Programming with Concurrency for Quantum Computers

As the hardware for quantum computers becomes physically realisable for larger numbers of qubits, the question arises on how to efficiently program them at scale. In particular, unlike classical computers, quantum computers admit an inherent notion of parallelism that should be exploited programmatically. Furthermore, size constraints of individual quantum computers suggest that there should be a future for distributed quantum computing - multiple quantum computers working together by passing messages to solve a single larger problem.

Due to the novelty of the paradigm, models and programming expressions for these are relatively understudied in the field of quantum programming languages. In classical programming languages, methods of expressing parallelism tend to be added as an extra feature to existing languages. If instead concurrent programs and distribution of these should be core primitives of quantum programs, what do models of these look like, how can we give them a semantics, and how do they relate their classical analogues?

This project aims to answer these questions by taking inspiration from developments in programming languages for classical concurrency and completing them to align with our known models of quantum computing. This stems from the idea that the general model of quantum computing itself already contains parallelism intrinsically.

From this follows three core objectives: 1. Develop a model of classical concurrency and extend it to model quantum computing.

2. From this derive a quantum programming language with primitives for expressing parallelism and distributed quantum computing with message passing. 3. Prototype an implementation of this language.

To do this we begin by building a category theoretic model of distributed computation with message passing, drawing on recent developments in programming languages for this such as choreographic programming. These are languages which model communication between systems and their concurrent computation explicitly, so provide a good foundation for our model.

Working within a category theoretic setting will allow us to take advantage of the mathematical bridge it provides between categorical models of type theories for programming languages and for axiomatisations of quantum systems and quantum computation. In doing this we hope to develop clean mathematical models of distributed quantum computation and gain further insight into useful and expressive ways to program quantum computers.