quAPL: Modeling Quantum Computation in an Array Programming Language - Nuncz-Corrales, Santiago; Frenkel, Marcos; Abreu, Bruno (2023 IEEE International Conference on Quantum Computing and Engineering (QCE), 2023)
Most contemporary quantum programming languages describe computation as circuits, using a host classical counterpart to drive the execution of quantum programs. However, the circuit model adds expensive complexity to quantum algorithmic development and decreases the transparency of connections between syntax and formal semantics in quantum programs. We argue that producing a high-level quantum programming language without reference to circuits is possible and necessary. We summarize desirable features in future high-level quantum programming languages and provide evidence supporting array pro-gramming languages as a natural paradigm for quantum algorithmic expression at the circuit level and beyond. We highlight why APL is a profitable host programming language to attain this goal progressively. In particular, we demonstrate how features provided by APL, such as native support of complex numbers and matrix operations, naturally capture quan-tum operations while bringing a less cluttered syntax that encodes and encapsulates the linear character of quantum circuit execution. We discuss implementation details of quAPL, an APL library for quantum circuit specification, simulation, and execution intended to provide a gradual ramp toward developing composable procedural abstractions. Finally, we discuss the broader implications of our work and the next steps in our research program.