A quantum algorithm to solve nonlinear differential equations

Leyton, Sarah K.; Osborne, Tobias J.

A quantum algorithm to solve nonlinear differential equations

Dec 23, 2008

11 pages

e-Print:

0812.4423 [quant-ph]

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Abstract: (submitter)

In this paper we describe a quantum algorithm to solve sparse systems of nonlinear differential equations whose nonlinear terms are polynomials. The algorithm is nondeterministic and its expected resource requirements are polylogarithmic in the number of variables and exponential in the integration time. The best classical algorithm runs in a time scaling linearly with the number of variables, so this provides an exponential improvement. The algorithm is built on two subroutines: (i) a quantum algorithm to implement a nonlinear transformation of the probability amplitudes of an unknown quantum state; and (ii) a quantum implementation of Euler's method.

differential equations: nonlinear
transformation: nonlinear
quantum algorithm
quantum state
Hamiltonian

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