chain. The temperature the cold qubits reach is inverse polynomial in $n$.

*created Tue Mar 14 17:48:16 PST 2000
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