QC Optimization
Savo Glisic, Beatriz Lorenzo · 2022
This chapter discusses a class of hybrid quantum-classical algorithms based on the variational approach. These algorithms provide an approximate solution to the problem at hand by encoding it in the state of a quantum computer. The chapter also discusses more general problem of convex optimization in quantum information theory. Combinatorial optimization problems are specified by n bits and m clauses. Each clause is a constraint on a subset of the bits that is satisfied for certain assignments of those bits and unsatisfied for the other assignments. Having discussed the general idea behind the HHL algorithm and its possible application in drastically speeding up multiple regression, the chapter moves on to the quantum circuit design meant to solve the 4 × 4 linear system. It presents the solutions of a set of n first-order nonlinear ordinary differential equations.