Approximate Quantum Algorithms as a Multiphoton Raman Excitation of a Quasicontinuum Edge
Many quantum algorithms can be seen as a transition from a well-defined initial quantum state of a complex quantum system, to an unknown target quantum state, corresponding to a certain eigenvalue either of the Hamiltonian or of a transition operator. Often such a target state corresponds to the min...
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Zusammenfassung: | Many quantum algorithms can be seen as a transition from a well-defined
initial quantum state of a complex quantum system, to an unknown target quantum
state, corresponding to a certain eigenvalue either of the Hamiltonian or of a
transition operator. Often such a target state corresponds to the minimum
energy of a band of states. In this context, approximate quantum calculations
imply transition not to the single, minimum energy, state but to a group of
states close to the minimum. We consider dynamics and the result of two
possible realization of such a process -- transition of population from a
single initially populated isolated level to the quantum states at the edge of
a band of levels. The first case deals with the time-independent Hamiltonian,
while the other with a moving isolated level. We demonstrate that the energy
width of the population energy distribution over the band is mainly dictated by
the time-energy uncertainty principle, although the specific shape of the
distribution depends on the particular setting. We consider the role of the
statistics of the coupling matrix elements between the isolated level and the
band levels. We have chosen the multiphoton Raman absorption by an ensemble of
Rydberg atoms as the model for our analysis, although the results obtained can
equally be applied to other quantum computing platforms. |
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DOI: | 10.48550/arxiv.2207.08561 |