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arXiv:2511.13882

Hybrid continuous-discrete-variable quantum computing: a guide to utility

A. F. Kemper, Antonios Alvertis, Muhammad Asaduzzaman, Bojko N. Bakalov, Dror Baron, Joel Bierman, Blake Burgstahler, Srikar Chundury, Elin Ranjan Das, Jim Furches, Fucheng Guo, Raghav G. Jha, Katherine Klymko, Arvin Kushwaha, Ang Li, Aishwarya Majumdar, Carlos Ortiz Marrero, Shubdeep Mohapatra, Christopher Mori, Frank Mueller, Doru Thom Popovici, Tim Stavenger, Mastawal Tirfe, Norm M. Tubman, Muqing Zheng, Huiyang Zhou, Yuan Liu

quant-phSubmitted Nov 17, 2025• Announced Nov 19, 2025• 0 citations
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Abstract

Quantum computing has traditionally centered around the discrete variable paradigm. A new direction is the inclusion of continuous variable modes and the consideration of a hybrid continuous-discrete approach to quantum computing. In this paper, we discuss some of the advantages of this modality, and lay out a number of potential applications that can make use of it; these include applications from physics, chemistry, and computer science. We also briefly overview some of the algorithmic and software considerations for this new paradigm.

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28 pages, 9 figures

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Quantum computing has traditionally centered around the discrete variable paradigm. A new direction is the inclusion of continuous variable modes and the consideration of a hybrid continuous-discrete approach to quantum computing. In this paper, we discuss some of the advantages of this modality, and lay out a number of potential applications that can make use of it; these include applications from physics, chemistry, and computer science. We also briefly overview some of the algorithmic and software considerations for this new paradigm.
Quantum computing, built on the principles of quantum mechanics, has emerged as a transformative paradigm with the potential to revolutionize computational capabilities, enabling solutions to problems that are currently intractable for classical systems. Quantum computing integrates hardware, architectures, and software for improved applications while utilizing superposition, entanglement, and interference to promote materials science, cryptography, optimization, and artificial intelligence. Sections introduce and describe the model components needed in order to create quantum processors, including qubits, quantum gates and control electronics, as well as a review of new developments in quantum software frameworks and programming tools. Notable examples, such as Shor’s algorithm for cryptographic caveat, Grover’s algorithm for inefficient search processes, and quantum-enhanced optimization, illuminate the position of quantum computing as a means of tackling tough problems that span disciplines, such as pharmaceuticals, predictors of climate, and finance modeling. However, the field continues to face significant challenges, like limited scalability, quantum gate error rates, qubit coherence times, and difficulties integrating with classical systems. Future efforts will focus on developing hybrid quantum-classical systems, scalable architectures, and industry- specific applications to transition quantum computing from exploration to practical deployment. This review provides a comprehensive analysis of quantum computing, covering its potential, trends, and challenges, while exploring hardware-software integration, classicalquantum comparisons, and insights to guide research and industry in unlocking its revolutionary possibility.
This tutorial offers a pedagogical guide to hybrid quantum processors that integrate discrete-variable (DV) qubits and continuous-variable (CV) oscillators. Aimed at computer scientists, engineers, and physicists, it provides an overview of the experimental, algorithmic, and architectural aspects of this novel and rapidly developing hardware model. Experimental realizations of this model include superconducting, trapped-ion, and neutral-atom platforms. By combining DV and CV components, hybrid oscillator-qubit processors enable a powerful new paradigm that offers complementary strengths for quantum control, error correction, computation, and simulation. Working toward the goal of a full-stack system connecting applications to CV-DV hardware, we define and formulate abstract machine models and instruction set architectures. These essential abstractions enable codesign of hardware and software, and resource estimation for exploring the potential of current and future hardware for computational and simulation tasks. Using these abstractions, we present both new and existing examples that illustrate the benefits of hybrid CV-DV processors relative to traditional DV-only hardware in computation as well as quantum simulation of physical models. Examples include algorithms for transferring states between DV and CV systems, performing the quantum Fourier transform, and simulation of lattice gauge theories. Relative to qubit-only hardware, the bosonic degrees of freedom natively available in hybrid architectures can substantially reduce the circuit complexity of simulations for physical models containing bosons. A key technique is the extension of quantum signal processing ideas to CV-DV systems. This work is intended to serve as a timely and comprehensive guide to this relatively unexplored yet promising approach to quantum computation and to provide a road map to guide future development.
Quantum computing is usually associated with discrete quantum states and physical quantities possessing discrete eigenvalue spectrum. However, quantum computing in general is any computation accomplished by the exploitation of quantum properties of physical quantities, discrete or otherwise. It has been shown that physical quantities with continuous eigenvalue spectrum can be used for quantum computing as well. Currently, continuous variable quantum computing is a rapidly developing field both theoretically and experimentally. In this pedagogical introduction we present the basic theoretical concepts behind it and the tools for algorithm development. The paper targets readers with discrete quantum computing background, who are new to continuous variable quantum computing.
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