01162nas a2200133 4500008004100000245006200041210006200103260001400165490000700179520076300186100002400949700001800973856003700991 2009 eng d00aEfficient quantum circuits for arbitrary sparse unitaries0 aEfficient quantum circuits for arbitrary sparse unitaries c2009/12/10 v803 a 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.
1 aJordan, Stephen, P.1 aWocjan, Pawel uhttp://arxiv.org/abs/0904.2211v2