On Penalty Functions for Variational Quantum Algorithms

Situated between a dedicated quantum emulator—which bootstraps one quantum system to mimic another—and a fully programmable quantum processor, lies the celebrated gate-based quantum processors of today. For utilitarian purposes, today's quantum processors embody what is known as the variational or hybrid-quantum-classical model of quantum computation. While theoretically universal for quantum computation, the practical appeal of the variational model lies in maximizing the use-case capacity of low-depth, parameterized quantum circuits, albeit at the cost of outer loop classical optimization. This model, a Hamiltonian-based computation framework, hinges on minimizing an energy function to prepare an approximate ground state. This talk presents recent findings related to penalty function constructions.