RapunSL: Untangling Quantum Computing with Separation, Linear Combination and Mixing

TL;DR

RapunSL is a novel quantum separation logic that enhances reasoning scalability for quantum programs by introducing new locality notions and connectives, enabling effective reasoning about superposition and mixed states.

Contribution

It introduces RapunSL, a quantum separation logic with new locality notions and connectives, improving reasoning scalability for quantum states.

Findings

Soundly reduces superposition reasoning to pure states

Simplifies mixed state reasoning via outcome-locality

Demonstrates scalability improvements on case studies

Abstract

Quantum Separation Logic (QSL) has been proposed as an effective tool to improve the scalability of deductive reasoning for quantum programs. In QSL, separation is interpreted as disentanglement, and the frame rule brings a notion of entanglement-local specification (one that only talks about the qubits entangled with those acted upon by the program). In this paper, we identify two notions of locality unique to the quantum domain, and we construct a novel quantum separation logic, RapunSL, which is able to soundly reduce reasoning about superposition states to reasoning about pure states (basis-locality), and reasoning about mixed states arising from measurement to reasoning about pure states (outcome-locality). To do so, we introduce two connectives, linear combination and mixing, which together with separation provide a dramatic improvement in the scalability of reasoning, as we demonstrate on a series of challenging case studies.