TY - JOUR T1 - Efficient quantum circuits for arbitrary sparse unitaries JF - Physical Review A Y1 - 2009 A1 - Stephen P. Jordan A1 - Pawel Wocjan AB - Arbitrary exponentially large unitaries cannot be implemented efficiently by quantum circuits. However, we show that quantum circuits can efficiently implement any unitary provided it has at most polynomially many nonzero entries in any row or column, and these entries are efficiently computable. One can formulate a model of computation based on the composition of sparse unitaries which includes the quantum Turing machine model, the quantum circuit model, anyonic models, permutational quantum computation, and discrete time quantum walks as special cases. Thus we obtain a simple unified proof that these models are all contained in BQP. Furthermore our general method for implementing sparse unitaries simplifies several existing quantum algorithms. VL - 80 UR - http://arxiv.org/abs/0904.2211v2 CP - 6 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.80.062301 ER -