A long-standing aim of quantum information research is to understand 
what gives quantum computers their advantage. Such an understanding 
would be of great benefit when attempting to build a quantum computer. 
Here we present a framework that uses classical resources but still is 
able to efficiently run, for example Deutsch-Jozsa and Simon's 
algorithms, and also can run Shor's factoring algorithm with some 
systematic errors. We also perform an experiment factoring 15 using 
classical pass-transistor logic at room temperature, with smaller 
systematic errors than any former experimental implementation, and the 
same amount of resources in time and space as a scalable quantum 
computer. Our results give further insight into the resources needed for 
quantum computation, aiming for a true understanding of the subject.