To grasp the potential power of quantum computing, consider its most basic ingredient, the qubit. Unlike the classical binary bit, the qubit can be on or off or anywhere in between. When qubits are combined, their multiplicity of states balloons to fill a huge Hilbert space in which unitary transformations change myriad states at once.

Quantum mechanics is manifest in small, cold enclaves within the classical macroworld. When heat and other environmental disturbances intrude, they rob a quantum system of its coherence and its ability to compute. Error correction schemes can forestall the loss. But because the schemes work by hiding information among additional qubits, they tax efficiency.

In the face of those limitations, quantum computation based on isolated two-state systems, such as trapped ions, continues to progress. Logic gates and error correction schemes have already been built and run. Still, any computer has to execute long trains of operations....

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