A Quantum Interpretation of Bunched Logic for Quantum Separation Logic

TL;DR

This paper introduces a quantum-compatible model of Bunched Implications logic to reason about quantum states, enabling formal verification of quantum protocols and identifying flaws in quantum algorithm tutorials.

Contribution

It develops a novel quantum interpretation of BI logic and a program logic for quantum programs, extending separation logic to quantum computing.

Findings

Proved security of quantum one-time pad and secret sharing

Identified a flaw in Google Cirq's VQA tutorial

Demonstrated the logic's usefulness in quantum program verification

Abstract

We propose a model of the substructural logic of Bunched Implications (BI) that is suitable for reasoning about quantum states. In our model, the separating conjunction of BI describes separable quantum states. We develop a program logic where pre- and post-conditions are BI formulas describing quantum states -- the program logic can be seen as a counterpart of separation logic for imperative quantum programs. We exercise the logic for proving the security of quantum one-time pad and secret sharing, and we show how the program logic can be used to discover a flaw in Google Cirq's tutorial on the Variational Quantum Algorithm (VQA).