A Quantum Programming Language for Coherent Control

2025-07-14

AI Summary

This paper addresses the challenge of recursive and iterative coherent control under non-unitary operations—such as decoherence and measurement—in open quantum systems. To this end, it introduces the first quantum programming language supporting arbitrary quantum operations, including non-unitary evolutions. Methodologically, it pioneers the integration of Kraus operator–based operational semantics with denotational semantics grounded in vacuum extension, establishing a unified semantic framework; it further adopts observational equivalence as the criterion for semantic equivalence, ensuring precise characterization of open-system behavior. Theoretically, the work proves the language’s universality under vacuum extension, establishes adequacy for both operational and denotational semantics, and demonstrates full abstraction of the denotational semantics with respect to observational equivalence—thereby providing a rigorous foundation for verification and optimization of quantum programs.

Technology Category

• Machine Learning: Quantum Machine Learning
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Non-convex Optimization

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Security and Privacy: Data transparency and provenance
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems

Abstract

We introduce a programming language that allows for the coherent control of arbitrary quantum operations. The problem of defining coherent control beyond the unitary case, using, for example, a quantum conditional in the presence of recursion or iteration has long been known to be a major difficulty. We resolve this problem by defining an operational semantics based on appropriate Kraus decompositions and a denotational semantics based on vacuum-extensions. We show that the language is universal for vacuum-extensions and that the two semantics are adequate. Moreover, we define a notion of observational equivalence: two programs are equivalent if their probability of termination is the same in any context. The denotational semantics is shown to be fully abstract for observational equivalence.

Problem

• Defining coherent control beyond unitary quantum operations
• Resolving recursion and iteration in quantum conditionals
• Establishing observational equivalence for quantum programs

Innovation

• Programming language for coherent quantum control
• Operational semantics using Kraus decompositions
• Denotational semantics based on vacuum-extensions