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:2411.19505 · Physical Review Research

Unitary-transformed projective squeezing: Applications for circuit knitting and state preparation of non-Gaussian states

Keitaro Anai, Yasunari Suzuki, Yuuki Tokunaga, Yuichiro Matsuzaki, Shuntaro Takeda, Suguru Endo

Published Nov 12, 2025• 0 citations
arXivHTMLPDF

Abstract

Continuous-variable (CV) quantum computing is a promising candidate for quantum computation because it can, even with one mode, utilize infinite-dimensional Hilbert spaces and can efficiently handle continuous values. Although photonic platforms have been considered as a leading platform for CV computation, hybrid systems that use both qubits and bosonic modes, e.g., superconducting hardware, have shown significant advances because they can prepare non-Gaussian states by utilizing the nonlinear interaction between the qubits and the bosonic modes. However, the size of hybrid hardware is currently restricted. Moreover, the fidelity of the non-Gaussian state is also restricted. This work extends the projective squeezing method to establish a formalism for projecting quantum states onto the states that are unitary-transformed from the squeezed vacuum at the expense of the sampling cost. Based on this formalism, we propose methods for simulating larger quantum devices and projecting states onto the cubic phase state, a typical non-Gaussian state, with a higher squeezing level and higher nonlinearity. To make implementation practical, we can, by leveraging the interactions in hybrid systems of qubits and bosonic modes, apply the smeared projector by using either the linear-combination-of-unitaries or virtual quantum error detection algorithms. We numerically verify the performance of our methods and show that projection can suppress the effect of photon-loss errors.

DOI
10.1103/q15h-nmq9

Related papers

Taming numerical errors in simulations of continuous variable non-Gaussian state preparation

Jan Provazník, Radim Filip, Petr Marek

Numerical simulation of continuous variable quantum state preparation is a necessary tool for optimization of existing quantum information processing protocols. A powerful instrument for such simulation is the numerical computation in the Fock state representation. It unavoidably uses an approximation of the infinite-dimensional Fock space by finite complex vector spaces implementable with classical digital computers. In this approximation we analyze the accuracy of several currently available methods for computation of the truncated coherent displacement operator. To overcome their limitations we propose an alternative with improved accuracy based on the standard matrix exponential. We then employ the method in analysis of non-Gaussian state preparation scheme based on coherent displacement of a two mode squeezed vacuum with subsequent photon counting measurement. We compare different detection mechanisms, including avalanche photodiodes, their cascades, and photon number resolving detectors in the context of engineering non-linearly squeezed cubic states and construction of qubit-like superpositions between vacuum and single photon states.

arXiv:2202.07332•Scientific Reports•Oct 4, 2022•10 citations

Projective squeezing for translation symmetric bosonic codes

Suguru Endo, Keitaro Anai, Yuichiro Matsuzaki +2 more

The design of translation symmetric bosonic codes, e.g., Gottesmann-Kitaev-Preskill and squeezed cat codes, is robust against photon loss, but the computation accuracy is limited by the available squeezing level. Here, we introduce the \textit{projective squeezing} (PS) method for computing outcomes for a higher squeezing level by revealing that a linear combination of displacement operators with periodic displacement values constitutes the smeared projector onto the better code space; we also show the analytical relationship between the increased squeezing level and the projection probability. We introduce concrete implementation methods for PS based on linear-combination-of-unitaries and virtual quantum error detection. We also numerically verify our analytical arguments and show that our protocol can mitigate the effect of photon loss.

arXiv:2403.14218•Mar 21, 2024•1 citation

Generation of non-Gaussian Bosonic states in quantum technological platforms

Peter McConnell

The generation of non-Gaussian states of bosonic systems described by continuous quantum degrees of freedom is of interest in a variety of contexts, ranging from quantum foundations to computation and communication. A crucial feature of genuine non-Gaussian states is that they cannot be described in general with a non-negative Wignerquasi-probability distribution. In particular, this feature is equivalent to contextuality and it underpins all attempts at attaining quantum computational advantage in a universal setting. In this thesis, the generation of Wigner-negative states is addressed, pursuing two approaches. First, in an optomechanical-like setting, we develop schemes to generate Wigner-negative states of two massive mechanical systems, in turn correlated such that they also feature entanglement, another genuine quantum hallmark. These schemes are based on driven-dissipative systems where dissipation is properly engineered by taking advantage of linear-and-quadratic optomechanical interactions. We address the robustness of these schemes when uncontrollable noisy channels are included in the dynamics, proving that their resilience is comparable to Gaussian schemes that have already been implemented experimentally. Second, considering in particular circuit QED systems and trapped ions, we propose a method to engineer a set of Hamiltonian evolutions that are universal in terms of single-mode state preparation. This method is based on a driven quantum Rabi model, where the desired evolution is effectively imprinted on a continuous-variable degree of freedom by its interaction with a properly driven two-level system. We demonstrate the universality of such approach by simulating the generation of multi-squeezed and other states, including the celebrated cubic-phase state. We also consider the effect of noise in realistic settings, showing in particular that in systems involving superconducting qubits, the generation of tri-squeezed states --- a universal resource for continuous-variable quantum computation which we prove to display larger Wigner negativities with respect to Fock and cubic-phase states for the same energy --- is within experimental reach.

