# Making Trotters Sprint: A Variational Imaginary Time Ansatz for Quantum Many-body Systems

## TL;DR

This paper presents a variational imaginary time ansatz for quantum many-body ground states, demonstrating improved scaling and potential mitigation of the sign problem in certain models.

## Contribution

The authors introduce a novel variational wavefunction using alternating imaginary time evolution, showing superior scaling properties and entanglement growth management.

## Key findings

- Imaginary time scales logarithmically with system size.
- Alternating evolution dynamics enable exponential entanglement growth.
- Potential to mitigate the sign problem in quantum simulations.

## Abstract

We introduce a variational wavefunction for many-body ground states that involves imaginary time evolution with two different Hamiltonians in an alternating fashion with variable time intervals. We successfully apply the ansatz on the one- and two-dimensional transverse-field Ising model and systematically study its scaling for the one-dimensional model at criticality. We find the total imaginary time required scales logarithmically with system size, in contrast to the linear scaling in conventional Quantum Monte Carlo. We suggest this is due to unique dynamics permitted by alternating imaginary time evolution, including the exponential growth of bipartite entanglement. For generic models, the superior scaling of our ansatz potentially mitigates the negative sign problem at the expense of having to optimize variational parameters.