Quantum computing for biophysical and optimization problems

The remarkable progress of quantum technologies over recent years has driven significant efforts toward developing algorithms with applications to a wide range of research fields. Beyond fully quantum algorithms — whose efficacy remains constrained by technological limitations — hybrid quantum-classical algorithms and quantum-inspired methods have emerged as promising avenues for tackling real-world problems. In this study, we focus on two particularly challenging biophysics problems: protein design and polymer sampling. Protein design involves engineering the primary sequence of a protein to ensure that it folds into a specific target conformation of biological interest. Our approach employs a physics-based machine learning model that incorporates a QUBO (Quadratic Unconstrained Binary Optimization) encoding of the design problem that is amenable to adiabatic quantum platforms such as the D-Wave device. For the polymer sampling problem — where the objective is to sample both the sequence and the conformation of polymers according to a thermal distribution — we establish a deep connection with an Abelian lattice gauge theory populated with fermions. Building on this theoretical framework, we develop a quantum-inspired Monte Carlo protocol that not only eliminates the sign problem but also features a decorrelation time that scales linearly with the system size in the dense-melt polymer regime, providing a novel approach to computational polymer physics. Within the framework of lattice gauge theories, where physically realizable measurements are heavily constrained by local symmetries, we analyze from the quantum-information perspective the problem of pinpointing entangled states by resorting to entanglement witnesses. Furthermore, we develop a numerical optimization protocol that enhances the effectiveness of entanglement witnesses while ensuring their physical implementation within the lattice gauge theory framework.