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Efficient quantum algorithms for state measurement and linear algebra applications

Patel, Apoorva and Priyadarsini, Anjani (2018) Efficient quantum algorithms for state measurement and linear algebra applications. In: INTERNATIONAL JOURNAL OF QUANTUM INFORMATION, 16 (6).

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Official URL: http://dx.doi.org/10.1142/S021974991850048X

Abstract

We present an algorithm for measurement of k-local operators in a quantum state, which scales logarithmically both in the system size and the output accuracy. The key ingredients of the algorithm are a digital representation of the quantum state, and a decomposition of the measurement operator in a basis of operators with known discrete spectra. We then show how this algorithm can be combined with (a) Hamiltonian evolution to make quantum simulations efficient, (b) the Newton-Raphson method based solution of matrix inverse to efficiently solve linear simultaneous equations, and (c) Chebyshev expansion of matrix exponentials to efficiently evaluate thermal expectation values. The general strategy may be useful in solving many other linear algebra problems efficiently.

Item Type: Journal Article
Additional Information: Copy right for this article belong to WORLD SCIENTIFIC PUBL CO PTE LTD
Keywords: Chebyshev polynomials; computational complexity; digital representation; Newton-Raphson method; quantum simulations
Department/Centre: Division of Physical & Mathematical Sciences > Centre for High Energy Physics
Depositing User: Id for Latest eprints
Date Deposited: 22 Nov 2018 15:03
Last Modified: 22 Nov 2018 15:03
URI: http://eprints.iisc.ac.in/id/eprint/61124

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