Making Quantum Algorithms Scalable: Simplifying Quantum Expressions and Encoding in High-level Quantum Programming

Quantum programming often navigates the challenge of balancing low-level control with high-level abstractions to streamline algorithm development. An example of such a challenge is encoding a number into a quantum state. While traditional digital encoding methods, such as computational-basis encoding, are conceptually similar to classical encoding, they must account for the unique features of quantum mechanics, including superposition and entanglement. However, these can still be represented in high-level quantum programming languages similarly to their representations in classical languages. It becomes more complicated regarding analog encoding, which uses amplitude or phase. In these cases, quantum programming languages need new constructs that don’t exist in classical programming languages.

This talk introduces a higher-level language construct from the Qmod programming language for phase encoding. This construct simplifies the representation of quantum expressions and makes the development of algorithms more intuitive, allowing for scalable algorithms that are almost impossible to write using gate-based descriptions. A key advancement in this approach is the ability to represent cost functions without explicit Hamiltonians. We will explore how this abstraction improves the development of quantum algorithms like the Quantum Approximate Optimization Algorithm (QAOA), showing how it enables more intuitive, scalable, and powerful algorithm design