© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

arXiv:2609.06743

Staged Hybrid Quantum-Classical Programming

Chuta Sano, Peng Fu, Ryan Kavanagh, Jennifer Paykin, Brigitte Pientka

Published Sep 6, 2026• 0 citations

Abstract

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.

DOI: 10.48550/arxiv.2609.06743

Related papers

Foundational Design of Multi-Modal Typed Programming Language for Quantum-Classical Hybrid Computing System

Shota Arakaki, Masao Hirokawa

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.

International Conference on Artificial Intelligence, Computer, Data Sciences and Applications (ACDSA)•Feb 5, 2026•0 citations

Efficient Parameterised Compilation for Hybrid Quantum Programming

Anna M. Krol, Koen J. Mesman, Aritra Sarkar +1 more

Near term quantum devices have the potential to outperform classical computing through the use of hybrid classical-quantum algorithms such as Variational Quantum Eigensolvers. These iterative algorithms use a classical optimiser to update a parameterised quantum circuit. Each iteration, the circuit is executed on a physical quantum processor or quantum computing simulator, and the average measurement result is passed back to the classical optimiser. When many iterations are required, the whole quantum program is also recompiled many times. We have implemented explicit parameters that prevent recompilation of the whole program in the quantum programming framework OpenQL, called OpenQLPC. These parameters improve the compilation and therefore total runtime for hybrid quantum-classical algorithms. We compare the time required for compilation and simulation of the MAXCUT algorithm in OpenQLpcto the same algorithm in both PyQuil and Qiskit. We show that efficient handling of parameterised circuits results in up to 70 % reduction in total compilation time for the MAXCUT benchmark, and leads to a reduced total execution time. When using OpenQLPC, compilation of hybrid algorithms is up to two times faster than when using PyQuil or Qiskit.

arXiv:2208.07683•IEEE International Conference on Quantum Computing and Engineering (QCE)•Sep 17, 2023•3 citations

Advancing hybrid quantum–classical computation with real-time execution

Thomas Lubinski, Cassandra Granade, Amos Anderson +4 more

The use of mid-circuit measurement and qubit reset within quantum programs has been introduced recently and several applications demonstrated that perform conditional branching based on these measurements. In this work, we go a step further and describe a next-generation implementation of classical computation embedded within quantum programs that enables the real-time calculation and adjustment of program variables based on the mid-circuit state of measured qubits. A full-featured Quantum Intermediate Representation (QIR) model is used to describe the quantum circuit including its embedded classical computation. This integrated approach eliminates the need to evaluate and store a potentially prohibitive volume of classical data within the quantum program in order to explore multiple solution paths. It enables a new type of quantum algorithm that requires fewer round-trips between an external classical driver program and the execution of the quantum program, significantly reducing computational latency, as much of the classical computation can be performed during the coherence time of quantum program execution. We review practical challenges to implementing this approach along with developments underway to address these challenges. An implementation of this novel and powerful quantum programming pattern, a random walk phase estimation algorithm, is demonstrated on a physical quantum computer with an analysis of its benefits and feasibility as compared to existing quantum computing methods.

arXiv:2206.12950•Frontiers in Physics•Aug 5, 2022•50 citations

From AI-Generated Circuits to Accountable Quantum Execution: A Hybrid Workflow Framework

Taylor Miss

Connecting AI-generated quantum programs to executable experiments requires more than syntactically valid code: the workflow must also control execution authority and preserve the basis for interpreting its results. This paper develops a conceptual architecture organized around three responsibilities: AI-assisted circuit proposal, deterministic classical validation, and quantum measurement execution. A quantum-job contract binds circuit artifacts, measurement settings, resource allocations, backend information, and provenance to explicit admission conditions. The design separates permission to run an experiment from evidence that its output answers the intended scientific question. An analytical single-qubit variational example demonstrates this distinction through exact energy calculations, finite-shot variance, and budget-constrained measurement allocation. Responsibility allocation, runtime interception, and staged transformation provide the architectural principles, while uncertainty reporting and reference calculations supply the scientific checks. A prospective evaluation protocol covers accuracy, policy violations, reproducibility, end-to-end cost, and researcher effort. The framework is presented as a design proposal supported by mathematical illustration, not as a tested implementation; its operational benefits and applicability to larger quantum workloads remain to be established.

