Universal Prony fitting decomposition for optimized hierarchical quantum master equations

Abstract

In this work, we propose the Prony fitting decomposition (PFD) as an accurate and efficient exponential series method, applicable to arbitrary interacting bath correlation functions. The resulting hierarchical equations of motion (HEOM) formalism is greatly optimized, especially in extremely low temperature regimes that would be inaccessible with other methods. For demonstration, we calibrate the present PFD against the celebrated Padé spectrum decomposition method, followed by converged HEOM evaluations on the single-impurity Anderson model system.

4 pages, 3 figures

References in corpus (4)

• Continuous-time Monte Carlo methods for quantum impurity models
• Non-perturbative treatment of non-Markovian dynamics of open quantum systems
• Dynamics of quantum dissipation systems interacting with bosonic canonical bath: Hierarchical equations of motion approach
• Taming Quantum Noise for Efficient Low Temperature Simulations of Open Quantum Systems

Cited by in corpus (34)

• Taming Quantum Noise for Efficient Low Temperature Simulations of Open Quantum Systems
• Tree tensor network state approach for solving hierarchical equations of motion
• Efficient low temperature simulations for fermionic reservoirs with the hierarchical equations of motion method: Application to the Anderson impurity model
• Quantum Monte Carlo in the steady-state
• Quantum mechanics of open systems: Dissipaton theories
• Quasi-Lindblad pseudomode theory for open quantum systems
• Towards Quantum Simulation of Non-Markovian Open Quantum Dynamics: A Universal and Compact Theory
• Survey of the Hierarchical Equations of Motion in Tensor-Train format for non-Markovian quantum dynamics
• A simple improved low temperature correction for the hierarchical equations of motion
• Simulating Non-Markovian Quantum Dynamics on NISQ Computers Using the Hierarchical Equations of Motion
• Discretized hierarchical equations of motion in mixed Liouville--Wigner space for two-dimensional vibrational spectroscopies of liquid water
• Managing Temperature in Open Quantum Systems Strongly Coupled with Structured Environments
• A statistical quasi-particles thermofield theory with Gaussian environments: System-bath entanglement theorem for nonequilibrium correlation functions
• Thermodynamic quantum Fokker-Planck equations and their application to thermostatic Stirling engine
• Current-induced bond rupture in single-molecule junctions: Effects of multiple electronic states and vibrational modes
• Extended dissipaton equation of motion for electronic open quantum systems: Application to the Kondo impurity model
• Open quantum systems with nonlinear environmental backactions: Extended dissipaton theory versus core-system hierarchy construction
• Dissipatons as generalized Brownian particles for open quantum systems: Dissipaton-embedded quantum master equation
• QD3SET-1: A Database with Quantum Dissipative Dynamics Data Sets
• Current-induced forces in nanosystems: A hierarchical equations of motion approach
• Minimal pole representation for spectral functions
• Tree tensor network hierarchical equations of motion based on time-dependent variational principle for efficient open quantum dynamics in structured thermal environments
• Coupled Lindblad pseudomode theory for simulating open quantum systems
• Correlated vibration-solvent and Duschinsky effects on electron transfer dynamics and optical spectroscopy
• Universal Structure of Computing Moments for Exact Quantum Dynamics: Application to Arbitrary System-Bath Couplings
• Multimode Brownian oscillators: Exact solutions to heat transport
• Spin-lattice relaxation with non-linear couplings: Comparison between Fermi's golden rule and extended dissipaton equation of motion
• Spectral Densities, Structured Noise and Ensemble Averaging within Open Quantum Dynamics
• Machine learning meets $\mathfrak{su}(n)$ Lie algebra: Enhancing quantum dynamics learning with exact trace conservation
• Environment-Mediated Long-Ranged Correlations in Many-Body System
• Extended Non-Markovian Stochastic Schrödinger Equation with Complex Frequency Modes for General Basis Functions
• Toward Quantum-Aware Machine Learning: Improved Prediction of Quantum Dissipative Dynamics via Complex Valued Neural Networks
• Generalized quantum master equation from memory kernel coupling theory
• Subtleties in the pseudomodes formalism