Most contemporary quantum programming languages describe computation as circuits, using a host classical counterpart to drive the execution of quantum programs. However, the circuit model adds expensive complexity to quantum algorithmic development and decreases the transparency of connections between syntax and formal semantics in quantum programs. We argue that producing a high-level quantum programming language without reference to circuits is possible and necessary. We summarize desirable features in future high-level quantum programming languages and provide evidence supporting array pro-gramming languages as a natural paradigm for quantum algorithmic expression at the circuit level and beyond. We highlight why APL is a profitable host programming language to attain this goal progressively. In particular, we demonstrate how features provided by APL, such as native support of complex numbers and matrix operations, naturally capture quan-tum operations while bringing a less cluttered syntax that encodes and encapsulates the linear character of quantum circuit execution. We discuss implementation details of quAPL, an APL library for quantum circuit specification, simulation, and execution intended to provide a gradual ramp toward developing composable procedural abstractions. Finally, we discuss the broader implications of our work and the next steps in our research program.
Most contemporary quantum programming languages describe computation as circuits, using a host classical counterpart to drive the execution of quantum programs. However, the circuit model adds expensive complexity to quantum algorithmic development and decreases the transparency of connections between syntax and formal semantics in quantum programs. We argue that producing a high-level quantum programming language without reference to circuits is possible and necessary. We summarize desirable features in future high-level quantum programming languages and provide evidence supporting array pro-gramming languages as a natural paradigm for quantum algorithmic expression at the circuit level and beyond. We highlight why APL is a profitable host programming language to attain this goal progressively. In particular, we demonstrate how features provided by APL, such as native support of complex numbers and matrix operations, naturally capture quan-tum operations while bringing a less cluttered syntax that encodes and encapsulates the linear character of quantum circuit execution. We discuss implementation details of quAPL, an APL library for quantum circuit specification, simulation, and execution intended to provide a gradual ramp toward developing composable procedural abstractions. Finally, we discuss the broader implications of our work and the next steps in our research program.
Quantum computing hardware is advancing at a rapid pace, yet the lack of high-level programming abstractions remains a serious bottleneck in the development of new applications. Widely used frameworks still rely on gate-level circuit descriptions, causing the algorithm's functional intent to become lost in low-level implementation details, and hindering flexibility and reuse. While various high-level quantum programming languages have emerged in recent years - offering a significant step toward higher abstraction - many still lack support for classical-like expression syntax, and native constructs for useful quantum algorithmic idioms. This paper presents Qmod, a high-level quantum programming language designed to capture algorithmic intent in natural terms while delegating implementation decisions to automation. Qmod introduces quantum numeric variables and expressions, including digital fixed-point arithmetic tuned for compact representations and optimal resource usage. Beyond digital encoding, Qmod also supports non-digital expression modes - phase and amplitude encoding - frequently exploited by quantum algorithms to achieve computational advantages. We describe the language's constructs, demonstrate practical usage examples, and outline future work on evaluating Qmod across a broader set of use cases.
Quantum computing hardware is advancing at a rapid pace, yet the lack of high-level programming abstractions remains a serious bottleneck in the development of new applications. Widely used frameworks still rely on gate-level circuit descriptions, causing the algorithm's functional intent to become lost in low-level implementation details, and hindering flexibility and reuse. While various high-level quantum programming languages have emerged in recent years - offering a significant step toward higher abstraction - many still lack support for classicallike expression syntax, and native constructs for useful quantum algorithmic idioms. This paper presents Qmod, a high-level quantum programming language designed to capture algorithmic intent in natural terms while delegating implementation decisions to automation. Qmod introduces quantum numeric variables and expressions, including digital fixed-point arithmetic tuned for compact representations and optimal resource usage. Beyond digital encoding, Qmod also supports nondigital expression modes phase and amplitude encoding - frequently exploited by quantum algorithms to achieve computational advantages. We describe the language's constructs, demonstrate practical usage examples, and outline future work on evaluating Qmod across a broader set of use cases.
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.
Existing abstract models of quantum computation make reference to circuit elements, much in contrast to their classical counterparts. Circuits, as a model of computation, substantially limit algorithmic expression and obscure high-level connections between problems and quantum resources. It is argued here that new models are needed to achieve high-level algorithmic expressiveness that allow composable procedural abstractions to manifest, leading to the development of instructions in the sense usually understood in high-level programming languages. Doing so appears essential to the discovery of new quantum algorithms, and deeper understanding of how quantum resources compose into useful patterns, or \emph{quantum motifs}. To achieve this, stronger investment in the intersection between higher-algebra, mathematical physics and quantum science is required to cope with future challenges brought forth by \textit{very large quantum scale integration}.
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.
This thesis contains contributions to the mathematical foundations of quantum programming languages. The likely arrival of scalable quantum computers in the not-so-distant future has resulted in a flurry of activity in the development of quantum programming languages. As in classical computing, the transition from a description of a quantum algorithm found in the literature to a hardware-specific set of instructions run on a quantum device is a complex process, prone to errors. This issue is exacerbated in the quantum setting not only by the complexity of quantum algorithms but also by the fragility of quantum information, which renders ineffective some of the classical techniques used to debug programs. In this thesis, we contribute to the solution of some of these issues. We introduce Proto-Quipper-M, a new quantum programming language designed to serve as a testbed for the research and development of sound mathematical semantics and reasoning techniques for quantum programs. We first present Proto-Quipper-M as a formalization of a fragment of Quipper, a high-level functional programming language for describing families of quantum circuits. In particular, we define Proto-Quipper-M as a simply-typed lambda calculus with a special type for quantum circuits and a strong type system designed to enforce linearity on quantum data, and thus prevent violations of the no-cloning property of quantum information. We endow Proto-Quipper-M with computational meaning via a big-step operational semantics and prove that the language is type-safe by showing that it enjoys the type-preservation and error-freeness properties. We also give Proto-Quipper-M a denotational semantics in a suitable class of monoidal categories and show that these categories give rise to linear-non-linear models in the sense of Benton, and thus models of intuitionistic linear logic. Finally, we crystallize the connection between the syntax and the semantics of the language by proving the soundness theorem for Proto-Quipper-M.