# Wavefunction positivization via automatic differentiation

## TL;DR

This paper presents a method using automatic differentiation to find local unitary transformations that convert complex wavefunctions into positive-real forms, improving the sign structure analysis in quantum many-body systems.

## Contribution

It introduces a systematic approach to wavefunction positivization using quantum circuits and automatic differentiation, applicable to complex quantum phases.

## Key findings

- Significant improvement in wavefunction positivity for a Heisenberg ladder model.
- Identification of phases where simple local unitaries suffice for sign removal.
- Demonstration of complex phases requiring deeper circuits for sign structure removal.

## Abstract

We introduce a procedure to systematically search for a local unitary transformation that maps a wavefunction with a non-trivial sign structure into a positive-real form. The transformation is parametrized as a quantum circuit compiled into a set of one and two qubit gates. We design a cost function that maximizes the average sign of the output state and removes its complex phases. The optimization of the gates is performed through automatic differentiation algorithms, widely used in the machine learning community. We provide numerical evidence for significant improvements in the average sign for a two-leg triangular Heisenberg ladder with next-to-nearest neighbour and ring-exchange interactions. This model exhibits phases where the sign structure can be removed by simple local one-qubit unitaries, but also an exotic Bose-metal phase whose sign structure induces "Bose surfaces" with a fermionic character and a higher entanglement that requires deeper circuits.