A Projector Quantum Monte Carlo Method for non-linear wavefunctions

Abstract

We reformulate the projected imaginary-time evolution of Full Configuration Interaction Quantum Monte Carlo in terms of a Lagrangian minimization. This naturally leads to the admission of polynomial complex wavefunction parameterizations, circumventing the exponential scaling of the approach. While previously these functions have traditionally inhabited the domain of Variational Monte Carlo, we consider recently developments for the identification of deep-learning neural networks to optimize this Lagrangian, which can be written as a modification of the propagator for the wavefunction dynamics. We demonstrate this approach with a form of Tensor Network State, and use it to find solutions to the strongly-correlated Hubbard model, as well as its application to a fully periodic ab-initio Graphene sheet. The number of variables which can be simultaneously optimized greatly exceeds alternative formulations of Variational Monte Carlo, allowing for systematic improvability of the wavefunction flexibility towards exactness for a number of different forms, whilst blurring the line between traditional Variational and Projector quantum Monte Carlo approaches.

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• Complementary First and Second Derivative Methods for Ansatz Optimization in Variational Monte Carlo
• Excited-state diffusion Monte Carlo calculations: a simple and efficient two-determinant ansatz
• Symmetry projected Jastrow mean field wavefunction in variational Monte Carlo
• An accelerated linear method for optimizing non-linear wavefunctions in variational Monte Carlo
• Iterative Power Algorithm for Global Optimization with Quantics Tensor Trains
• Improved Optimization for the Neural-network Quantum States and Tests on the Chromium Dimer
• Charge-transfer excited states: Seeking a balanced and efficient wave function ansatz in variational Monte Carlo
• A hybrid approach to extending selected configuration interaction and full configuration interaction quantum Monte Carlo
• Reduced Scaling Hilbert Space Variational Monte Carlo
• The full configuration interaction quantum Monte Carlo method in the lens of inexact power iteration
• Constructing `full-frequency' spectra via moment constraints for coupled cluster Green's functions
• Accelerating Stochastic Quantum Chemistry
• Fixed and partial-node approximations in Slater determinant space for molecules
• Full Configuration Interaction Excited-State Energies in Large Active Spaces from Subspace Iteration with Repeated Random Sparsification
• All-mode Renormalization for Tensor Network with Stochastic Noise
• Quantum-Classical Auxiliary Field Quantum Monte Carlo with Matchgate Shadows on Trapped Ion Quantum Computers
• In-Depth Investigation of Phase Transition Phenomena in Network Models Derived from Lattice Models
• Improved Fast Randomized Iteration Approach to Full Configuration Interaction