QRL: A Relations-First Quantum Programming Language

We present QRL (Quantum Relational Language), a relations-first quantum programming language built from first principles of information theory and relational physics. QRL treats quantum entanglement as a first-class citizen rather than a derived concept. The language includes core abstractions for quantum causal models (CPTPMap, ProcessMatrix, QuantumSwitch, QuantumCausalDAG) and domain libraries for quantum chemistry (FCI, Jordan-Wigner transformation, orbital entanglement), quantum sensing (quantum Fisher information, Heisenberg limit), and quantum biology (FMO photosynthetic complex, radical pair mechanism). Bell inequality and GHZ/Mermin tests are hardware-verified on Quandela qpu:belenos (S = 2.61 ± 0.08, 7σ violation). Bell (https://bell.entangledcode.dev) is the natural language interface platform built on QRL, live — ask a quantum question in plain English and receive a first-principles computation. Source code: https://github.com/entangledcode/qrl. Paper in preparation, targeting QPL 2027.