An open source MATLAB program for fast numerical Feynman integral calculations for open quantum system dynamics on GPUs

Abstract

This MATLAB program calculates the dynamics of the reduced density matrix of an open quantum system modeled by the Feynman-Vernon model. The user gives the program a vector describing the coordinate of an open quantum system, a hamiltonian matrix describing its energy, and a spectral distribution function and temperature describing the environment's influence on it, in addition to the open quantum system's intial density matrix and a grid of times. With this, the program returns the reduced density matrix of the open quantum system at all (or some) moments specified by that grid of times. This overall calculation can be divided into two stages: the setup of the Feynman integral, and the actual calculation of the Feynman integral for time-propagation of the density matrix. When this program calculates this propagation on a multi-core CPU, it is this propagation that is usually the rate limiting step of the calculation, but when it is calculated on a GPU, the propagation is calculated so quickly that the setup of the Feynman integal actually becomes the rate limiting step for most cases tested so far. The overhead of transfrring information from the CPU to the GPU and back seems to have negligible effect on the overall runtime of the program. When the required information cannot fit on the GPU, the user can choose to run the entire program on a CPU.

8 pages, 2 figures, 1 table, 22 references

References in corpus (4)

• Phonon induced Rabi frequency renormalization of optically driven single InGaAs/GaAs quantum dots
• Quantum dot Rabi rotations beyond the weak exciton-phonon coupling regime
• A general approach to quantum dynamics using a variational master equation: Application to phonon-damped Rabi rotations in quantum dots
• Optimal representation of the bath response function & fast calculation of influence functional coefficients in open quantum systems with BATHFIT 1

Cited by in corpus (10)

• Reduced hierarchical equations of motion in real and imaginary time: Correlated initial states and thermodynamic quantities
• Exploiting the causal tensor network structure of quantum processes to efficiently simulate non-Markovian path integrals
• Real-Time and Imaginary-Time Quantum Hierarchal Fokker-Planck Equations
• Path-integral methodology and simulations of quantum thermal transport: Full counting statistics approach
• Pulsed excitation dynamics in quantum dot-cavity systems: limits to optimizing the fidelity of on-demand single photon sources
• Towards a feasible implementation of quantum neural networks using quantum dots
• Spin-boson model as a simulator of non-Markovian multiphoton Jaynes-Cummings models
• Entanglement in a quantum neural network based on quantum dots
• Beyond the Born-Markov approximation: dissipative dynamics of a single qubit
• Non-Markovian trajectories involving future in the semi-classical path integral expression