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 exact numerical approach to solve the dynamics and find the steady-state of a quantum system coupled to a non-Markovian and non-perturbative 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 include demonstrations of fitting arbitrary spectral densities, and an example of the dynamics of energy transfer in the Fenna-Matthews-Olson photosynthetic complex, showing how a suitable non-Markovian environment can protect against pure dephasing. We also demonstrate how the HEOM can be used to benchmark different strategies for dynamical decoupling of a spin from its environment, and show that the Uhrig pulse-spacing scheme is less optimal than equally spaced pulses when the environment's spectral density is very broad. 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 to single-molecule electronics.

arXiv comment20 pages, 15 figures. Updated to describe package inclusion in QuTiP v4.7 (www.qutip.org), new examples (optimal pulse spacing in dynamical decoupling, quantum heat transport), and inclusion of additional contributors in author list. Further updates to expand examples, clarify content and summarize existing packages

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• Non-Markovian Quantum Exceptional Points
• Non-Hermitian Pseudomodes for Strongly Coupled Open Quantum Systems: Unravelings, Correlations and Thermodynamics
• Quasi-Lindblad pseudomode theory for open quantum systems
• A pseudo-fermion method for the exact description of fermionic environments: from single-molecule electronics to Kondo resonance
• HierarchicalEOM.jl: An efficient Julia framework for hierarchical equations of motion in open quantum systems
• Cyclic quantum engines enhanced by strong bath coupling
• ACE: A general-purpose non-Markovian open quantum systems simulation toolkit based on process tensors
• Simulating Non-Markovian Quantum Dynamics on NISQ Computers Using the Hierarchical Equations of Motion
• QuantumToolbox.jl: An efficient Julia framework for simulating open quantum systems
• Effective-Hamiltonian theory: An approximation to the equilibrium state of open quantum systems
• Controlling Matter Phases beyond Markov
• Stable bipolarons in open quantum systems
• Kondo QED: The Kondo effect and photon trapping in a two-impurity Anderson model ultra-strongly coupled to light
• Steady state in ultrastrong coupling regime: perturbative expansion and first orders
• Bath-induced interactions and transient dynamics in open quantum systems at strong coupling: Effective Hamiltonian approach
• Fixing detailed balance in ancilla-based dissipative state engineering
• Modeling the unphysical pseudomode model with physical ensembles: simulation, mitigation, and restructuring of non-Markovian quantum noise
• Non-Markovian skin effect
• Simulating spin biology using a digital quantum computer: Prospects on a near-term quantum hardware emulator
• Page-curve-like entanglement dynamics in open quantum systems
• Intermediate Times Dilemma for Open Quantum System: Filtered Approximation to The Refined Weak Coupling Limit
• Spectral theory of non-Markovian dissipative phase transitions
• Dynamics of the Non-equilibrium spin Boson Model: A Benchmark of master equations and their validity
• A hierarchical equations of motion (HEOM) analog for systems with delay: illustrated on inter-cavity photon propagation
• Grassmann time-evolving matrix product operators: An efficient numerical approach for fermionic path integral simulations
• Unifying methods for optimal control in non-Markovian quantum systems via process tensors
• From Stochastic Hamiltonian to Quantum Simulation: Exploring Memory Effects in Exciton Dynamics
• Nonequilibrium quantum heat transport between structured environments
• Time-dependent electron transfer and energy dissipation in condensed media
• Input-Output Hierarchical Equations Of Motion
• Schwinger-Keldysh non-perturbative field theory of open quantum systems beyond the Markovian regime: Application to spin-boson and spin-chain-boson models
• High-frequency tails in spectral densities
• Non-perturbative exciton transfer rate analysis of the Fenna-Matthews-Olson photosynthetic complex under reduced and oxidised conditions
• Limitations of strong coupling in non-Markovian quantum thermometry
• Quantum-inspired dynamical models on quantum and classical annealers
• Continuous quantum correction on Markovian and Non-Markovian models
• Separation of relaxation timescales via strong system-bath coupling: Dissipative three-level system as a case study
• Quantum Jump Approach for Photosynthetic Energy Transfer with Chemical Reaction and Fluorescence Loss
• Making Non-Markovian master equations accessible with approximate environments