Constrained quantum optimisation for customer data science

Abstract

One of the potential use cases of a quantum computer is to solve combinatorial optimisation problems more efficiently than is possible with the most advanced classical computers. Combinatorial optimisation problems that appear in industry often involve a large number of constraints. This thesis investigates algorithmic techniques that improve the performance of quantum optimisation algorithms in solving problems with constraints. We test these techniques on customer data science problems.

We study an alternative penalty method for encoding constraints in Ising Hamiltonians, which can be applied to various quantum algorithms. This method only introduces linear terms to the Ising Hamiltonian, allowing for more efficient use of hardware resources than the standard quadratic penalty method. These efficiency improvements are particularly beneficial for near-term devices with a limited number of qubits that are sparsely connected. We analyse the impact of using this alternative encoding method on the performance of the quantum approximate optimisation algorithm and quantum annealing applied to example problems in customer data science. Our results are based on numerical simulations and experiments on quantum hardware.

We introduce a new variant of the quantum approximate optimisation algorithm that improves its ability to solve problems with constraints. In this variant of the algorithm, the strengths of penalty functions are associated with additional variational parameters, allowing them to take different values in each layer of the quantum circuit. We perform numerical simulations of multiple variants of the quantum approximate optimisation algorithm and compare their performance.