The basic infrastructure developed so far is sufficient for small-scale quantum algorithms. It is also a great learning tool. However, for complex algorithms with many more qubits and gates, this matrix-based infrastructure does not scale. This chapter improves the infrastructure to scale to problems with up to 30 qubits and tens of thousands of gates.

First, the chapter introduces an elegant circuit abstraction. A method to apply operators with linear complexity comes next, which is a significant improvement over the cubic or quadratic methods presented previously. Acceleration with C++ enables another 100x speedup. Finally, a sparse state representation is being discussed at length, which can be the best-performing implementation for many circuits.