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【期刊论文】Optimal Query Error of Quantum Approximation on Some Sobolev Classes
叶培新, SONG ZhanJie, , YE PeiXin
Science in China Series A: Mathematics 2008 Vol. 51 No. 1 1{16,-0001,():
-1年11月30日
We study the approximation of the imbedding of functions from anisotropic and generalized Sobolev classes into Lq([0, 1]d) space in the quantum model of computation. Based on the quantum algorithms for approximation of finite imbedding from LNp to LNq , we develop quantum algorithms for approximating the imbedding from anisotropic Sobolev classes B(Wrp ([0, 1]d)) to Lq([0, 1]d) space for all 1 6 q; p 6 1 and prove their optimality. Our results show that for p < q the quantum model of computation can bring a speedup roughly up to a squaring of the rate in the classical deterministic and randomized settings.
quantum approximation, Sobolev classes, n-th minimal query error
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