Quantum algorithm for obtaining the eigenstates of a physical system

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.

14 pages, 5 figures

References in corpus (2)

• Efficient quantum algorithm for preparing molecular-system-like states on a quantum computer
• Quantum algorithm for obtaining the energy spectrum of a physical system

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