Foundations of Quantum Programming

7.4 Solving recursive equations in the free fock space

As convinced by an example of a recursive quantum walk at the end of Section 7.2, we have to deal with a quantum system with a variable number of identical particles in order to model the behavior of quantum “coins” employed in the execution of a quantum recursive program. So, a mathematical framework for this purpose, namely second quantization, was introduced in the last section. Indeed, second quantization provides us with all of the necessary tools for defining the semantics of quantum recursion. The purpose of this and the next sections is to carefully define the semantics of quantum recursive programs. This will be done in two steps. In this section, we show how to solve recursive ...