Quantum computers promise to solve mathematical problems that cannot be  solved efficiently on conventional computers.  Many of these problems have important practical applications in the areas of quantum physics simulation, cryptography, and combinatorial optimization.  The challenge today is to implement a quantum computer and demonstrate scalable operation.  This paper reviews one of the most promising schemes, Linear Optics Quantum Computation (LOQC), a recent proposal that requires only ordinary (linear) optical elements.  We pay particular attention to recent theoretical and experimental developments that have significantly eased the complexity and experimental requirements of the original proposal, and list remaining technical challenges. 

To anyone younger than 40, Moore's law of the exponential increase in transistor density on microchips might seem as permanent a fixture as, say, the law of gravity.  But the end is in sight, with feature sizes over the next 10 to 20 years projected to reach atomic scales, where the classical paradigm for chip design will break down.

But one person's curse is another's blessing: the revelation of quantum mechanics in nanostructures may seem as an annoyance to current chip-makers, but many researchers see it as the beginning of a new era of computation, one that exploits quantum effects for computations not possible on classical computers.  The idea for such a quantum computer is relatively recent.  In 1982, Feynman posed the question, ``Can quantum systems be probabilistically simulated by a classical computer?'' The immense benefit of such a quantum simulator approach becomes clear when one considers how many bits a computer must store to track the simulation of a quantum system of n components.  

 LOQC_englund.pdf (1.37 MB) 

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