Quantum relaxation of multilevel particles

A. A. Demidenko, Elmar G. Petrov

Maria V. Bogdanova, Tamara M. Il'inova, R. V. Khokhlov

The results are given of a theoretical investigation of the interaction of a laser pulse with a molecular medium. Allowance for the vibrational relaxation processes is made within the diffusion approximation framework which makes it possible to describe relaxation as the diffusion of particles in continuous electron energy bands. A simultaneous solution is obtained of the diffusion equations for the medium and the equations for the radiation field in the special cases of slow and fast vibrational relaxation. It is shown that the fast relaxation, which prevents gain saturation, increases the signal energy compared with the case of slow relaxation in an amplifying medium and reduces this energy compared with such relaxation in an absorbing medium. Expressions are obtained for the functions which describe the distributions of the band particles established by the investigated signal. The analysis made shows that the diffusion model can be applied to the interaction between laser pulses and molecular media.

E Vaz, Jordan Kyriakidis

We have investigated the dynamics of bound particles in multilevel current-carrying quantum dots. We look specifically in the regime of resonant tunnelling transport, where several channels are available for transport. Through a non-Markovian formalism under the Born approximation, we investigate the real-time evolution of the confined particles including transport-induced decoherence and relaxation. In the case of a coherent superposition between states with different particle number, we find that a Fock-space coherence may be preserved even in the presence of tunneling into and out of the dot. Real-time results are presented for various asymmetries of tunneling rates into different orbitals.

Bao Gia Bach, Filip B. Maciejewski, Ilya Safro

The Quantum Approximate Optimization Algorithm (QAOA) is a promising quantum approach for tackling combinatorial optimization problems. However, hardware constraints such as limited scaling and susceptibility to noise pose significant challenges when applying QAOA to large instances. To overcome these limitations, scalable hybrid multilevel strategies have been proposed. In this work we propose a fast hybrid multilevel algorithm with QAOA parameterization throughout the multilevel hierarchy and its reinforcement with genetic algorithms, which results in a high-quality, low-depth QAOA solver. Notably, we propose transferring parameters from the coarsest level to the finer level, demonstrating that the relaxation-based coarsening preserves the problem's structural information required for QAOA parametrization. Our strategy improves the coarsening phase and leverages both Quantum Relax & Round and genetic algorithms to incorporate$p=1$QAOA samples effectively. The results highlight the practical potential of multilevel QAOA as a scalable method for combinatorial optimization on near-term quantum devices.

Karl Blum