Tailored Quantum Alternating Operator Ansätzes for Circuit Fault Diagnostics

Abstract

The quantum alternating operator ansatz (QAOA) and constrained quantum annealing (CQA) restrict the evolution of a quantum system to remain in a constrained space, often with a dimension much smaller than the whole Hilbert space. A natural question when using quantum annealing or a QAOA protocol to solve an optimization problem is to select an initial state for the wavefunction and what operators to use to evolve it into a solution state. In this work, we construct several ansatzes tailored to solve the combinational circuit fault diagnostic (CCFD) problem in different subspaces related to the structure of the problem, including superpolynomially smaller subspaces than the whole Hilbert space. We introduce a family of dense and highly connected circuits that include small instances but can be scaled to larger sizes as a useful collection of circuits for comparing different quantum algorithms. We compare the different ansätzes on instances randomly generated from this family under different parameter selection methods. The results support that ansätzes more closely tailored to exploiting the structure of the underlying optimization problems can have better performance than more generic ansätzes.