Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2604.12157

Scalable Qumode-Qubit State Transfer and Fast-forward Quantum Fourier Transform using Oscillators

Joel Bierman, Shubdeep Mohapatra, Huiyang Zhou, Yuan Liu

quant-phSubmitted Apr 14, 2026• Announced Apr 15, 2026• 0 citations
arXivHTMLPDF

Abstract

Transferring the information stored in the expansion coefficients of a multi-qubit state to the coefficients of a continuous-variable state is an important protocol for communicating quantum information. It was shown in previous work how to transfer an $n$-qubit state to a single qumode in $\mathcal{O}(2^n)$ time. We show that by transferring this state to $m$ qumodes, the runtime can be improved to $\mathcal{O}(2^{n/m})$. Furthermore, we demonstrate how multi-qumode state transfer can be used as a subroutine for approximately realizing the $n$-qubits quantum Fourier transform on $m$-qumode with runtime scaling $\mathcal{O}(m2^{n/m}/ε+m^2)$, accelerating qubit quantum Fourier transform using qumodes. This work presents a scalable approach to convert discrete and continuous quantum information between an arbitrary number of qubits and qumodes. It represents a crucial step forward in mixed analog-digital quantum signal processing for computing, sensing, and communication.

Related papers

Toward Mixed Analog-Digital Quantum Signal Processing: Quantum AD/DA Conversion and the Fourier Transform

Yuan Liu, John M. Martyn, Jasmine Sinanan-Singh +3 more

Signal processing stands as a pillar of classical computation and modern information technology, applicable to both analog and digital signals. Recently, advancements in quantum information science have suggested that quantum signal processing (QSP) can enable more powerful signal processing capabilities. However, the developments in QSP have primarily leverageddigitalquantum resources, such as discrete-variable (DV) systems like qubits, rather thananalogquantum resources, such as continuous-variable (CV) systems like quantum oscillators. Consequently, there remains a gap in understanding how signal processing can be performed on hybrid CV-DV quantum computers. Here we address this gap by developing a new paradigm of mixed analog-digital QSP. We demonstrate the utility of this paradigm by showcasing how it naturally enables analog-digital conversion of quantum signals— specifically, the transfer of states between DV and CV quantum systems. We then show that such quantum analog-digital conversion enables new implementations of quantum algorithms on CV-DV hardware. This is exemplified by realizing the quantum Fourier transform of a state encoded on qubits via the free-evolution of a quantum oscillator, albeit with a runtime exponential in the number of qubits due to information theoretic arguments. Collectively, this work marks a significant step forward in hybrid CV-DV quantum computation, providing a foundation for scalable analog-digital signal processing on quantum processors.

arXiv:2408.14729•IEEE Transactions on Signal Processing•Jan 1, 2025•11 citations

Qumode transfer between continuous and discrete variable devices

Alexandru Macridin, Li, Andy C. Y., Panagiotis Spentzouris

Transferring quantum information between different types of quantum hardware is crucial for integrated quantum technology. In particular, converting information between continuous-variable (CV) and discrete-variable (DV) devices enables many applications in quantum networking, quantum sensing, quantum machine learning, and quantum computing. This paper addresses the transfer of CV-encoded information between CV and DV devices. We present a resource-efficient method for encoding CV states and implementing CV gates on DV devices, as well as two measurement-based protocols for transferring CV states between CV and DV devices. The success probability of the transfer protocols depends on the measurement outcome and can be increased to near-deterministic values by adding ancillary qubits to the DV devices.

arXiv:2305.03179•May 4, 2023•1 citation

Qumode transfer between continuous- and discrete-variable devices

Alexandru Macridin, Andy C. Y. Li, Panagiotis Spentzouris

Transferring quantum information between different types of quantum hardware is crucial for integrated quantum technology. In particular, converting information between continuous variable (CV) and discrete variable (DV) devices enables many applications in quantum networking, quantum sensing, quantum machine learning, and quantum computing. This paper addresses the transfer of CV-encoded information between CV and DV devices. We present a resource-efficient method for encoding CV states and implementing CV gates on DV devices, as well as two measurement-based protocols for transferring CV states between CV and DV devices. The success probability of the transfer protocols depends on the measurement outcome and can be increased to near-deterministic values by adding ancillary qubits to the DV devices.

