Quantum Programming Without the Quantum Physics
Jun Inoue
TL;DR
The paper addresses the steep entry barrier of traditional quantum programming by recasting quantum computation as probabilistic programming with negative probabilities, thereby removing the need to manipulate qubits directly. It introduces QPP, a paradigm where classical data undergoes quantum-like nondeterminism via signed amplitudes, and presents QPPL, a language whose operations are implementable and universal under this view. Key contributions include a formal two-layer probability semantics for measurement, a Deutsch-like programming example illustrating destructive interference, and a demonstration that quantum behavior can be captured without qubits while preserving unitarity and reversibility. This framework aims to make quantum programming more accessible to general programmers and to provide intuitive tools for understanding and designing quantum algorithms, with potential for practical language growth, uncomputation, and inter-program communication across multiple quantum resources.
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.