Beyond the Born-Markov approximation: dissipative dynamics of a single qubit

TL;DR

This paper introduces a numerical method combining Lanczos and exact diagonalization to simulate the dissipative dynamics of a single qubit interacting with an environment, capturing effects beyond traditional approximations.

Contribution

The authors develop a flexible numerical technique that includes multiple-excitation processes and surpasses weak coupling and Markovian assumptions in qubit-environment simulations.

Findings

Method accurately reproduces thermodynamic behavior.

Bath can aid in reaching the qubit's ground state during annealing.

Outperforms Lindblad and other approximate approaches.

Abstract

We propose a numerical technique based on a combination of short-iterative Lanczos and exact diagonalization methods, suitable for simulating the time evolution of the reduced density matrix of a single qubit interacting with an environment. By choosing a mode discretization method and a flexible bath states truncation scheme, we are able to include in the physical description multiple-excitation processes, beyond weak coupling and Markov approximations. We apply our technique to the simulation of three different model Hamiltonians, which are relevant in the field of adiabatic quantum computation. We compare our results with those obtained on the basis of the widely used Lindblad master equation, as well as with well-known exact and approximated approaches. We show that our method is able to recover the thermodynamic behavior of the qubit-bath system, beyond the Born-Markov approximation. Finally, we show that even in the case of the adiabatic quantum annealing of a single qubit the bath can be beneficial in reaching the reduced system ground state.