•Sep 11, 2026•0 citations

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

M, Gurukasi

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

•Dec 8, 2025•0 citations

Automatic De-Quantization of Quantum Programs Using Constant Propagation

Lian Remme, Alexander Weinert, Andre Waschk +2 more

Quantum computing promises to solve problems beyond the reach of classical computers, but today's quantum hardware is error-prone and much slower than classical hardware. Every quantum operation is costly, making it crucial to minimize quantum resource usage in near-term algorithms. Quantum resources should only be used when they are truly essential for quantum advantage, and not wasted on operations that can be efficiently handled by classical computation. In this work, we focus on de-quantizing quantum operations to classical computation whenever possible. The approach we propose for this is hybrid quantum-classical constant propagation, an optimization which reduces quantum operations by trading them for fast, reliable classical instructions. This is done by tracking between quantum and classical states to identify and eliminate unnecessary quantum gates and controls. We formalize a hybrid state model for quantum-classical constant propagation, implement our optimizations in the open-source MQT Core tool, and evaluate them on benchmark circuits. The obtained results show that quantum-classical constant propagation can reduce costly multi-qubit operations, making quantum programs more practical and robust for near-term devices. This opens the door to new hybrid compiler strategies that leverage the best of both quantum and classical worlds.

quant-pharXiv:2605.22980•IEEE International Conference on Quantum Software (QSW)•May 25, 2026•0 citations

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.

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.

Near term quantum devices have the potential to outperform classical computing through the use of hybrid classical-quantum algorithms such as Variational Quantum Eigensolvers. These iterative algorithms use a classical optimiser to update a parameterised quantum circuit. Each iteration, the circuit is executed on a physical quantum processor or quantum computing simulator, and the average measurement result is passed back to the classical optimiser. When many iterations are required, the whole quantum program is also recompiled many times. We have implemented explicit parameters that prevent recompilation of the whole program in the quantum programming framework OpenQL, called OpenQLPC. These parameters improve the compilation and therefore total runtime for hybrid quantum-classical algorithms. We compare the time required for compilation and simulation of the MAXCUT algorithm in OpenQLpcto the same algorithm in both PyQuil and Qiskit. We show that efficient handling of parameterised circuits results in up to 70 % reduction in total compilation time for the MAXCUT benchmark, and leads to a reduced total execution time. When using OpenQLPC, compilation of hybrid algorithms is up to two times faster than when using PyQuil or Qiskit.

The use of mid-circuit measurement and qubit reset within quantum programs has been introduced recently and several applications demonstrated that perform conditional branching based on these measurements. In this work, we go a step further and describe a next-generation implementation of classical computation embedded within quantum programs that enables the real-time calculation and adjustment of program variables based on the mid-circuit state of measured qubits. A full-featured Quantum Intermediate Representation (QIR) model is used to describe the quantum circuit including its embedded classical computation. This integrated approach eliminates the need to evaluate and store a potentially prohibitive volume of classical data within the quantum program in order to explore multiple solution paths. It enables a new type of quantum algorithm that requires fewer round-trips between an external classical driver program and the execution of the quantum program, significantly reducing computational latency, as much of the classical computation can be performed during the coherence time of quantum program execution. We review practical challenges to implementing this approach along with developments underway to address these challenges. An implementation of this novel and powerful quantum programming pattern, a random walk phase estimation algorithm, is demonstrated on a physical quantum computer with an analysis of its benefits and feasibility as compared to existing quantum computing methods.

Connecting AI-generated quantum programs to executable experiments requires more than syntactically valid code: the workflow must also control execution authority and preserve the basis for interpreting its results. This paper develops a conceptual architecture organized around three responsibilities: AI-assisted circuit proposal, deterministic classical validation, and quantum measurement execution. A quantum-job contract binds circuit artifacts, measurement settings, resource allocations, backend information, and provenance to explicit admission conditions. The design separates permission to run an experiment from evidence that its output answers the intended scientific question. An analytical single-qubit variational example demonstrates this distinction through exact energy calculations, finite-shot variance, and budget-constrained measurement allocation. Responsibility allocation, runtime interception, and staged transformation provide the architectural principles, while uncertainty reporting and reference calculations supply the scientific checks. A prospective evaluation protocol covers accuracy, policy violations, reproducibility, end-to-end cost, and researcher effort. The framework is presented as a design proposal supported by mathematical illustration, not as a tested implementation; its operational benefits and applicability to larger quantum workloads remain to be established.

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

Quantum computing promises to solve problems beyond the reach of classical computers, but today's quantum hardware is error-prone and much slower than classical hardware. Every quantum operation is costly, making it crucial to minimize quantum resource usage in near-term algorithms. Quantum resources should only be used when they are truly essential for quantum advantage, and not wasted on operations that can be efficiently handled by classical computation. In this work, we focus on de-quantizing quantum operations to classical computation whenever possible. The approach we propose for this is hybrid quantum-classical constant propagation, an optimization which reduces quantum operations by trading them for fast, reliable classical instructions. This is done by tracking between quantum and classical states to identify and eliminate unnecessary quantum gates and controls. We formalize a hybrid state model for quantum-classical constant propagation, implement our optimizations in the open-source MQT Core tool, and evaluate them on benchmark circuits. The obtained results show that quantum-classical constant propagation can reduce costly multi-qubit operations, making quantum programs more practical and robust for near-term devices. This opens the door to new hybrid compiler strategies that leverage the best of both quantum and classical worlds.