Re-anchoring quantum monte-carlo with tensor-train sketching

Abstract:

We propose a novel algorithm for calculating the ground-state energy of quantum many-body systems by combining auxiliary-field quantum Monte Carlo (AFQMC) with tensor-train sketching. In AFQMC, having an effective trial wavefunction to guide the random walk is crucial for reducing sign problems. Typically, this trial wavefunction is fixed throughout the simulation.

Our proposed method iterates between determining a new trial wavefunction in the form of a tensor train, derived from the current walkers, and using this updated trial wavefunction to anchor the next phase of AFQMC. Numerical results demonstrate that our algorithm is highly accurate for large spin systems, achieving a relative error of 1e-5 in estimating ground-state energies. Additionally, the overlap between our estimated trial wavefunction and the ground-state wavefunction converges to a value between 0.7 and 0.9. We provide a convergence proof, highlighting how an effective trial wavefunction can reduce the variance in the AFQMC energy estimate.