Linear Dependent Type Theory for Quantum Programming Languages

Fu, Peng; Kishida, Kohei; Selinger, Peter

doi:10.1145/3373718.3394765

Cited by 16 publications

(28 citation statements)

References 19 publications

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“…In this case, the output circuit might be equivalent to the Idris implementation, but there are no guarantees about wordlengths checked by the compiler -this is what we have addressed with dependent types. Similar benefits are demonstrated in an adjacent domain; the language Proto-Quipper-D uses dependent types to ensure correctness of entire "families" of parameterised quantum circuits [5]. Without these compiler checks, there is a large burden on the developer to provide good evidence of testing.…”

Section: B Comparisons To Existing Hdlsmentioning

confidence: 96%

“…We acknowledge the rich history of functional HDLs, including [1]- [3] but we focus on the narrower field of dependently typed languages. The work in [5] introduces an application of dependent types for generating families of quantum circuits, hinting towards an exciting future for synthesis of digital circuits using similar techniques. Ref.…”

Section: Related Workmentioning

confidence: 99%

“…We use the language Idris [4] to make this demonstration of modeling DSP circuits. Currently this is in simulation only, but synthesis remains a promising avenue for future work given the success of similar synthesisable languages without dependent types [1]- [3] and dependently typed tools from other domains [5].…”

Section: Introductionmentioning

confidence: 99%

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On Applications of Dependent Types to Parameterised Digital Signal Processing Circuits

Ramsay

Crockett

Stewart

2021

2021 IEEE International Midwest Symposium on Circuits and Systems (MWSCAS)

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We explore the use of dependent types to address the disparity between the theory and the practical hardware description of DSP circuits. After discussing an approach to modeling synchronous circuit behaviour in Idris (a pure functional language with dependent types), two DSP case studies are introduced -an FIR filter with optimal wordlengths and a CIC decimator with register pruning. Both of these scenarios prove difficult to describe in a parameterised fashion using traditional HDLs and, as such, many implementations rely on ad hoc circuit generators which are challenging to test and evaluate. This work demonstrates that such circuits are readily described in an environment with dependent types. Dependent types can also encode various contracts between the IP designer and its user. These contracts are automatically verified by the Idris type checker before compilation, precluding many common mistakes in IP development and evaluation.

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Section: B Comparisons To Existing Hdlsmentioning

confidence: 96%

Section: Related Workmentioning

confidence: 99%

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On Applications of Dependent Types to Parameterised Digital Signal Processing Circuits

Ramsay

Crockett

Stewart

2021

2021 IEEE International Midwest Symposium on Circuits and Systems (MWSCAS)

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“…However, this semantics has never been fully formalized in the context of higher-order, functional quantum languages. Besides operational semantics, programming languages for quantum circuits have been formalized using denotational semantics based on density matrices [11] and categorical semantics based on symmetric monoidal categories [16,14,9,14,5], or on the category of C * -algebras [19,13]. However, these examples of formalization do not solve the problem in that they either ignore the structure of circuit or keep the term with dynamic lifting abstract.…”

Section: Introductionmentioning

confidence: 99%

“…However, these examples of formalization do not solve the problem in that they either ignore the structure of circuit or keep the term with dynamic lifting abstract. In particular, in [14,5], the authors construct expressive categorical models for the family of circuits -or parameterized circuits-and linear dependent type theory, respectively, while they do not provide semantics of dynamic lifting explicitly.…”

Section: Introductionmentioning

confidence: 99%

Concrete Categorical Model of a Quantum Circuit Description Language with Measurement

Lee,

Perrelle,

Valiron

et al. 2021

Preprint

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In this paper, we introduce dynamic lifting to a quantum circuit-description language, following the Proto-Quipper language approach. Dynamic lifting allows programs to transfer the result of measuring quantum data -qubits-into classical data -booleans-. We propose a type system and an operational semantics for the language and we state safety properties. Next, we introduce a concrete categorical semantics for the proposed language, basing our approach on a recent model from Rios&Selinger for Proto-Quipper-M. Our approach is to construct on top of a concrete category of circuits with measurements a Kleisli category, capturing as a side effect the action of retrieving classical content out of a quantum memory. We then show a soundness result for this semantics.

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Quantum computing: A taxonomy, systematic review and future directions

et al. 2021

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Quantum computing (QC) is an emerging paradigm with the potential to offer significant computational advantage over conventional classical computing by exploiting quantum‐mechanical principles such as entanglement and superposition. It is anticipated that this computational advantage of QC will help to solve many complex and computationally intractable problems in several application domains such as drug design, data science, clean energy, finance, industrial chemical development, secure communications, and quantum chemistry. In recent years, tremendous progress in both quantum hardware development and quantum software/algorithm has brought QC much closer to reality. Indeed, the demonstration of quantum supremacy marks a significant milestone in the Noisy Intermediate Scale Quantum (NISQ) era—the next logical step being the quantum advantage whereby quantum computers solve a real‐world problem much more efficiently than classical computing. As the quantum devices are expected to steadily scale up in the next few years, quantum decoherence and qubit interconnectivity are two of the major challenges to achieve quantum advantage in the NISQ era. QC is a highly topical and fast‐moving field of research with significant ongoing progress in all facets. A systematic review of the existing literature on QC will be invaluable to understand the state‐of‐the‐art of this emerging field and identify open challenges for the QC community to address in the coming years. This article presents a comprehensive review of QC literature and proposes taxonomy of QC. The proposed taxonomy is used to map various related studies to identify the research gaps. A detailed overview of quantum software tools and technologies, post‐quantum cryptography, and quantum computer hardware development captures the current state‐of‐the‐art in the respective areas. The article identifies and highlights various open challenges and promising future directions for research and innovation in QC.

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Linear Dependent Type Theory for Quantum Programming Languages

Cited by 16 publications

References 19 publications

On Applications of Dependent Types to Parameterised Digital Signal Processing Circuits

On Applications of Dependent Types to Parameterised Digital Signal Processing Circuits

Concrete Categorical Model of a Quantum Circuit Description Language with Measurement

Quantum computing: A taxonomy, systematic review and future directions

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