QuTiP-BoFiN: A bosonic and fermionic numerical hierarchical-equations-of-motion library with applications in light-harvesting, quantum control, and single-molecule electronics

Abstract

The "hierarchical equations of motion" (HEOM) method is a powerful numerical approach to solve the dynamics and steady-state of a quantum system coupled to a non-Markovian and nonperturbative environment. Originally developed in the context of physical chemistry, it has also been extended and applied to problems in solid-state physics, optics, single-molecule electronics, and biological physics. Here we present a numerical library in Python, integrated with the powerful QuTiP platform, which implements the HEOM for both bosonic and fermionic environments. We demonstrate its utility with a series of examples. For the bosonic case, we present examples for fitting arbitrary spectral densities, modelling a Fenna-Matthews-Olsen photosynthetic complex, and simulating dynamical decoupling of a spin from its environment. For the fermionic case, we present an integrable single-impurity example, used as a benchmark of the code, and a more complex example of an impurity strongly coupled to a single vibronic mode, with applications in singlemolecule electronics.

Pulse-level noisy quantum circuits with QuTiP

“…Other dynamical solvers. QuTiP also provides solvers for other noise models and dynamics, such as the (secular and non-secular) Bloch-Redfield equation [34], the (non-Markovian) hierarchical equation of motion (HEOM) [21,38], and stochastic master equations. These are not currently supported for the pulse-level circuit simulation of qutip-qip.…”

“…QuTiP provides useful tools for handling quantum operators and simplifies the simulation of a quantum system under a noisy environment by providing a number of solvers, such as the Lindblad master equation solver. An ecosystem of software tools for quantum technology is growing around it [13,15,[18][19][20][21][22][23][24][25]. Hence, it is a natural base to start connecting the simulation of quantum circuits and the time evolution of the quantum system representing the circuit registers.…”

Steady state in ultrastrong coupling regime: perturbative expansion and first orders

“…The dynamics of quantum systems strongly coupled to thermal baths have recently received a lot of interest fuelled by hopes of understanding or even discovering new phenomena in quantum transport [1][2][3][4][5][6][7][8], quantum thermodynamics [9][10][11][12][13][14][15], quantum sensing [16][17][18], as well as understanding better the underlying physics of some essential biological functions [19][20][21][22]. In most of these applications, to know the steady state of the system strongly coupled to the bath is often essential and sufficient.…”

“…To obtain some information about strongly coupled steady states, several strategies have been developed, including embedding techniques like reaction coordinate [10,23,29,30] and pseudo-mode [31][32][33][34], or numerical techniques (Hierarchical Equation of Motion) [22,35,36]. One alternative strategy focusing directly on the steady state without going through the description of the whole dynamics is to consider the global steady state of the system and bath, namely the global thermal state at the bath temperature [37][38][39][40][41][42] (see more details in the following).…”

Pseudomode description of general open quantum system dynamics: non-perturbative master equation for the spin-boson model

“…2, we compare the reduced system dynamics computed from the pseudomode master equation and the HEOM for different values of ω 0 in the strong coupling and narrow bath regime, assuming the TLS to be initialized in the state ρ S (0) = |e e|. The two approaches have been implemented numerically using the Python library QuTiP [71] and the integrated QuTiP package BoFiN-HEOM provided in [72,73]. As expected, we find close correspondence between the predictions of the master equation and HEOM over both short and long time scales.…”