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.
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.
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.
Abstract Quantum computing offers transformative capabilities by exploiting quantum mechanical principles to solve problems that are intractable for classical systems, particularly in areas like cryptography, optimization, and data analysis. However, most current quantum programming languages operate at a low level, requiring in-depth expertise in quantum mechanics and circuit theory, which presents a barrier to wider adoption. In this work, we introduce Qutes, a high-level quantum programming language that simplifies the development of quantum algorithms while preserving the flexibility needed for advanced applications. Qutes abstracts low-level quantum operations through intuitive syntax and high-level constructs, enabling developers to express complex algorithms without detailed circuit knowledge. Built atop Qiskit, Qutes transpiles seamlessly into executable code, ensuring compatibility with real quantum hardware. We present the architecture, language design, and hybrid classical-quantum integration of Qutes, and demonstrate its use through implementations of canonical quantum algorithms. Our results highlight Qutes’ potential to democratize quantum programming by lowering the entry threshold and accelerating prototyping for researchers and developers alike.
Quantum computing (QC) is an emerging computational paradigm that leverages the laws of quantum mechanics to perform elementary logic operations. Existing programming models for QC were designed with fault-tolerant hardware in mind, envisioning stand-alone applications. However, the susceptibility of near-term quantum computers to noise limits their stand-alone utility. To better leverage limited computational strengths of noisy quantum devices, hybrid algorithms have been suggested whereby quantum computers are used in tandem with their classical counterparts in a heterogeneous fashion. This modus operandi calls out for a programming model and a high-level programming language that natively and seamlessly supports heterogeneous quantum-classical hardware architectures in a single-source-code paradigm. Motivated by the lack of such a model, we introduce a language extension specification, called QCOR , which enables single-source quantum-classical programming. Programs written using the QCOR library–based language extensions can be compiled to produce functional hybrid binary executables. After defining QCOR’s programming model, memory model, and execution model, we discuss how QCOR enables variational, iterative, and feed-forward QC. QCOR approaches quantum-classical computation in a hardware-agnostic heterogeneous fashion and strives to build on best practices of high-performance computing. The high level of abstraction in the language extension is intended to accelerate the adoption of QC by researchers familiar with classical high-performance computing.
Quantum computing is an emerging computational paradigm that leverages the laws of quantum mechanics to perform elementary logic operations. Existing programming models for quantum computing were designed with fault-tolerant hardware in mind, envisioning standalone applications. However, near-term quantum computers are susceptible to noise which limits their standalone utility. To better leverage limited computational strengths of noisy quantum devices, hybrid algorithms have been suggested whereby quantum computers are used in tandem with their classical counterparts in a heterogeneous fashion. This {\it modus operandi} calls out for a programming model and a high-level programming language that natively and seamlessly supports heterogeneous quantum-classical hardware architectures in a single-source-code paradigm. Motivated by the lack of such a model, we introduce a language extension specification, called QCOR, that enables single-source quantum-classical programming. Programs written using the QCOR library and directives based language extensions can be compiled to produce functional hybrid binary executables. After defining the QCOR's programming model, memory model, and execution model, we discuss how QCOR enables variational, iterative, and feed forward quantum computing. QCOR approaches quantum-classical computation in a hardware-agnostic heterogeneous fashion and strives to build on best practices of high performance computing (HPC). The high level of abstraction in the developed language is intended to accelerate the adoption of quantum computing by researchers familiar with classical HPC.
In this talk, I will give an overview of some recent progress and current challenges in the design of quantum programming languages. Unlike classical programs, which can in principle be debugged by stopping the program at critical moments and examining the contents of variables, quantum programs are not amenable to traditional debugging because the state of a quantum system cannot usually be examined in a meaningful way. Therefore, we need other methods for ensuring the correctness of quantum programs, such as formal verification. For this reason, I advocate the use of strongly typed, functional programming languages for quantum computing. As far as functional quantum programming languages are concerned, there is currently a relatively wide gap between theory and practice. On the one hand, we have languages with strong theoretical foundations, such as the quantum lambda calculus, which operate at a relatively low level of abstraction and lack many features that would be useful to practical quantum programmers. On the other hand, we have practical functional quantum programming languages such as Quipper, which is implemented as an embedded language in Haskell, has many high-level features, and has been used in large-scale projects, but lacks a theoretical basis and a strong type system [Green et al., 2013; Green et al., 2013; Green et al., 2013; Smith et al., 2014]. We have recently attempted to narrow this gap through a family of languages called Proto-Quipper, which are designed to offer Quipper-like features while having sound theoretical foundations [Ross, 2015; Rios and Selinger, 2018]. I will give an overview of Quipper and its most useful features, report on the progress we made with formalizing fragments of Quipper, and outline several of the still remaining challenges.
Quantum computing leverages the principles of quantum mechanics to perform computations far beyond the capabilities of classical systems, particularly in fields such as cryptography and optimization. However, current quantum programming languages often require low-level implementation, posing significant barriers for many developers due to their steep learning curve and limited abstraction. In response, we introduce Qutes, a high-level quantum programming language designed to simplify quantum algorithm development while maintaining the flexibility required for advanced applications. By abstracting complex quantum operations and allowing intuitive expressions through high-level constructs, Qutes enables users to write efficient quantum programs without extensive knowledge of quantum mechanics or circuit design. Built upon Qiskit, Qutes translates its syntax directly into executable quantum code, facilitating seamless integration with quantum hardware. This paper provides an overview of the language's architecture, core functionalities, and its ability to unify classical and quantum operations within a single framework. Additionally, we demonstrate Qutes' application in key quantum algorithms, showcasing its potential to make quantum programming more accessible and practical for a wider range of developers and researchers.