  We propose a hybrid classical-quantum digitized-counterdiabatic algorithm to
tackle the protein folding problem on a tetrahedral lattice.
Digitized-counterdiabatic quantum computing is a paradigm developed to compress
quantum algorithms via the digitization of the counterdiabatic acceleration of
a given adiabatic quantum computation. Finding the lowest energy configuration
of the amino acid sequence is an NP-hard optimization problem that plays a
prominent role in chemistry, biology, and drug design. We outperform
state-of-the-art quantum algorithms using problem-inspired and
hardware-efficient variational quantum circuits. We apply our method to
proteins with up to 9 amino acids, using up to 17 qubits on quantum hardware.
Specifically, we benchmark our quantum algorithm with Quantinuum's trapped
ions, Google's and IBM's superconducting circuits, obtaining high success
probabilities with low-depth circuits as required in the NISQ era.
