Efficient Quantum Algorithms for Simulating Sparse Hamiltonians

被引：0
|
作者：
Dominic W. Berry
Graeme Ahokas
Richard Cleve
Barry C. Sanders
机构：
[1] The University of Queensland,Department of Physics
[2] University of Calgary,Institute for Quantum Information Science
[3] University of Calgary,Department of Computer Science
[4] University of Waterloo,School of Computer Science
[5] University of Waterloo,Institute for Quantum Computing
[6] Macquarie University,Centre for Quantum Computer Technology
来源：
Communications in Mathematical Physics | 2007年 / 270卷
关键词：
Quantum Algorithm; Quantum Walk; Trace Distance; Nonzero Matrix Element; Tensor Product Structure;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We present an efficient quantum algorithm for simulating the evolution of a quantum state for a sparse Hamiltonian H over a given time t in terms of a procedure for computing the matrix entries of H. In particular, when H acts on n qubits, has at most a constant number of nonzero entries in each row/column, and ||H|| is bounded by a constant, we may select any positive integer k such that the simulation requires O((log*n)t1+1/2k) accesses to matrix entries of H. We also show that the temporal scaling cannot be significantly improved beyond this, because sublinear time scaling is not possible.
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页码：359 / 371
页数：12
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