Imaginary-time-enhanced feedback-based quantum algorithms for universal ground-state preparation

TL;DR

This paper introduces ITE-FALQON, an improved quantum algorithm that enhances feedback-based ground-state preparation by incorporating imaginary-time steps, effectively handling degeneracies in strongly correlated systems.

Contribution

The paper proposes a novel imaginary-time-enhanced feedback quantum algorithm that overcomes degeneracy issues in FALQON, enabling reliable ground-state preparation.

Findings

ITE-FALQON achieves consistent ground-state convergence across various fillings.

The hybrid method suppresses excited states and escapes degenerate subspaces.

It provides a practical approach for scalable quantum ground-state preparation.

Abstract

Preparing ground states of strongly correlated quantum systems is a central goal in quantum simulation and optimization. The feedback-based quantum algorithm (FALQON) provides an attractive alternative to variational methods with a fully quantum feedback rule, but it fails in the presence of spectral degeneracies, where the feedback signal collapses and the evolution cannot reach the ground state. Using the Fermi-Hubbard model on lattices up to 3x3, we show that this breakdown appears at half-filling on the 2x2 lattice and extends to both half-filled and doped configurations on the 3x3 lattice. We then introduce an imaginary-time-enhanced FALQON (ITE-FALQON) scheme, which inserts short imaginary-time evolution steps into the feedback loop. The hybrid method suppresses excited-state components, escapes degenerate subspaces, and restores monotonic energy descent. The ITE-FALQON achieves a reliable ground-state convergence across all fillings, providing a practical route to scalable ground-state preparation in strongly correlated quantum systems.