  The ground state properties of quantum many-body systems are a subject of
interest across chemistry, materials science, and physics. Thus, algorithms for
finding ground states can have broad impacts. Variational quantum algorithms
are one class of ground state algorithms that has received significant
attention in recent years. These algorithms utilize a hybrid quantum-classical
computing framework to prepare ground states on quantum computers. However,
this requires solving a classical optimization problem that can become
prohibitively expensive in high dimensions. Here, we develop formulations of
feedback-based quantum algorithms for ground state preparation that can be used
to address this challenge for two broad classes of Hamiltonians: Fermi-Hubbard
Hamiltonians, and molecular Hamiltonians represented in second quantization.
Feedback-based quantum algorithms are optimization-free; in place of classical
optimization, quantum circuit parameters are set according to a deterministic
feedback law derived from quantum Lyapunov control principles. This feedback
law guarantees a monotonic improvement in solution quality with respect to the
depth of the quantum circuit. A variety of numerical illustrations are provided
that analyze the convergence and robustness of feedback-based quantum
algorithms for these problem classes.
