Iterative quantum optimization with an adaptive problem Hamiltonian for the shortest vector problem


Iterative quantum optimization with an adaptive problem Hamiltonian for the shortest vector problem

Zhu, Y. R.; Joseph, D.; Ling, C.; Mintert, F.

Quantum optimization algorithms hold the promise of solving classically hard, discrete optimization problems
in practice. The requirement of encoding such problems in a Hamiltonian realized with a finite (and currently
small) number of qubits, however, poses the risk of finding only the optimum within the restricted space
supported by this Hamiltonian. We describe an iterative algorithm in which a solution obtained with such
a restricted problem Hamiltonian is used to define a new problem Hamiltonian that is better suited than the
previous one. In numerical examples of the shortest vector problem, we show that the algorithm with a sequence
of improved problem Hamiltonians converges to the desired solution.

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Permalink: https://www.hzdr.de/publications/Publ-35629
Publ.-Id: 35629