Quantum-inspired algorithms for multivariate analysis: from interpolation to partial differential equations
In this work we study the encoding of smooth, differentiable multivariate functions in quantum registers, using quantum computers or tensor-network representations. We show that a large family of distributions can be encoded as low-entanglement states of the quantum register. These states can be eff...
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Published in | Quantum (Vienna, Austria) Vol. 5; p. 431 |
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Main Author | |
Format | Journal Article |
Language | English |
Published |
Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
15.04.2021
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Online Access | Get full text |
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Summary: | In this work we study the encoding of smooth, differentiable multivariate functions in quantum registers, using quantum computers or tensor-network representations. We show that a large family of distributions can be encoded as low-entanglement states of the quantum register. These states can be efficiently created in a quantum computer, but they are also efficiently stored, manipulated and probed using Matrix-Product States techniques. Inspired by this idea, we present eight quantum-inspired numerical analysis algorithms, that include Fourier sampling, interpolation, differentiation and integration of partial derivative equations. These algorithms combine classical ideas – finite-differences, spectral methods – with the efficient encoding of quantum registers, and well known algorithms, such as the Quantum Fourier Transform.
When these heuristic methods work
, they provide an exponential speed-up over other classical algorithms, such as Monte Carlo integration, finite-difference and fast Fourier transforms (FFT). But even when they don't, some of these algorithms can be translated back to a quantum computer to implement a similar task. |
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ISSN: | 2521-327X 2521-327X |
DOI: | 10.22331/q-2021-04-15-431 |