Physical Review A•Mar 19, 2024•4 citations

A quantum-bit encoding converter

Tom Darras, Beate E. Asenbeck, Giovanni Guccione +3 more

From telecommunication to computing architectures, the realm of classical information hinges on converter technology to enable the exchange of data between digital and analog formats, a process now routinely performed across a variety of electronic devices. A similar exigency exists as well in quantum information technology where different frameworks are being developed for quantum computing, communication, and sensing. Thus, efficient quantum interconnects are a major need to bring these parallel approaches together and scale up quantum information systems. So far, however, the conversion between different optical quantum-bit encodings has remained challenging due to the difficulty of preserving fragile quantum superpositions and the demanding requirements for postselection-free implementations. Here we demonstrate such a conversion of quantum information between the two main paradigms, namely discrete- and continuous-variable qubits. We certify the protocol on a complete set of single-photon qubits, successfully converting them to cat-state qubits with fidelities exceeding the classical limit. Our result demonstrates an essential tool for enabling interconnected quantum devices and architectures with enhanced versatility and scalability.

arXiv:2211.10457•Nov 18, 2022•0 citations

Efficient Qubit Simulation of Hybrid Oscillator-Qubit Quantum Computation

Xi Lu, Bojko N. Bakalov, Yuan Liu

We introduce a framework for simulating hybrid oscillator-qubit quantum processors on qubit-only systems through position encoding. By encoding continuous-variable position and momentum wave functions into qubit amplitudes, our method efficiently simulates all Gaussian and conditional Gaussian operations -- encompassing the phase-space instruction set (beam splitter, single-qubit rotation, conditional displacement) and extending to squeezing, conditional squeezing, conditional rotation, and conditional beam splitter -- using $O\!\left(\log^2\!\left(Γ+ \log(1/ε)\right)\right)$ qubit gates per hybrid gate, where $Γ$ is the Fock-level bound and $ε$ is the target precision. This polylogarithmic per-gate complexity represents an exponential improvement over Fock basis encoding approaches, which require exponential quantum or classical resources in the number of qubits per mode. We provide rigorous numerical characterization of quantum Fourier transform errors for Fock-bounded states, enabling precise resource estimation for practical implementations. This work establishes that hybrid oscillator-qubit algorithms can be implemented on qubit processors with polynomial overhead, providing new insights into the computational power trade-offs between discrete-variable and hybrid continuous-discrete-variable quantum computing.

quant-pharXiv:2603.09233•Mar 11, 2026•0 citations

Digital-analog quantum algorithm for the quantum Fourier transform

Ana Martin, Lamata Manuel, Lucas, E. Solano +1 more

Quantum computers will allow calculations beyond existing classical computers. However, current technology is still too noisy and imperfect to construct a universal digital quantum computer with quantum error correction. Inspired by the evolution of classical computation, an alternative paradigm merging the flexibility of digital quantum computation with the robustness of analog quantum simulation has emerged. This universal paradigm is known as digital-analog quantum computing. Here, we introduce an efficient digital-analog quantum algorithm to compute the quantum Fourier transform, a subroutine widely employed in several relevant quantum algorithms. We show that, under reasonable assumptions about noise models, the fidelity of the quantum Fourier transformation improves considerably using this approach when the number of qubits involved grows. This suggests that, in the noisy intermediate-scale quantum era, hybrid protocols combining digital and analog quantum computing could be a sensible approach to reach useful quantum supremacy.

