Unitary Expressions: A Necessary Abstraction for Quantum Programming Languages and Systems

Quantum programs use gates represented by unitary operators as their basic instructions. Current programming languages, systems, and software development toolkits identify these operational gates by their labels, which requires a common understanding of their meanings. However, in the developing software ecosystem surrounding quantum computing—spanning high-level programming systems to low-level control stacks—this identification process is often error-prone, challenging to debug, maintenance-heavy, and resistant to change. In this work, we shift the burden of identification from gate labels to unitary expressions, a form of symbolic computation. This novel embeddable domain-specific language is adaptive to emerging technologies and enables longer software lifecycles. We introduce OpenQudit, a system for describing, parsing, optimizing, analyzing, and utilizing unitary expressions to automatically accommodate emerging gates and effortlessly translate programs between software ecosystems without bias towards binary quantum computation.