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The Sign Problem in Density Matrix Quantum Monte Carlo.

Hayley R Petras1, William Z Van Benschoten1, Sai Kumar Ramadugu1

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Summary
This summary is machine-generated.

Density matrix quantum Monte Carlo (DMQMC) faces a sign problem, requiring large populations. An interaction picture modification (IP-DMQMC) significantly reduces this computational cost for quantum systems.

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Area of Science:

  • Computational Quantum Chemistry
  • Quantum Monte Carlo Methods
  • Electronic Structure Theory

Background:

  • Density matrix quantum Monte Carlo (DMQMC) stochastically samples the N-particle thermal density matrix for accurate energy calculations.
  • The sign problem in DMQMC necessitates a large walker population (N_c), limiting its application due to storage and compute time constraints.
  • DMQMC represents the density matrix in an outer product basis of Slater determinants, leading to a large sampling space.

Purpose of the Study:

  • To systematically investigate the sign problem in DMQMC using atomic and molecular systems.
  • To compare the computational cost and scaling of canonical DMQMC with its interaction picture modification (IP-DMQMC).
  • To assess the impact of propagation symmetry on the sign problem and computational efficiency.

Main Methods:

  • Numerical simulations of atomic and molecular systems using DMQMC.
  • Analysis of the critical walker population (N_c) required to mitigate the sign problem.
  • Comparison of canonical DMQMC with IP-DMQMC, focusing on propagation characteristics (symmetric vs. asymmetric).

Main Results:

  • The critical walker population for DMQMC scales quadratically with that of Full Configuration Interaction Quantum Monte Carlo (FCIQMC).
  • IP-DMQMC exhibits a linearly scaling critical walker population with FCIQMC, significantly reducing the computational cost.
  • Asymmetric propagation in canonical DMQMC leads to prohibitive stochastic errors, unlike the adapted IP-DMQMC.
  • The equivalence between IP-DMQMC and FCIQMC extends to the initiator approximation, facilitating studies of larger systems.

Conclusions:

  • IP-DMQMC effectively ameliorates the sign problem in DMQMC, making it more computationally feasible.
  • The choice of propagation mode (symmetric vs. asymmetric) critically impacts the efficiency and error of DMQMC.
  • IP-DMQMC offers a promising approach to overcome the cost associated with basis transformations in quantum Monte Carlo methods.