•Oct 1, 2026•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

Combining Continuous and Discrete Variables for Quantum Information Processing

Luca Bianchi, Carlo Marconi, Davide Bacco

Quantum technologies are rapidly emerging as a foundation for next-generation information processing, communication, and sensing. In particular, optical platforms stand out as a promising avenue for scalable and efficient architectures. Here, information can be encoded either in discrete variables (DV)—such as polarization, path, frequency, or angular momentum—or in continuous variables (CV) of the optical field, such as quadratures. We develope a new formalism for the joint description of multiphoton and multimode light undergoing Gaussian transformations, and we use it to explore two DV-CV hybrid protocols. The first unifies and extends distinct forms of boson sampling, merging DV scattershot boson sampling with CV Gaussian boson sampling, thereby enabling quantum advantage demonstrations with squeezed photons. The second protocol deals with the Bell state measurement (BSM) for qudits, which are a higher-dimensional generalization of the qubit. Bell measurements play a key role in fusion-based quantum computation entanglement distribution and secret key sharing. We therefore introduce high-dimensional BSMs through linear interferometry combined with multiple single-mode squeezers, outperforming state-of-the-art theoretical methods in linear optics without using auxiliary states. This result shows how bridging the DV and CV paradigms provides a framework in which their combined strengths can outperform their standalone applications and overcome their individual limitations.

International Conference on Quantum Communications, Networking, and Computing (QCNC)•Apr 6, 2026•0 citations

Generating and characterizing generalized squeezed states in a superconducting microwave cavity

Xiaowei Deng, Yanyan Cai, Zhongchu Ni +4 more

Continuous-variable quantum information processing necessitates the generation and manipulation of non-Gaussian photonic states, such as higher-order generalized squeezed states and cubic phase states. These non-Gaussian states are distinguished from conventional Gaussian states by their pronounced Wigner negativity in phase space. However, generating these states with large Wigner negativity remains experimentally challenging, hindering their practical applications. Here, we experimentally generate non-Gaussian generalized microwave squeezed states (including tri- and quad-squeezed states) and cubic phase states within a high-quality superconducting cavity. This is achieved by engineering generalized photon-number filter operations in a programmable parameterized quantum circuit that efficiently projects cavity states onto target non-Gaussian states. These generalized squeezed photonic states are demonstrated to exhibit large Wigner negativity and quantum Fisher information as the squeezing order and squeezing parameter increase, thereby confirming their non-Gaussianity and highlighting potential applications in continuous-variable quantum information processing and quantum metrology.

