Problem
Research questions and friction points this paper is trying to address.
Continuous-variable quantum computing
formal semantics
program verification
quantum programming languages
semantic foundations
Reasoning about Continuous-Variable Quantum Systems
🤖 AI Summary
This work addresses the lack of a formal semantic foundation for continuous-variable quantum computing, which hinders rigorous program verification. To overcome this, the paper proposes closed positive quadratic forms as semantic predicates, providing a unified characterization of finite expectations, domains of finiteness, and infinite penalties while satisfying essential closure properties such as those of weakest preconditions. Building upon formal semantics, quantitative predicate domain theory, and weakest precondition calculus, the authors develop a program verification framework capable of reasoning about unbounded values in infinite-dimensional quantum systems. The framework is successfully applied to practical cases such as Gottesman–Kitaev–Preskill (GKP) error-correcting codes, yielding the first rigorous proof of their second-moment bounds and thereby demonstrating both the effectiveness and expressive power of the proposed approach.
📝 Abstract
Continuous-variable quantum computing (CVQC) is a computing paradigm in which measurements yield values over a continuous domain. CVQC is both a convenient omputational framework for modeling physical quantum systems, and a good abstraction for hardware platforms based on quantum optics. Yet, the semantic foundations of CVQC remain underdeveloped. To address this gap, we develop a formal semantics for a core CV quantum programming language, and sound verification methods for program correctness.
A main contribution of this work is to isolate a well-behaved quantitative predicate domain that achieves sufficient expressiveness to accommodate unbounded values as they arise in the infinite-dimensional, continuous setting. Specifically, we choose closed positive quadratic forms as semantic predicates, representing finite expectations, domains of finiteness, and infinite penalties in one ordered object. We validate our choice by establishing that our semantic predicates satisfy desirable closure properties including the definition of weakest preconditions.
We validate our design with two case studies, including an example based on the celebrated GKP error-correcting code, for which we establish a second moment bound.
Innovation
Methods, ideas, or system contributions that make the work stand out.
continuous-variable quantum computing
formal semantics
quadratic forms
program verification
GKP code
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