  This paper presents a theory and an empirical evaluation of Higher-Order
Quantum-Inspired Genetic Algorithms. Fundamental notions of the theory have
been introduced, and a novel Order-2 Quantum-Inspired Genetic Algorithm (QIGA2)
has been presented. Contrary to all QIGA algorithms which represent quantum
genes as independent qubits, in higher-order QIGAs quantum registers are used
to represent genes strings which allows modelling of genes relations using
quantum phenomena. Performance comparison has been conducted on a benchmark of
20 deceptive combinatorial optimization problems. It has been presented that
using higher quantum orders is beneficial for genetic algorithm efficiency, and
the new QIGA2 algorithm outperforms the old QIGA algorithm which was tuned in
highly compute intensive metaoptimization process.