•Jan 1, 2020•28 citations
Transferring the information stored in the expansion coefficients of a multi-qubit state to the coefficients of a continuous-variable state is an important protocol for communicating quantum information. It was shown in previous work how to transfer an nnn-qubit state to a single qumode in O(2n)\mathcal{O}(2^n)O(2n) time. We show that by transferring this state to mmm qumodes, the runtime can be improved to O(2n/m)\mathcal{O}(2^{n/m})O(2n/m). Furthermore, we demonstrate how multi-qumode state transfer can be used as a subroutine for approximately realizing the nnn-qubits quantum Fourier transform on mmm-qumode with runtime scaling O(m2n/m/ε+m2)\mathcal{O}(m2^{n/m}/ε+m^2)O(m2n/m/ε+m2), accelerating qubit quantum Fourier transform using qumodes. This work presents a scalable approach to convert discrete and continuous quantum information between an arbitrary number of qubits and qumodes. It represents a crucial step forward in mixed analog-digital quantum signal processing for computing, sensing, and communication.
Signal processing stands as a pillar of classical computation and modern information technology, applicable to both analog and digital signals. Recently, advancements in quantum information science have suggested that quantum signal processing (QSP) can enable more powerful signal processing capabilities. However, the developments in QSP have primarily leverageddigitalquantum resources, such as discrete-variable (DV) systems like qubits, rather thananalogquantum resources, such as continuous-variable (CV) systems like quantum oscillators. Consequently, there remains a gap in understanding how signal processing can be performed on hybrid CV-DV quantum computers. Here we address this gap by developing a new paradigm of mixed analog-digital QSP. We demonstrate the utility of this paradigm by showcasing how it naturally enables analog-digital conversion of quantum signals— specifically, the transfer of states between DV and CV quantum systems. We then show that such quantum analog-digital conversion enables new implementations of quantum algorithms on CV-DV hardware. This is exemplified by realizing the quantum Fourier transform of a state encoded on qubits via the free-evolution of a quantum oscillator, albeit with a runtime exponential in the number of qubits due to information theoretic arguments. Collectively, this work marks a significant step forward in hybrid CV-DV quantum computation, providing a foundation for scalable analog-digital signal processing on quantum processors.
Transferring quantum information between different types of quantum hardware is crucial for integrated quantum technology. In particular, converting information between continuous-variable (CV) and discrete-variable (DV) devices enables many applications in quantum networking, quantum sensing, quantum machine learning, and quantum computing. This paper addresses the transfer of CV-encoded information between CV and DV devices. We present a resource-efficient method for encoding CV states and implementing CV gates on DV devices, as well as two measurement-based protocols for transferring CV states between CV and DV devices. The success probability of the transfer protocols depends on the measurement outcome and can be increased to near-deterministic values by adding ancillary qubits to the DV devices.
Transferring quantum information between different types of quantum hardware is crucial for integrated quantum technology. In particular, converting information between continuous variable (CV) and discrete variable (DV) devices enables many applications in quantum networking, quantum sensing, quantum machine learning, and quantum computing. This paper addresses the transfer of CV-encoded information between CV and DV devices. We present a resource-efficient method for encoding CV states and implementing CV gates on DV devices, as well as two measurement-based protocols for transferring CV states between CV and DV devices. The success probability of the transfer protocols depends on the measurement outcome and can be increased to near-deterministic values by adding ancillary qubits to the DV devices.
From telecommunication to computing architectures, the realm of classical information hinges on converter technology to enable the exchange of data between digital and analog formats, a process now routinely performed across a variety of electronic devices. A similar exigency exists as well in quantum information technology where different frameworks are being developed for quantum computing, communication, and sensing. Thus, efficient quantum interconnects are a major need to bring these parallel approaches together and scale up quantum information systems. So far, however, the conversion between different optical quantum-bit encodings has remained challenging due to the difficulty of preserving fragile quantum superpositions and the demanding requirements for postselection-free implementations. Here we demonstrate such a conversion of quantum information between the two main paradigms, namely discrete- and continuous-variable qubits. We certify the protocol on a complete set of single-photon qubits, successfully converting them to cat-state qubits with fidelities exceeding the classical limit. Our result demonstrates an essential tool for enabling interconnected quantum devices and architectures with enhanced versatility and scalability.
We introduce a framework for simulating hybrid oscillator-qubit quantum processors on qubit-only systems through position encoding. By encoding continuous-variable position and momentum wave functions into qubit amplitudes, our method efficiently simulates all Gaussian and conditional Gaussian operations -- encompassing the phase-space instruction set (beam splitter, single-qubit rotation, conditional displacement) and extending to squeezing, conditional squeezing, conditional rotation, and conditional beam splitter -- using O ⁣(log⁡2 ⁣(Γ+log⁡(1/ε)))O\!\left(\log^2\!\left(Γ+ \log(1/ε)\right)\right)O(log2(Γ+log(1/ε))) qubit gates per hybrid gate, where ΓΓΓ is the Fock-level bound and εεε is the target precision. This polylogarithmic per-gate complexity represents an exponential improvement over Fock basis encoding approaches, which require exponential quantum or classical resources in the number of qubits per mode. We provide rigorous numerical characterization of quantum Fourier transform errors for Fock-bounded states, enabling precise resource estimation for practical implementations. This work establishes that hybrid oscillator-qubit algorithms can be implemented on qubit processors with polynomial overhead, providing new insights into the computational power trade-offs between discrete-variable and hybrid continuous-discrete-variable quantum computing.
Quantum computers will allow calculations beyond existing classical computers. However, current technology is still too noisy and imperfect to construct a universal digital quantum computer with quantum error correction. Inspired by the evolution of classical computation, an alternative paradigm merging the flexibility of digital quantum computation with the robustness of analog quantum simulation has emerged. This universal paradigm is known as digital-analog quantum computing. Here, we introduce an efficient digital-analog quantum algorithm to compute the quantum Fourier transform, a subroutine widely employed in several relevant quantum algorithms. We show that, under reasonable assumptions about noise models, the fidelity of the quantum Fourier transformation improves considerably using this approach when the number of qubits involved grows. This suggests that, in the noisy intermediate-scale quantum era, hybrid protocols combining digital and analog quantum computing could be a sensible approach to reach useful quantum supremacy.