Optica•Jun 26, 2026•0 citations
Continuous-variable (CV) quantum computing is a promising candidate for quantum computation because it can, even with one mode, utilize infinite-dimensional Hilbert spaces and can efficiently handle continuous values. Although photonic platforms have been considered as a leading platform for CV computation, hybrid systems that use both qubits and bosonic modes, e.g., superconducting hardware, have shown significant advances because they can prepare non-Gaussian states by utilizing the nonlinear interaction between the qubits and the bosonic modes. However, the size of hybrid hardware is currently restricted. Moreover, the fidelity of the non-Gaussian state is also restricted. This work extends the projective squeezing method to establish a formalism for projecting quantum states onto the states that are unitary-transformed from the squeezed vacuum at the expense of the sampling cost. Based on this formalism, we propose methods for simulating larger quantum devices and projecting states onto the cubic phase state, a typical non-Gaussian state, with a higher squeezing level and higher nonlinearity. To make implementation practical, we can, by leveraging the interactions in hybrid systems of qubits and bosonic modes, apply the smeared projector by using either the linear-combination-of-unitaries or virtual quantum error detection algorithms. We numerically verify the performance of our methods and show that projection can suppress the effect of photon-loss errors.
Numerical simulation of continuous variable quantum state preparation is a necessary tool for optimization of existing quantum information processing protocols. A powerful instrument for such simulation is the numerical computation in the Fock state representation. It unavoidably uses an approximation of the infinite-dimensional Fock space by finite complex vector spaces implementable with classical digital computers. In this approximation we analyze the accuracy of several currently available methods for computation of the truncated coherent displacement operator. To overcome their limitations we propose an alternative with improved accuracy based on the standard matrix exponential. We then employ the method in analysis of non-Gaussian state preparation scheme based on coherent displacement of a two mode squeezed vacuum with subsequent photon counting measurement. We compare different detection mechanisms, including avalanche photodiodes, their cascades, and photon number resolving detectors in the context of engineering non-linearly squeezed cubic states and construction of qubit-like superpositions between vacuum and single photon states.
The design of translation symmetric bosonic codes, e.g., Gottesmann-Kitaev-Preskill and squeezed cat codes, is robust against photon loss, but the computation accuracy is limited by the available squeezing level. Here, we introduce the \textit{projective squeezing} (PS) method for computing outcomes for a higher squeezing level by revealing that a linear combination of displacement operators with periodic displacement values constitutes the smeared projector onto the better code space; we also show the analytical relationship between the increased squeezing level and the projection probability. We introduce concrete implementation methods for PS based on linear-combination-of-unitaries and virtual quantum error detection. We also numerically verify our analytical arguments and show that our protocol can mitigate the effect of photon loss.
The generation of non-Gaussian states of bosonic systems described by continuous quantum degrees of freedom is of interest in a variety of contexts, ranging from quantum foundations to computation and communication. A crucial feature of genuine non-Gaussian states is that they cannot be described in general with a non-negative Wignerquasi-probability distribution. In particular, this feature is equivalent to contextuality and it underpins all attempts at attaining quantum computational advantage in a universal setting. In this thesis, the generation of Wigner-negative states is addressed, pursuing two approaches. First, in an optomechanical-like setting, we develop schemes to generate Wigner-negative states of two massive mechanical systems, in turn correlated such that they also feature entanglement, another genuine quantum hallmark. These schemes are based on driven-dissipative systems where dissipation is properly engineered by taking advantage of linear-and-quadratic optomechanical interactions. We address the robustness of these schemes when uncontrollable noisy channels are included in the dynamics, proving that their resilience is comparable to Gaussian schemes that have already been implemented experimentally. Second, considering in particular circuit QED systems and trapped ions, we propose a method to engineer a set of Hamiltonian evolutions that are universal in terms of single-mode state preparation. This method is based on a driven quantum Rabi model, where the desired evolution is effectively imprinted on a continuous-variable degree of freedom by its interaction with a properly driven two-level system. We demonstrate the universality of such approach by simulating the generation of multi-squeezed and other states, including the celebrated cubic-phase state. We also consider the effect of noise in realistic settings, showing in particular that in systems involving superconducting qubits, the generation of tri-squeezed states --- a universal resource for continuous-variable quantum computation which we prove to display larger Wigner negativities with respect to Fock and cubic-phase states for the same energy --- is within experimental reach.
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 technologies are rapidly emerging as a foundation for next-generation information processing, communication, and sensing. In particular, optical platforms stand out as a promising avenue for scalable and efficient architectures. Here, information can be encoded either in discrete variables (DV)—such as polarization, path, frequency, or angular momentum—or in continuous variables (CV) of the optical field, such as quadratures. We develope a new formalism for the joint description of multiphoton and multimode light undergoing Gaussian transformations, and we use it to explore two DV-CV hybrid protocols. The first unifies and extends distinct forms of boson sampling, merging DV scattershot boson sampling with CV Gaussian boson sampling, thereby enabling quantum advantage demonstrations with squeezed photons. The second protocol deals with the Bell state measurement (BSM) for qudits, which are a higher-dimensional generalization of the qubit. Bell measurements play a key role in fusion-based quantum computation entanglement distribution and secret key sharing. We therefore introduce high-dimensional BSMs through linear interferometry combined with multiple single-mode squeezers, outperforming state-of-the-art theoretical methods in linear optics without using auxiliary states. This result shows how bridging the DV and CV paradigms provides a framework in which their combined strengths can outperform their standalone applications and overcome their individual limitations.
Continuous-variable quantum information processing necessitates the generation and manipulation of non-Gaussian photonic states, such as higher-order generalized squeezed states and cubic phase states. These non-Gaussian states are distinguished from conventional Gaussian states by their pronounced Wigner negativity in phase space. However, generating these states with large Wigner negativity remains experimentally challenging, hindering their practical applications. Here, we experimentally generate non-Gaussian generalized microwave squeezed states (including tri- and quad-squeezed states) and cubic phase states within a high-quality superconducting cavity. This is achieved by engineering generalized photon-number filter operations in a programmable parameterized quantum circuit that efficiently projects cavity states onto target non-Gaussian states. These generalized squeezed photonic states are demonstrated to exhibit large Wigner negativity and quantum Fisher information as the squeezing order and squeezing parameter increase, thereby confirming their non-Gaussianity and highlighting potential applications in continuous-variable quantum information processing and quantum metrology.