Efficient sampling avoids the exponential wall in classical simulations of fidelity

Area of Science:

• Computational Physics
• Quantum Chemistry

Background:

• Simulating classical fidelity is crucial for understanding complex systems.
• Current algorithms face exponential computational costs with increasing degrees of freedom.

Purpose of the Study:

• To analyze the efficiency of existing algorithms for classical fidelity simulation.
• To develop a novel algorithm with improved scalability.
• To propose a general analytical method for estimating trajectory-based method efficiency.

Main Methods:

• Analysis of computational costs for existing fidelity simulation algorithms.
• Development and presentation of a new dimensionality-independent algorithm.
• Formulation of an analytical approach for efficiency estimation.
• Numerical validation on systems with extremely large phase space volumes.

Main Results:

• Existing algorithms exhibit exponential scaling of computational cost with system dimensionality.
• The proposed algorithm achieves convergence independent of system dimensionality.
• The new algorithm is unique within its continuous family for this property.
• Numerical results confirm convergence for systems vastly exceeding initial state volumes.

Conclusions:

• The novel algorithm offers significant computational advantages for classical fidelity simulation.
• The analytical approach can accelerate calculations of classical correlation functions.
• This work provides a scalable method for high-dimensional classical simulations.