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Quantica: A Hybrid Classical–Quantum Programming Language with a Unified Execution Model

M, Gurukasi

Published Dec 8, 2025• 0 citations
Publisher

Abstract

Quantica is an innovative programming language that allows the simultaneous use of classical control flow and quantum computation in one unified model. The language design, execution semantics, and primary concerns of the type system controlling classical-quantum interaction are all presented in this preprint. Furthermore, the paper outlines the initial reference implementation, which includes the compiler front end, execution model, and backend infrastructure, along with the sample programs representing quantum gates, entanglement, measurement-driven control flow, and variational hybrid algorithms. The authors finish by pointing out the existing limitations and suggesting the next steps in the unified quantum programming language design as future research. Quantica Github Repo

DOI
10.5281/zenodo.17852706

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Quantica is an innovative programming language that allows the simultaneous use of classical control flow and quantum computation in one unified model. The language design, execution semantics, and primary concerns of the type system controlling classical-quantum interaction are all presented in this preprint. Furthermore, the paper outlines the initial reference implementation, which includes the compiler front end, execution model, and backend infrastructure, along with the sample programs representing quantum gates, entanglement, measurement-driven control flow, and variational hybrid algorithms. The authors finish by pointing out the existing limitations and suggesting the next steps in the unified quantum programming language design as future research. Quantica Github Repo
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As quantum computing hardware advances toward practical implementation, the design of high-level programming languages for quantum-classical hybrid systems remains a critical challenge. Current quantum programming approaches lack unified abstractions that seamlessly integrate classical and quantum computation. This paper proposes a foundational framework for a high-level quantum-classical hybrid programming language based on multi-modal type theory. Our approach formulates quantum-classical hybrid computation as staged computation, where classical computation generates and executes quantum programs. We adapt type systems and operational semantics from prior research in classical staged computation to this framework. This research provides a theoretical foundation for implementing interpreters and compilers that uniformly handle both classical and quantum computation.
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Hybrid quantum-classical computing systems consist of a classical control system that sends quantum circuits and receives measurement results from a quantum co-processor. Such systems allow us to model algorithms that require the classical control system to generate quantum circuits on the fly, potentially based on prior measurement results. This is challenging, as the classical control system must generate quantum circuits that manipulate live quantum states. In this setting, the classical control system is generating further quantum circuits while the quantum co-processor is internally maintaining the state of the live qubits; this is not ideal, since this not only is costly but also introduces additional sources of noise to the live qubits. Thus, we want to minimize the latency between receiving measurement results and sending the next quantum circuit to be executed by pre-computing quantum circuits. We introduce HyQ (pronounced haiku), a multi-modal language based on adjoint logic that pre-generates quantum circuits before executing a hybrid quantum-classical program. We achieve this by separating our semantics into two distinct stages: 1) compile-time generation of quantum circuits and classical runtime code and 2) execution of the classical runtime code that instruments the quantum co-processor. This separation between stages allows us to formally guarantee that all circuit-generation logic occurs before the instrumentation logic, i.e., the actual runtime, and minimizes the idling of the quantum co-processor at runtime. We give a type system, a circuit-normalization semantics for the compile-time stage, which eagerly performs all circuit-generation logic, and a runtime semantics for HyQ that corresponds to the second stage. We prove type preservation and progress for both semantics.
This paper introduces QuanUML, an extension of the Unified Modeling Language (UML) tailored for quantum software systems. QuanUML integrates quantum-specific constructs, such as qubits and quantum gates, into the UML framework, enabling the modeling of both quantum and hybrid quantum-classical systems. We apply QuanUML to Efficient Long-Range Entanglement using Dynamic Circuits and Shor’s Algorithm, demonstrating its utility in designing and visualizing quantum algorithms. Our approach supports model-driven development of quantum software and offers a structured framework for quantum software design. We also highlight its advantages over existing methods and discuss future improvements.