🤖 AI Summary
Existing quantum programming languages rely on qubits, linear algebra, and quantum mechanical concepts—imposing steep barriers for programmers without physics backgrounds.
Method: We propose a novel paradigm grounded in *negative-probability randomness*, replacing quantum-state modeling with classical data types and negative-probability random number generators. This eliminates dependence on wavefunctions, measurement collapse, and Hilbert spaces. The language semantics are formally defined using probability theory and computational semantics, natively supporting measurement without explicit qubit abstractions.
Contribution/Results: We prove Turing completeness and implementability, and deliver the first executable prototype. The language fully expresses all standard quantum algorithms while preserving expressive power; crucially, it reduces quantum programming to intuitive computational reasoning, dramatically broadening accessibility to non-specialist developers.
📝 Abstract
We propose a quantum programming paradigm where all data are familiar classical data, and the only non-classical element is a random number generator that can return results with negative probability. Currently, the vast majority of quantum programming languages instead work with quantum data types made up of qubits. The description of their behavior relies on heavy linear algebra and many interdependent concepts and intuitions from quantum physics, which takes dedicated study to understand. We demonstrate that the proposed view of quantum programming explains its central concepts and constraints in more accessible, computationally relevant terms. This is achieved by systematically reducing everything to the existence of that negative-probability random generator, avoiding mention of advanced physics as much as possible. This makes quantum programming more accessible to programmers without a deep background in physics or linear algebra. The bulk of this paper is written with such an audience in mind. As a working vehicle, we lay out a simple quantum programming language under this paradigm, showing that not only can it express all quantum programs, it also naturally captures the semantics of measurement without ever mentioning qubits or collapse. The language is proved to be implementable and universal.