Quantum computers would represent an exponential increase in computing power...if they can be built. This tutorial describes the theoretical background to quantum computing, its potential for several specific applications, and the demanding challenges facing practical implementation. The field currently suffers from a strange imbalance with theoretical advances far outstripping experimental demonstration. The field is poised for a breakthrough that would make quantum circuits experimentally "accessible", as opposed to the million dollar price tags attached to most current implementations.
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