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arXiv · 1510.00820

Quantum algorithm for obtaining the eigenstates of a physical system

Hefeng Wang
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Abstract

We propose a quantum algorithm for solving the following problem: given the Hamiltonian of a physical system and one of its eigenvalues, how to obtain the corresponding eigenstate? The algorithm is based on the resonance phenomena. For a probe qubit coupled to a quantum system, the system exhibits a resonance dynamics when the frequency of the probe qubit matches a transition frequency in the system. Therefore the system can be guided to evolve to the eigenstate with known eigenvalue by inducing resonance between the probe qubit and a designed transition in the system. This algorithm can also be used to obtain the energy spectrum of a physical system and can achieve even a quadratic speedup over the phase estimation algorithm.

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Hefeng Wang. 2015-10-03. Quantum algorithm for obtaining the eigenstates of a physical system. https://doi.org/10.1103/physreva.93.052334

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