Implementing smooth functions of a Hermitian matrix on a quantum computer

We consider methods for implementing smooth functions f(A) of a sparse Hermitian matrix A on a quantum computer, and analyse a further combination of these techniques which has advantages of simplicity and resource consumption in some cases. Our construction uses the linear combination of unitaries...

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Bibliographic Details
Published in:Journal of physics communications 2019-06, Vol.3 (6), p.65002
Main Authors: Subramanian, Sathyawageeswar, Brierley, Stephen, Jozsa, Richard
Format: Article
Language:English
Subjects:
matrix functions
quantum algorithms
Quantum computing
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Summary:We consider methods for implementing smooth functions f(A) of a sparse Hermitian matrix A on a quantum computer, and analyse a further combination of these techniques which has advantages of simplicity and resource consumption in some cases. Our construction uses the linear combination of unitaries method with Chebyshev polynomial approximations. The query complexity we obtain is  log C ϵ where ϵ is the approximation precision, and C > 0 is an upper bound on the magnitudes of the derivatives of the function f over the domain of interest. The success probability depends on the 1-norm of the Taylor series coefficients of f, the sparsity d of the matrix, and inversely on the smallest singular value of the target matrix f(A).
ISSN:2399-6528
2399-6528
DOI:10.1088/2399-6528/ab25a2