Approximate Quantum Algorithms as a Multiphoton Raman Excitation of a Quasicontinuum Edge

TL;DR

This paper explores approximate quantum algorithms through a model involving multiphoton Raman excitation of a quasicontinuum edge, analyzing the dynamics and energy distribution of population transfer in quantum systems.

Contribution

It introduces a novel perspective on quantum state transitions as multiphoton Raman processes at a band edge, linking quantum algorithms to physical excitation mechanisms.

Findings

Energy width of population distribution follows the time-energy uncertainty principle.

Distribution shape depends on the specific transition setup.

Model applicable to various quantum computing platforms.

Abstract

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.