qPCF: a language for quantum circuit computations

We propose qPCF, a functional language able to define and manipulate quantum circuits in an easy and intuitive way. qPCF follows the tradition of “quantum data & classical control” languages, inspired to the QRAM model. Ideally, qPCF computes finite circuit descriptions which are offloaded to a quantum co-processor (i.e. a quantum device) for the execution. qPCF extends PCF with a new kind of datatype: quantum circuits. The typing of qPCF is quite different from the mainstream of “quantum data & classical control” languages that involves linear/exponential modalities. qPCF uses a simple form of dependent types to manage circuits and an implicit form of monad to manage quantum states via a destructive-measurement operator.