QPL: A Relations-First Programming Language for Measurement-Based Quantum Computing

    We present QPL (Quantum Process Language), a relations-first quantum programming language that compiles directly to Measurement-Based Quantum Computing (MBQC) patterns without intermediate gate decomposition. Unlike gate-based quantum languages that must convert circuits to cluster states through expensive decomposition, QPL treats quantum entanglement as a first-class primitive, enabling natural expression of the graph states and measurement patterns that power photonic quantum computers and fault-tolerant surface codes.

     We introduce four core abstractions—QuantumRelation, QuantumQuestion, MeasurementPattern, and Perspective—that map directly to MBQC concepts. Our implementation demonstrates complete compilation from relations-first programs to executable measurement patterns, including graph state extraction, pattern generation for standard quantum gates (H, X, Z, S, T, CNOT, CZ), and adaptive Pauli corrections. Validation against quantum teleportation achieves fidelity of 1.0, with 47 tests verifying physics correctness including Bell correlations and cross-basis measurements.

     QPL targets photonic quantum computing platforms where MBQC is the native execution model, addressing the semantic gap between current gate-based programming abstractions and measurement-based hardware.